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Does Gold act as a Safe haven against Exchange Rate Fluctuations? The case of Pakistan Rupee
Saba QureshiUniversity of Sindh, Jamshoro, Pakistan, 76090
Email: [email protected]
Dr Ijaz Ur RahmanCollege of Business Administration
Al Falah University, DubaiUnited Arab Emirate, 128821Email: [email protected]
Dr Fiza Qureshi**Corresponding Author
University of Malaya, Malaysia, 50603University of Sindh, Jamshoro, Pakistan, 76090
Email: [email protected]
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Does Gold act as a Safe haven against Exchange Rate Fluctuations? The case of Pakistan Rupee
Abstract
Investors often look for a refuge to avoid undesirable exposures to risk during period of extreme downturns in currency returns. We investigate daily gold and Rupee exchange rates depreciation against set of currencies over the period of 1992-2015. Using Wavelets at multiple time horizons; we find that gold act as a consistent short run hedge against exchange rate hence validating the exchange rate destruction hypothesis. This finding is helpful for speculators in their decision making while taking long and short positions accordingly. This finding suggests that central bank also need to keep other safe haven assets in reserves because the hedging ability of gold is only limited to short run. Further, the role of gold in providing protection against currency risks is also confirmed using Quintile regression. These results assist portfolio managers and governments in formulating effectual diversification strategy for preserving investment portfolio any extreme event condition. Our results also suggest that gold has a lead relationship with exchange rate; however, this relationship switches over specific time intervals. This finding is of major concern for policy makers in determining the extent of stabilization in gold prices to bring consistency to exchange rate. Finally, the Granger coherence coefficients confirm that the strength of the causal relationship varies across over all frequencies. These conclusions have important implications for policy makers, economic analysts, portfolio managers and institutional investors.
Keywords: Gold; Hedge; Safe haven; Exchange rate destruction, Wavelets, Quantile Regression.
JEL Code: F3, F31, G1, G10, G15, G32
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1. Introduction
The recent years have witnessed continuous decline in currency with devastating effects on macroeconomic factors such as balance of payments, GDP, and external debt. The devaluation of currency is considered as prolific by governments and economic analysts because it boosts national exports and augments a country’s employment. However, persistence in unfavorable balance of payments pushes the currency to lose its financial worth for external debt settlement (Arslan, Kılınç, & Turhan, 2015; Irfan, 2013). Such devastating effects of macro-economic factors have been experienced by several economies. The economies have been completely disintegrated by the debt slumps (Azam and Asmatullah, 2009). Peculiarly, the debt crisis vulnerability in these economies is because of the lack of resources, meager investment and obsolete technology for development of economy(Siddique, Selvanathan, & Selvanathan, 2016; Baharumshah, Soon, & Lau, 2017).
The general argument that currency devaluation increases employment level1 has been inapplicable in case of Pakistan rupee depreciation since the repayment of debt became hard for large organizations in the past with outcomes of reduced investment activities and lesser employment opportunities (Parveen, 2008). The rationale behind rupee depreciation is hyperinflation, floods, energy crisis and political instabilities. The non-commensurate depreciation of currency in the past has badly affected Pakistan’s credit rating in international market. Moreover, Pakistan is still experiencing stern burden of external debt of dollar denomination.
Although, currency devaluation manages trade deficits and enhances exports temporarily, the unexpected fall of rupee brings in the limitations
1 The currency devaluation increases exports as the currency becomes cheaper relative to foreign currencies. At the same time imports become costly and are reduced thus expanding the domestic demand of the country.
3
which resist foreign investments with strenuous conditions to subsidize the current account(Adams, 2009). Pakistan has been facing same situation from the past couple of decades. The prevailing situation remained in Pakistan from 1955 to 2010. For example, Ahmed, Zakarya and Iqbal (2007), Jiménez-Rodríguez and Morales-Zumaquero (2016) and Mundell (2013)find that the main cause of exchange rate instability is sudden unanticipated policy changes. Furthermore, Erum (2013) argue that Pakistan rupee has been recently ranked as region’s third worst currency subsequent to Indonesian and Indian currencies. The Pakistan currency has faced constant dismal in the past. Exchange rate of Pakistan Rupee (PKR) has been persistently depressing thus experiencing severe volatility since the last decade (Mahmood, Ehsanullah et al, 2011).2
The higher returns in gold investment have attracted institutional investors in Pakistan because gold investment yields more returns than the alternative investments3 (Aazim, 2011). In addition, investment in gold have witnessed a sudden surge following the depression in the real estate market, low economic growth, and high volatility in exchange rate in emerging markets especially in Pakistan.
The unusual increase in gold prices and contemporaneous decline in value of currency, particularly after global financial crisis, have attracted the interest of policy makers and practitioners to examine movements between gold and exchange rates. Of particular interest is the outcome of recent crisis that has stressed the role of safe haven investments. Such role during crisis is traditionally witnessed in gold which has long been considered as a hedge investment (Capie et al, 2005; Baur and McDraper et al, 2006; Baur and Lucey, 2010; Dermott, 2010; Bruno and Chicarini, 2010; Reboredo, 2013). The distinctive characteristic of Gold is its less sensitivity and
2 Figure 1 shows the quarterly exchange rate (USD/PKR) from 1957-2015.3Such as national saving schemes, bank deposits, Pakistan investment bond or corporate bond, mutual funds. See Qureshi, Ismail, and Gee Chan (2016) and Qureshi, Kutan, Ismail, and Gee (2017)
4
uncorrelatedness to exchange rate instability. This commonly held belief with respect to gold is negative beta presumption.4
According to Nadeem et al (2014), increase in gold price from Rs.6280/Tolain 2002 to Rs.62,600/Tolain 2012 yielded 897% of the gold returns to investors during the past years. Subsequent to uncertainty in Rupee, surge in gold investment has been observed. Further, gold futures are also observed to trade highly in Pakistan Mercantile Exchange (PMEX) at domestic level (Shahbaz et al, 2014).5 In addition, the significance of the gold for Pakistan’s economy cannot be ignored. Along with the increase in economic downturns; Pakistan increased its gold’s holdings future stability and security.6
Generally, gold is seen to have significant potentials to play its roles as an invincible to financial crisis, inflation, credit default and declining returns on alternative assets. This unique characteristic of gold has propelled central banks, financial analysts and investors to value it continuously given the considerable qualms being faced by today’s global economy. The movements in gold are closely watched by governments for the reason that the commodity returns are generally influenced by interest rates. Thus, the unexpected gold prices will increase the inflationary expectations among investors which compel the central banks for vigilant strategy formulations.
Given the gold investment implications in a broader perspective of hedging means, several studies in literature have tinted its significance to form a well-diversified basket of portfolio to hedge against political uncertainty, low economic growth, inflation currency risk, oil price variations and other notable macro and financial variables (see for instance, Shahbaz et al. 2014; Reboredo, 2013; Joy, 2011; Lucey and Tully, 2006a; Lucey and Tully, 2006b; Capie et al. 2005; Ghosh et al. 2004; Adrangi et al. 2000; Smith, 4The details of negative beta presumption is discussed in section 2.4.1.5Figure 2 explains the gold price increases in PKR over the period of 1992-2015.6Figure 3 shows increasing trend of gold reserves in Pakistan for the period of 1980-2015.
5
2002). In empirical literature, a handful of studies are devoted to the role of gold and its movements with macro and financial variables. Several past studies have noted the linkages between constantly changing gold prices and inflation rate (See for instance, Neil-Fortune, 1987; Mahdavi and Zhou, 1997; Gosh et al. 2004; Worthington and Pahlavani, 2007; Blose, 2010; Tiwari, 2011; Beckmann and Czudaj, 2013; Shahbaz et al. 2014). Several other macro and financial variables have also been considered as determinants of fluctuations in gold prices such as business cycles, commodity prices and interest rates ( see for instance, Neil Fortune, 1987; Diba and Grossmann, 1984; Melvin and Sultan, 1990; Christie-David et al. 2000, Cai et al. 2001). Whether gold investment is as hedge against exchange rate deprecation is an important question which has gained momentum recently. Intuitively, the movement in value of US Dollar and gold prices holds a pullover with each other’s. This implies that, when US Dollar depreciates, prices of gold increases, suggesting implications of using gold as a hedge or safe haven against volatile currency movement. This proposed explanation is known to be exchange rate destruction assumption7 in financial mediaand implies that higher prices of gold are related to local currency weakness.8
Several studies have empirically examined the movement in the gold prices and exchange rate using variety of econometric techniques (i.e. Capie et al. 2005; Sjaastad 2008; Sari et al, 2010; Joy; 2011; Pukthuanthong and Roll, 2011; Reboredo, 2012;Reboredo, 2013; Reboredo and Rivera-Castro, 2014; Apergis, 2014; Beckmann et al, 2015; Zhang et al. 2016; Jain and Biswal, 2016; Zhang et al, 2016; Wang and Lee, 2016;Pershin, Molero, & de Gracia, 2016). From earlier studies, the general conclusion on the relationship between gold prices and currency movement are two-folds. First, gold can act as hedge against currency depreciation and second, prices of gold indicated in a currency can be linked with fragility in that currency.
7The details of exchange rate destruction assumption is discussed in section 2.4.28 See for instance, Pukthuanthong and Roll (2011)
6
Figure 1: USD/PKR Exchange rate 1957-2015
Source: International Financial Statistics
Figure 2: Gold Prices (Ounce) 1992-2015
2/28/1
992
4/28/1
993
6/28/1
994
8/28/1
995
10/28/1996
12/28/1997
2/28/1
999
4/28/2
000
6/28/2
001
8/28/2
002
10/28/2003
12/28/2004
2/28/2
006
4/28/2
007
6/28/2
008
8/28/2
009
10/28/2010
12/28/2011
2/28/2
013
4/28/2
014
6/28/2
0150
20000400006000080000
100000120000140000160000180000
Years
1 O
unce
Source: State Bank of PakistanFigure 3: National Gold holdings in Pakistan 1980-2015
7
Q1 1957Q4 1965Q3 1974Q2 1983Q1 1992Q4 2000Q3 20090
20
40
60
80
100
120
Year
Rupe
e to
US$
1980 Jan 1986 Jan 1992 Jan 1998 Jan 2004 Jan 2010 Jan0
5000000001000000000150000000020000000002500000000300000000035000000004000000000
Years
US D
olla
rs
Source: International Financial Statistics
Considering frequent gold prices and exchange rate volatility in Pakistan for several years, we propose to investigate whether our empirical results support the intuitions that gold investment provides hedge to the currency deprecation or safe haven belief, exchange rate destruction assumption and hypothesis of negative beta asset. The momentous issues in Pakistan also call for substantial attention from policymakers and financial analysts. As policy related goals for Pakistan is to maintain economic growth, managing the reserve currency and stabilizing value of PKR. However, the goals can often be conflicting. The paper provides some useful policy implications on conventional gold-exchange conceptions. The study uses wavelets9 to characterize the dynamics of gold as a hedge with various investment horizons concurrently. Our interest is to examine the proposition whether gold acts as a hedge and safe haven for investors against exchange rates in a different time scales using wide set of currencies against Pakistani Rupee. Contrary to the approaches adopted by the earlier studies on the hedging ability of gold against exchange rates, we take advantage of Wavelet based approaches to examine the hedging abilities of gold investment against Pakistani Rupee using daily data and wide set of currencies. Our work is closely related to, yet different from the work of Reboredo and Rivera Castro (2014) in a sense that their work did
9Gencay et al. (2005), Kim and In (2007), Rua and Nunes (2009), He et al. (2009), Genest et al. (2009), Masih et al. (2010), Rua (2010), He et al. (2012) and Jammazi (2012).
8
not consider examining Granger causality over different frequencies domain and multiple timescales. Our finding on one side, complement the findings of Reboredo and Rivera Castro, 2014) and on the other side supplement the findings on lead lag relationship and forecasting-ability of gold and exchange rate using Wavelet Coherence and Granger coherence in the short, medium and long run. In addition, our study also take into account the unusual dynamics that are exhibited in times of market turmoil, therefore use Quantile regressions following Baur and Lucey (2010) and Ciner et al. (2013)for analyzing safe haven properties.
Our findings suggest that gold investment is a short run hedge partly validating negative beta assumption for all set of currencies. Further, gold prices leads exchange rate however, the relation switches over specific time intervals. The results of Granger Coherence analysis suggest that causalities are usually prominent at shorter frequencies that points to the role of the predictive content for exchange rates in the short run. Finally, the Quantile regression estimates provide evidence that during times of intense decline in exchange rate, gold returns are positive which confirms the role of gold as an effective safe haven.
The remainder of the paper is structured as follow. Section two discusses the theoretical framework, the empirical model and the relevant hypothesis of the study. Section three provides description of data and methodology. Section four discusses empirical results followed by conclusion and implication in section five.
2. Theoretical Framework
We discuss the theoretical framework of the study that includes theoretical linkage of the variables. The question of rupee devaluation association with gold has so far grasped little significance by researchers, mainly in Pakistan. This study comprehends the relationship between exchange rate depreciation and gold. In the light of research hypotheses, the study
9
considers the portfolio management framework so that the conclusions on causality, hedge or safe haven findings are effectively drawn and the suggestions are advanced to policy devisors and investors accordingly. 2.1. Law of One PriceLaw of one price constitutes the basis for Arbitrage pricing theory and the foundation for theoretical development of the study. This theoretical model was first proposed by Ridler and Yandel (1972) who look into impact of adjustment rate of exchange over commodity prices. This approach has also been adopted by Sjaastad (1985); and Dornbusch (1987).
According to law of one price, a particular commodity or security in different locations must have an identical price when rate of exchange is considered. The assumption of APT is elimination of arbitrage profit opportunities. The concept behind is that the demand and supply impositions propel the prices to be same. Though security prices vary in two separate currencies, after that an arbitrageur will buy the security in the less expensive market and offer it where the prices would be higher. This theory presumes that participants in market wipe out this difference in prices thus bringing advantage about arbitrage chances. Stated more clearly, in any country if the gold price remains fixed as a unit of measurement, its price will rise in case of devaluation of currency and the price will tend to fall in case of appreciation.
2.2. Theoretical LinkageWe next discuss the theoretical linkage between main exchange rates and globally traded commodity prices. The continuously traded commodities of organized markets are instantly adjusted in prices to any exchange rate change. Sjaastad et al (1996) develop this relationship and explain that those commodity price adjustments may not be less than in one or both currencies. For instance, as the US dollar depreciation against the European euro, commodity prices denominated in dollar tend to ascend and the prices in euro descend despite the fact that the market fundamentals
10
and other pertinent factors remain unaltered(Mundell, 2007; Apergis, Zestos, & Shaltayev, 2012). Such hypotheses have been evidently suggested by prior events in 1980 till 1985. The overpowering dollar appreciated and witnessed 30% rise in US price level however the dollar expressed commodity index price drop by 30%.
The prospective significance of this situation is not confined to currency of major countries but the minor currency countries have also been directly or indirectly influenced. These smaller currency countries experience inflationary distresses spread by volatilities in international commodity prices(Mundell, 2000). Gold is the main commodity for analyzing major currency fluctuations on commodity prices as it is constantly traded in spot as well as organized future markets.
2.3. The Empirical Model
The theoretical footing of this study is drawn on the basis of the theoretical framework presented by Sjaastad, (1996). The model is focused on effects of exchange rate movements on international commodity price mostly traded in organized exchange; it is not related to returns on holding the commodity and hence is different from the asset pricing model. The law of one price and global market clearing in M currencies are the basic elements of the model. Disregard to trade barriers and along with variables in natural logarithm form, law of one price for commodity that is globally traded is shown as
P1=P j+E1 j , j= 1,…..M (1)
The price of the commodity in currency j is represented asP jand the
currency price j with regard to the reference currency 1 isE 1 j ,. The consideration for commodity price feedback to exchange rate is supposed as
negligible. The demand in excess or imports,Q j,for the commodity in
currency j its real price function, P j
R
=P j−P j
¿
. The price level is specified as P j
11
in that currency. Where the 1 by N vector is X j=(X j1 ,X j 2 , .. .. . .. . ,X jN ). The commodity market fundamental and currency j:
Q j=Q j(P j
R
,X j) ,∂Q j/∂P j
R
≤0 , j= 1,…..M
The global market clearing entails:∑j=1
M
Q j(P j
R
,X j)=0 ,
Therefore the log linear estimation is designated as
∑j=1
M
(∂Q j/∂P j
R
)(P j
R
−P−
j
R
)+∑j=1
M
(∑i=1
N
(∂Q j /∂X ji )(X ji−X¿̂
ji ) ¿) = 0 (2)
Where the means of P j
R
and X ji distributions are P−
j
R
andX¿̂
ji ¿
The equation (2) can be reorganized from equation (1), P j
R
=P1−E1 j−P j
¿
,The basic expression forP1 :
P1=cons+∑j=1
M
θ j (E1 j
R
+P j
¿
)+K (X ), (3)
The θ j=(∂Q j /∂P j
R
)/∑j=1
M(∂Q j/∂P j
R
);
The value ofQ jmay be positive or negative while there is non-positive value
of ∂Q j /∂P j
R
. As a result, the sum of θ j is unity and are nonnegative fractions.
Further, we get equation (4) by subtraction ofP1
¿
from both sides of equation (3)
P1
R
=∑j=1
M
θ jE 1 j
R
+K ( X ) (4)
The term E 1 j
R
≡E1 j+P j
¿
−P1
¿
.is the real exchange rate purchasing power parity between 1 and j currency blocs. The principal analysis in equation 3 is of thetas which determine the relative market power hold by participants in the world commodity. If the currency 1 slightly depreciates against other
currencies (with constantP j
¿
), the depreciation effect on P1is then ∑j=2
M
θ j=1−θ1 .
12
in case of price taker currency 1 in the world gold market, the depreciation will have no impact on gold prices of other currencies consequently the
complete effect falls on the gold price in currency 1 so θ1.=0. On the other side, the depreciation in price maker currency 1 will not influence gold price in currency 1 since it is totally denominated in the world .market of
gold so the θ1.=1, and the entire effect is viewed in gold prices of other currencies. In order to dominate the world commodity market, one must possess surfeit elastic demand for the commodity. The country with high proclivity to reserve gold may lead the world market of gold even if it is not a major or minor producer. The term in equation (3) is crucial source of fluctuations in the gold commodity price and the theta estimates are useful given the increasing instability in major exchange rates. Finally, theta can also be utilized for managing effective portfolio by liabilities and assets
denomination in foreign currency according toθ j .
2.4. Gold-Exchange rate Hypothesis
2.4.1. Safe Haven and Negative Beta propositions
The negative beta hypothesis states that gold proceeds up with the other assets moving down. This proposition is also tested by noting the correlations between gold and exchange rate. The common believed notion of gold is safe haven which describe that people are inclined to switch towards gold in ages of market commotions. For example, prices of gold should rise as the consumer confidence index declines. The study predominantly focuses on one of the measure of fear that is volatility of exchange rate in order to test the safe haven hypotheses.
Capie, Mills et al (2005) and Sjaastad (2008) confirms that gold provides protection against dollar and currency devaluations. Further, Joy (2011) extends the previous work and assesses gold’s hedging and safe haven property using 16 US dollar paired exchange rates. The finding of the study supports gold’s role as a hedge but on the other hand gold as a weak safe
13
haven. Similar findings have been observed in study of Reboredo and Rivera-Castro (2014a).Moreover, Wang and Lee (2011) identifies that the effectiveness of gold’s hedging depends on the extent of currency depreciation.Zagaglia and Marzo (2013) find that recent financial crisis has not affected gold-USD association leaving hedging properties unchanged. On the contrary, Reboredo (2013) concludes that gold acts as effective safe haven in periods of extreme USD market movements. The study concludes that gold is useful in portfolio risk management and confirms hedging property of gold.
2.4.2. Exchange Rate Destruction Proposition
The other relevant hypothesis is the dollar destruction hypothesis which claims that there exists inverse relation between the gold price and trade weighted dollar. The value of trade weighted illustrates the gain and loss of dollar purchasing power in comparison to the trade partners. Nevertheless, the relationship is not that explicit as it was in times of gold standard. Though, the gold standard has disappeared, yet psychological skepticism to gold among people still persist when the dollar decrease in value. The following reasons justify the inverse interrelation.
First, since the decrease in dollar elevates the value of other currencies hence the demand of gold in dollar increase. Second, the loss in value of the dollar urges investors to search for a possible value storage investment which is gold. It should be noted that this relation may deflect by gold and dollar price increases at the same time. The cause of this divergence is the predicament situation in other economies. Ultimately, such crisis would enforce towards acquisition of safe assets including gold and dollar.
Third, the theory, moreover, explains that due to money supply escalations, the general prices increase with output and efficiency remain constant. The homologous view concerning government practice is reduction in interest rate or going though budget deficit thereby decreasing the dollar or
14
currency value.It is postulated that best option to compensate and protect purchasing power loss is to purchase gold.
Reboredo and Rivera-Castro (2014b) examine gold’s hedging properties in different time horizons. Results of the study suggest that both USD depreciation and gold are positively dependent against all currencies (Australian dollar, British pound, Norwegian krone, Swiss franc, Canadian dollar and euro) except Japanese yen. On the contrary, Beckmann, Czudaj, and Pilbeam (2015) provides new standpoint regarding gold-exchange rate relationship. Results reveal that impact of exchange rate depreciation negatively affects gold price. However, this impact is regressed to positive after one day. While impact of gold price volatility on exchange rate is inconclusive since both positive and negative correlation results are observed. However, US dollar is an exception to these results and confirms strong hedging relation of gold. More recently, Wang and Lee (2016) explore that whether hedging effectiveness of gold varies in gold consuming, gold producing and international currencies. Results suggest that hedging effects are found to be stronger in gold consuming currencies than in the gold producing.
3. Data Description and Methodology
We consider set of currencies against PKR to examine hedging and safe haven characteristic of gold at various time horizons. Since high frequency data results in better hedge and safe haven effects because it takes greater fluctuation into account (Wang and Lee, 2016). Therefore, daily data on gold prices (PKR per ounce) and exchange rates (PKR per unit of foreign currency) has been taken for the sample period between January 1992 and July 2015. We consider US dollar, Euro, UAE Dirham and Saudi Riyal since these are strongly traded currencies. In addition, the hedging effectiveness is found to be stronger in major gold-consuming countries as compared to gold-producing countries (Wang and Lee, 2016), therefore, the study
15
examines the gold and exchange rate relation in a gold consuming country i.e. Pakistan.
Gold prices and exchange rates data we regathered from DataStream. Returns for variables were computed using log of first difference based on continuous compounding. Table 1shows the descriptive statistics and unit root test of gold and currency returns. We noted that, average return of the variables is close to zero and higher kurtosis values of the series suggest the existence of fat tails. On the other hand, ARCH-LM statistic indicates existence of autoregressive conditional heteroscedasticity.
Table 1: Descriptive Statistics and ADF Unit Root TestMean Std.de
vSkewne
ssKurtosi
sJarque-
BeraLM ARCH ADF Unit Root Test
Intercept Intercept & Trend
Gold
0.0005 0.0108
0.4968 13.4091 28914.99
0.703
0.000 -82.0616 -82.0563RDo 0.0002
30.0040
5.9964 127.8193
4159570
0.994
0.000 -87.9379 -87.9715
RDir
0.00022
0.0040
5.4513 117.4272
3495246
0.340
0.000 -88.72291
-88.7525
RR 0.00022
0.0040
5.4410 116.8082
3457750
0.352
0.000 -88.97676
-89.0064
RE 0.00019
0.0073
0.9115 14.4364 35479.26
0.223
0.000 -84.1095 -78.8339Note: The table reports the summary statistics of Gold and bilateral rates for US Dollar (RDo), UAE Dirham (RDir), Saudi Riyal (RR) and European Euro (RE). T is the number of observations. LM test is Breush Godfrey test for checking serial correlation with 12 lags in the return series. ARCH refers to autoregressive conditional heteroskedasticity. Table also shows the ADFunit root test at level for variables. All the variables are found to be significant at 1%
A brief note on Wavelet Analysis10
Wavelet analysis decomposes the data into several time scales. It is usually preferred over Fourier analysis due to the reason that it performs more decomposition and does not require stationary in the series.11 The analysis depends on two main functions. Father wavelet represented as'∅ '; explains
10Before exercise the wavelet computations, we considered to fix the issue of Bias correction as standard practices. We however for the reason of brevity did not report the results.11 For detailed discussion on wavelets, see for e.g.; Chui (1992), and Strang and Nguyen (1996), Gencayet al. (2002), Schleicher (2002)
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the trend of a signal with low frequencies. The mother wavelet ' τ 'represents the trend of a signal with high fluctuations in the trend.
The wavelet series estimate of a time series ' x t 'is given by:x ( t )=∑
ks J ,Kϕ j , k ( t )+∑
kd J ,Kϕ j ,k ( t )+∑
kd J−1, KϕJ−1, k ( t )+ . ..+∑
kd 1, Kϕ 1, k ( t ) (4)
Where J is number of multi resolution scales, and k ranges from 1 to the number of coefficients in the specified approximation. ThesJ , K ,dJ ,K …d1 ,kare the
wavelet transform coefficients. J is the maximum integer such that 2 jis less than the number of data points. The wavelet coefficients measure the impact of the corresponding wavelet function to the approximation sum and nearly specify the location of the corresponding wavelet function in the series. The coefficients can be estimated by the following integrals:
S J ,K (X )≈∫−∞
∞ ϕ j , k y ( x )dx(5)
D j , k ( x )≈∫−∞
∞ τ j , k y ( x )dx (j=1,2,..,J) (6)WhereSJ ,ksignifies the smooth coefficients that capture the trend, while the
detail coefficients such asdJ , K ,… ,d1 , kcapture the higher frequency alternations and represent increasing finer scale deviations from the smooth trend. The wavelet series approximation of the original time series x tgiven the
coefficients is expressed as the sum of the smooth signal SJ ,k and the detail signals.
x t=SJ ,k+D j , k+D j−1 , k+. ..+D 1, k(7)
This paper verifies prevalent explanations based on gold-exchange rate relation. The study relies on wavelet model to confirm the hypothesis. Maximal overlap discrete wavelet transform (MODWT) is applied to each process in x tto obtain wavelet coefficient process. D1 is the highest frequency constituent and corresponds to short run fluctuations explicated by shocks rising at time scale2i .Similarly, mid and long run fluctuations are
represented by rest of constituents at time scale 2 j .Since, the study uses
17
daily data, data is decomposed to eight levels following (Bredin et al, 2015) thus establishing J=8.Daily effects are captured by highest frequency component i.e. D1 which is then followed by medium term and long term
variations as21=2days ,22=4days ,23=8days ,………28=256days respectively.
The Maximal Overlap Discrete Wavelet Transform (MODWT)
The maximal overlap DWT is a substitute to DWT and is characterized by a non-orthogonal variant of DWT. Unlike DWT, the MODWT does not suppress the coefficients. Therefore, the number of wavelet and scaling coefficients at each degree of transform is identical to the number of observations in the sample. Nevertheless, the cost of MODWT mislays the orthogonality efficiency. Any restriction of the sample size is not required and this transform is shift immutable. The rescaled filters are used by the transform
~h j , l=h j , l
2 j /2 and
~g j , l=g j , l
2 j /2, j=1,…, J , where J is the total number of levels.It
obtains the Wavelet coefficientsas follows:
(8)
(9)
The difference of generalized data averages on scale is represented by the wavelet coefficients. The MODWT has additional advantages over DWT which is efficiently managing any sample size, it is also translation unvarying since the pattern of transform coefficients remain unchanged due to signal shift. Further, MODWT takes into account a considerable size of the sample in the analysis of wavelet correlation and presents asymptotically wavelet estimator of covariance which is more efficient than the DWT.
18
Wavelet Coherence Transformation
In order to assess the joint interactive coherence among the variables, it is better to rely on Wavelet coherence. It is a helpful tool that takes into account frequency space and time intervals and differentiates possible relationships between two time series. Specifically, wavelet coherence correlation analysis reveals infrequent periodic correlations between the series. It proclaims the significance of the correlation relationship of two time series and explains the coherence of cross wavelet of the series in time frequency space. The wavelet coherence is defined as the cross spectra normalized by the two related auto-spectra. Torrence and Webster (1999) represent the wavelet coherence of the time series as:
R n
2
( s)=|∀(s−1wn
xy
( s ))|2
∀(s−1
|w n
x
|(s )|2 )∀(s−1|
|w n
y
(s )|2 ) (10)
Where, Rn2 (s )indicates the squared value of wavelet coherency and ∀ is a
smoothing operator. This smoothing operator is defined as, ∀ (W )=∀ scale ¿. Smoothing along the wavelet scale axis is denoted by ∀ scale and smoothing in time denoted as∀ time.
The angle of the arrow of the wavelet coherenceϑ XY , is called phase-difference, which entails that phase lead of X over Y. In addition, same and reverse direction movement is depicted by phase and anti-phase respectively. Zero phase-difference imply that the two time series move together at the certain time frequency. π or −π expresses an anti-phase relation. The arrows in the wavelet coherence explain that the first variable is leading if arrows point to right down or left up. Whereas, in case of arrows pointing right up or left down the second variable is the leading one.
The time period in the wavelet coherence is plotted on horizontal axis and scale or frequency is plotted on vertical axis. The analysis is conducted in these axes to identify the areas that reveal wavelet coherence. The significant interdependence between the series is shown by warmer colors
19
in the graph. On the other side, the lower dependence among frequencies and time is associated with colder colors. The Monte Carlo method is used to estimate the significance level of wavelet coherence.
Wavelet Granger Coherence Analysis
The traditional approaches to granger causality have contributed remarkably in providing insightful causality perspectives. However, these approaches remain implicit in context of determining the strength of causality varying over frequencies. The method of spectral density presents a comprehensive scenario than the only measure applied across all time periodicities. Pierce (1979) devised an approach for decomposing the granger causality between time series across the spectrum. This granger causality test depends on a modified coherence coefficient and the measure is performed on the ut and vt, univariate innovation series that results from the derivation of Xt and Yt which are then formed as univariate ARMA model.
θx
(L )X t=Cx
+φx
(L )u t
θ y
(L )Y t=Cy
+φ y
(L )v t (11)
The autoregressive polynomials areθx (L)∧θy (L) respectively, moving average polynomials are represented as ∅ x (L) and ∅ y (L ) ,C xand C y are the potential deterministic components. Let the spectral density functions beSuλ andSvof ut∧vtat frequencyλ∈ ]0 , π [delineated as
Su λ=1
2π∑k=−∞
∞γu (k )e−1 λk
andS v λ=1
2 π∑k=−∞
∞γv (k )e−1 λk
(12)
Where the autocovariance of ut∧vt at k lag is represented as γ u (k) = cov(ut, ut-k)andγ v (k) = cov(vt, vt-k). Koopmans (1995) and Warner (1998) present detailed analysis on spectral time series. In order to assess the stochastic process, the allying ut∧vt cross spectrum Suvλ is considered.
Suv λ=Cuv ( λ )+iQuv ( λ)= 12 π∑k=−∞
∞γ uv (k )e−1 λk
(13)
The parts of cross spectrum are displayed as cospectrum Cuv(λ ) and the quadrature spectrum Quv.
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Koopmans (1995) explains that the cross spectrum permits the computation of coefficient of coherence
The coherence coefficient describes the linear relationship strength by frequency between the two series, yet it does not account for the associative direction in the time series. The interpretation of squared coefficient of coherence is similar to that of R squared regression. According to Pierce (1979), the cross spectrum (13) performs the decomposition into following parts.
i. Su↔v, the instant ut∧vt relationship
ii. Su→v, the immediate direct relationship of vt∧lagged u t
iii. Sv→u, the immediate direct relationship of ut∧lagged v t
That is, Suvλ= [Su↔v + Su→v +Sv→u]
=1
2π [γ uv(0 )+∑k=−∞
−1 γ uv( k )e−iλk
+∑k=1
∞ γ uv (k )e−iλk
](14)
Consequently, if the objective is to determine the predictive ability of Xt respective to Yt ,one’s interest would be in second part of equation 14.
Thus, granger coefficient coherence is specified as
hu↔v ( λ )=|s u↔v ( λ)|
√su ( λ )sv( λ ) (15)
Safe Haven dynamic
We further investigate gold as a safe haven for PKR. Regression models are normally concerned with considering the conditional mean of a dependent variable. However, modeling other aspects of the conditional distribution is increasing using quantile regression approach which simulates the quantiles of the dependent variable given a set of conditioning variables (Koenker and Bassett, 1978). Quantile regression estimates the linear relationship between regressors and a specified quantile of the dependent variable. It applies least absolute deviations (LAD) estimator, which corresponds to fitting the conditional median of the response variable. It allows comprehensive description of the conditional distribution and
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describes the way the median, 10th or 95th percentile of the response variable, is affected by regressor variables.
As a result, quantile regression provides an effective method of modeling these relationships and is useful in analyzing whether returns of financial assets provide security for each other during extreme price variations related to tail behavior of both. This behavior is shown as:
r gold ,t=a+btr ex , t+e t (16)b t=c0+c 1 D(r ex q10
)+c2 D(r ex , t−1q10)+c 3 D(r ex q5
)+c4 D(r ex , t−1q5)+c5 D(r exq2 .5
)+c6 D(r ex , t−1q2 .5)+c7 D (r exq1
)+c 8 D(r ex , t−1q1)(17)
h t=π+αet−1
2
+βht−1 (18)The equation depicts gold and exchange rate relation where α and b t are the
parameters, e t is the error term. Dummy variables to capture extreme volatility denoted by D and stipulate if the returns were in the lower 10th, 5th, 2.5th or 1st percentile of the distribution. GARCH (1,1) model is then estimated following approaches of Capie et al (2005) and Baur and Lucey (2010). Equation 18 specifies variance of the error term as asymmetric GARCH (1,1). Accordingly, gold return depends on contemporaneous and one lagged period on exchange rate and dummy variable.
4. Results and Discussion
Table 1 reports the results of ADF unit root tests of returns at level and shows that the data is stationary which suggests the integration of order 0.We first examine gold and exchange rate association is at a various time scales by wavelet covariance based on MODWT. This analysis shows covariance between both the series as depicted in Figure 5 and 6 for Dollar and Dirham exchange rates respectively.12The results confirm that there exist positive covariance between the variables in the short run, while there is no evidence of covariance in the medium and long run. Moreover, figures also show the Wavelet correlations between both the variables. It is evident that positive correlation exists between gold and exchange rate series in the 12 Wavelet covariance and correlation results for other exchange rates are available upon request
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short run and medium run (where an increase in exchange rate indicates decrease in PKR) thus confirming gold as a hedge against currency depreciation. These results are also confirmed from the findings presented in Table 2. Further, it is notable that the relationship becomes weaker with increase in time frame suggesting the gold as a short run hedge for all exchange rates. However, in the long runs specifically at D7, gold is a weak hedge except euro. These findings were consistent with Reboredo (2013b) and Reboredo and Castro (2014) for one of the cases. Though, this effect is reversed at annual scale. Gold may exhibit different pattern as fluctuations in long run trend is observed. The hedging effectiveness varies across all time scales which implies that the usefulness of gold in portfolio hedging differs scale to scale. This may eventually benefit the investor in decision making by preferring the portfolio that offers minimum risk.
The wavelet correlation affirms the exchange rate destruction assumption in the short run. The severe PKR depreciation also adversely affects the investor portfolio returns holding PKR currency as their asset. However, the investors should optimally include gold in the short term owing to the fact that value of gold fluctuates against value of rupee. The weak hedging in the long run further implies that gold counterbalance the downside risk of extreme rupee depreciation since its value remains unchanged during intense volatilities in exchange rates.
Figure 5: Wavelet covariance and correlation between Gold and Rupee Dollar Exchange rate
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Note: "U" and "L" represent the upper and lower bound correspondingly at 95% confidence interval. Covariance and correlation among Gold returns and Exchange rate is represented by black line
Figure 6: Wavelet covariance and correlation between Gold and Rupee Dirham Exchange rate
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Table 2: Wavelet Correlations for Gold-Currency rates at various horizons
D1 D2 D3 D4 D5 D6 D7 D8
RDo0.1660 0.1389 0.1550 0.1276 0.1084 0.0821
-0.0563 0.3150
RDir0.1203 0.0999 0.0895 0.0333 0.0783 0.0973
-0.0629 0.1861
RR0.1162 0.0902 0.1013 0.0740 0.0419 0.0082
-0.0248 0.1550
RE 0.3032 0.2582 0.2828 0.2891 0.2260 0.2836 0.1117 0.2417
Note: The table shows gold-exchange rate correlations at different time scales
Figure 7: Wavelet Coherence: Rupee dollar Exchange rate versus Gold
Figure 8: Wavelet Coherence: Rupee euro Exchange rate versus Gold
Figure 9: Wavelet Coherence: Rupee dirham Exchange rate versus Gold
Figure 10: Wavelet Coherence: Rupee riyal Exchange rate versus Gold
25
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Table 3: Wavelet Coherence Summary: PKR Exchange rates versus Gold
Exchange Rate High Coherency (Period)
High Coherency (Scale)
Phase-Difference
Exchange Rate (Lead/ Lag)
USD 1992-20022007-2008
256-850 In-phase Lagging
Euro 1995-2009 8-64 In phase LaggingDirham 1992-2001
2006-201216-32256-840
In-phase Anti-phase
Lagging Leading
Riyal 1992-20012008-2012
8-32256-860
In-phase Anti-phase
Lagging
We next examine the gold and exchange rate lead lag interlinks and assess the coherency by employing Wavelet coherence between variables. The wavelet coherency of the Rupee-Dollar exchange rate and gold is shown in Figure that shows the existence of weak dependency between variables in the short run. The interrelations however are also observed in different periods in 64 scales. In the long run, strong interrelation is observed from 1992-2000. As the arrows are in-phase for that period, thus it suggests that gold is leading the exchange rate in lower frequency period. Moreover, a different direction arrow is observed for 2007-2008 which indicates anti phase.
The link between Rupee-Euro exchange rate and gold is depicted in Figure 8. The in-phase moment in the Figure 8 suggest that if gold prices increases increase in the price of gold, exchange also tends to increase. However, it is noted that an exchange rate increase means depreciation in the value of PKR. Wavelet coherence of Rupee Dirham exchange rate and gold in the figure 9 depicts that most of the variables lie in the region of colder color in the short and medium run. An anti-phase movement is again observed for the year 2007-2009, thus suggesting significant interrelation persists from the year 1992-2002 in different frequencies. Most of the interrelation in scale falls almost in 512 day scale. It is interesting to note that there is a mixed pattern of direction of arrows for this frequency period moving
27
downward and then upward right thus indicating the reverse transitory influences between variables. We noted a strong the coherence of Rupee- Riyal strong interrelations over the period of 1992-2002 for different scales in Figure 10.The exchange rate and gold coherence relationship is summarized in Table 3. The results suggest that the exchange rate lags against gold yet the relationship distracts in the long run time spans over brief time spans.
The findings of wavelet coherence suggest that gold prices lead exchange rate which confirms that gold predict the PKR exchange rate volatilities. First, it can be concluded that the upswing and downswing in the value of PKR is in response of value of gold imports in the country. These findings affirm the interdependency between volatility in previous gold price and exchange rate. Second, these results are of serious concern for policy makers; that is to what level the steady gold price is imperative for stable exchange rate. Finally, Pakistan’s trade balance with respect to gold imports can also be the crucial factor in currency valuation. Since, the terms of trade directly influence the commodity price and net imports. As a result, the current account is also affected. The sudden deterioration in trade terms aggravates current account deficit as in the case of excessive gold demand in Pakistan. This unexpected worsening current account deficit brings up the real exchange rate depreciation. These inferences have important implications for the fund managers, foreign exchange traders and portfolio managers. They could possibly benefit with the currency trading which entails examining interrelations between divergent markets to exploit the opportunity.4.1. Granger Coherence analysisWe then analyze the granger causalities at different frequencies to reveal the predictive power and intermittent causalities between variables.
Figure 11: Granger Coefficient of Figure 12: Granger Coefficient of
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Coherence: Rupee dollar Exchange rate versus Gold
Coherence: Rupee euro Exchange rate versus Gold
Figure 13: Granger Coefficient of Coherence: Rupee euro dirham rate versus Gold
Figure 14: Granger Coefficient of Coherence: Rupee euro riyal rate versus Gold
The granger coefficients of coherence are presented in figure 11-14. These coefficients determine the magnitude to which exchange rates granger cause gold at various frequencies. The higher value of estimated coefficients indicates higher granger causality at that specific frequency. The baseline in the figures is the critical value at 5% level of probability for no Granger causality. A consistent pattern is observed for dollar, dirham and Riyal exchange rates which depict that there is no statistical significance. Beckmann, Czudaj et al. (2015) and Sujit and Kumar (2011) find no long run association of gold and exchange rate. However, the causality at lower frequencies cannot be neglected. There is an increase in Granger causality around 0.5 and 1.5 frequencies at higher frequencies. In contrast, Euro exchange rate does not confirm much evidence of causality at any frequency.
4.2. Safe Haven dynamic
29
Table 4 displays regression model results which include effects for intense market conditions. Findings reveal that response of gold returns to extreme variations is significantly different from zero for each parameter. This suggest that gold returns are positive when there is extreme decline in exchange rate confirming gold as a strong safe haven. Yet the magnitude of the effect differs across all quantiles. These findings confirm that, gold reduces downside risk of PKR depreciation thus substantiating its role as monetary asset. The results corroborate with Baur and Mc Dermott (2010), Joy (2011),Beckmann and Czudaj (2014) and Reboredo and Castro (2014). The hypothesis of gold’s insensitivity to bad news is confirmed. The findings proclaim gold as a safe haven therefore; it can be deduced that inclusion of gold reduces value-at-risk for portfolio managers. Furthermore, the central bank of Pakistan with gold reserves and different currencies may be benefited by gold and PKR dependence. Our empirical evidence provides central bank with a better diversification tactic for conserving portfolio value.13
13 For further readings on banks See Khan, Kutan, Naz, & Qureshi (2017) and Khan, Ghafoor, Qureshi, & Rehman (2018).
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Table 4: Quantile Regression Estimates for PakistanGold returns
0.1 0.05 0.025 0.01RDot 1.087*** 1.147*** 0.952*** 0.998***RDot-1 1.080*** 1.137** 0.932*** 0.970***RDirt 1.088*** 1.091*** 0.954*** 0.886***RDirt-1 1.088** 1.091** 0.954*** 0.886***RRt 1.087*** 1.040*** 0.839*** 0.822***RRt-1 1.087*** 1.040*** 0.839*** 0.822***REt 0.695*** 0.742** 0.802*** 0.871***REt-1 0.703 0.751** 0.819*** 0.898***
Coefficient P-valueGARCH 0.934 0.00ARCH 0.047 0.00Asymmetry parameter 0.037 0.21Note: The table shows gold-exchange rate correlations at different time scales. **, *** denote 5% and 1% level of significance respectively
5. Conclusions and Policy Implications
We empirically examine hypotheses of gold-exchange rate relationship. We test gold’s hedging and safe haven potential for exchange rates depreciation across various investment horizons. Market interdependence between gold and exchange rate has been examined using numerous techniques that provide guidance for policy options and implications. First, our findings reveal that gold act as a transitory hedge for all exchange rates considered in this study against Pakistan Rupee. Second, we noted that exchange rates have lagged relationship with gold. The coherency results indicate existence of intense coherency during high and medium frequency periods which may be of importance to speculator. Third, the Granger coherence analysis suggests that exchange rates also possess predictive ability over short frequencies. Finally, the evidence points that the role of gold as an effective safe haven for all set of currencies is confirmed which implies that during times of intense volatility in currency returns, investors switch towards gold purchases. Below are the significant implications for portfolio managers, investors and policy makers originated from the analyses.
31
First, given the gold as transitory hedge against weak Pakistani Rupees in a short and medium run, an immediate implication is a careful consideration of speculative behavior concerning gold prices. Uninformed speculations can potentially dent the hedging-ability of the gold investment. The coherency of Gold and Pakistan Rupee is stronger during higher and medium frequency periods, which may assist speculators to acquire long and short positions in the market and act accordingly. In addition, the portfolio managers may be interested in medium term for composition of their portfolios with minimum risk.
Second, since investors make frequent decisions in exchange rate market over different investment horizons, the difference in decision making based on time actually causes the structural relationship of gold and exchange rate to diverge. Our findings suggest that investor with short horizon investment motives may act in response to investment returns fluctuations. In contrast, the risk for longer horizon investors is considerably less. The higher volatility in gold also provides further implications in choosing low risk investment. In order to avoid losses arising from currency volatility, importers should buy gold and hedge their domestic currency risk by short selling. In addition, investors may be able to reduce their associated downside currency risks. Moreover, it may facilitate policy makers in devising the strategies for managing the risk considering the different horizons at different time scales against investments heterogeneity.
Third, the results also provide advisory to individual investors and the portfolio managers in choosing low risk investment and guide them in maintaining optimum portfolio that offers hedging and risk mitigation. As it is noted in the findings that there is low and weak coherency for 1024th
scale and onward between gold and exchange rate which may grab attention of institutional investors with trading of 1024 cycle days and forward. Similarly, the causal relationship results also provide useful
32
insights for assessing predictive ability that offer hedging and risk mitigation, particularly, at short term frequencies.
Fourth, although, gold investment act as hedge to Pakistan currency depreciation against wide set of currencies, this relationship might be accompanied by the volatility transmission/risk spillover from gold to exchange or exchange rate to gold or both. The volatility transmission from gold to exchange comprises a challenge that is expected to remain a top agenda in the policy circle as precious metals prices show growing volatility after the global financial crisis. Therefore, policy makers should pay particular attention to risks associated with gold prices and their spillover effects. In case of volatility in the gold prices, a strong impact on Rupee exchange rate against the selected currencies is expected which may further complicate the policies performance. Furthermore, due to the export- based nature of economy, stability in the exchange rate in the wake of volatile gold prices will be a challenge for Pakistan trade policy. In addition, Pakistan is a gold consuming country having high gold demand, may experience higher gold prices pattern in response to any short run international trade encouraging exchange rate measures.
Sixth, since gold hedging-ability against Pakistani Rupee depreciation is detached from exchange rate in the long run as findings suggest, it would be a wise option to for the policy makers and central bank to hold an alternative safe haven in the reserves for instances, US dollar to protect capital.
Seventh, Pakistan’s interest rate strategies depend on the economic upturns and the policies set by State bank of Pakistan (SBP) which exerts great impact on PKR exchange rate. Thus, the interest rate adjustments may provide guidelines to investors in anticipating future economic expansions and contractions. Further, the gold prices in this regard will be affected if
33
the country’s interest rate is comparatively higher than other markets, resulting appreciation in rupee which would lead to gold price suppressions. In addition, the sharp interest rate rise also depresses the commodity market creating instabilities. On the other hand, if SBP in the current period decides to lower the interest rates, investors will predict the economic depression leading to PKR depreciation. Such investor anticipations moves the capital in the PKR denominated gold following significant raise in gold prices for the succeeding period. Therefore, such policy dissensions require a vigilant and optimum solution without sacrificing long run economic well-being.
Lastly, since Pakistan rupee depreciation has continued to be a great risk to macroeconomic solidity since past several years hence policies for economic and political stabilization should be devised. Such proposed actions will support promotions of foreign portfolio investment and FDI. In addition, government should formulate well-built fiscal adjustments in Pakistan and withstand currency devaluation in any case regardless of improving trade balance in the short run.
References
Adams, S. (2009). Foreign direct investment, domestic investment, and economic growth in sub-saharan africa. Journal of Policy Modeling, 31(6), 939-949.
Apergis, N., Zestos, G. K., & Shaltayev, D. S. (2012). Do market fundamentals determine the dollar–euro exchange rate? Journal of Policy Modeling, 34(1), 1-15.
Apergis, N. (2014). "Can gold prices forecast the Australian dollar movements?" International Review of Economics & Finance29: 75-82.
Arslan, Y., Kılınç, M., & Turhan, M. I. (2015). Global imbalances, current account rebalancing and exchange rate adjustments. Journal of Policy Modeling, 37(2), 324-341.
Badshah, I. U., et al. (2013). "Contemporaneous Spill‐Over among Equity, Gold, and Exchange Rate Implied Volatility Indices." Journal of Futures Markets33(6): 555-572.
34
Baharumshah, A. Z., Soon, S.-V., & Lau, E. (2017). Fiscal sustainability in an emerging market economy: When does public debt turn bad? Journal of Policy Modeling, 39(1), 99-113.
Beckers, S. and L. Soenen (1984). "Gold: more attractive to non‐US than to US investors?" Journal of Business Finance & Accounting11(1): 107-112.
Beckmann, J., Czudaj, R., & Pilbeam, K. (2015). Causality and volatility patterns between gold prices and exchange rates. The North American Journal of Economics and Finance, 34, 292-300.
Capie, F., et al. (2005). "Gold as a hedge against the dollar." Journal of International Financial Markets, Institutions and Money15(4): 343-352.
Ciner, C., et al. (2013). "Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates." International Review of Financial Analysis29: 202-211.
Chen, Y.-C., et al. (2008). Can exchange rates forecast commodity prices? National Bureau of Economic Research.
Clarke, J. A. and S. Mirza (2006)."A comparison of some common methods for detecting Granger noncausality."Journal of Statistical Computation and Simulation76(3): 207-231.
Fan, Y., Gençay, R., (2010). Unit root tests with wavelets. Econometric Theory 26, 1305–1331.
Daubechies, I., (1992). Ten Lectures on Wavelets. SIAM, Philadelphia.Gourieroux C., &Monfort, A. (1997).Time Series and Dynamic Models,
Glasgow: Cambridge University Press. Gourevitch, B., Le Bouquin-Jeannµes, R. &Faucon, G. (2006). Linear and
nonlinear causality between signals: Methods, examples and neurophysiological applications. Biological Cybernetics, 95, 349-369.
Granger, C.W.J. (1969).Investigating causal relations by econometric models and cross-spectral methods, Econometrica, 37, 424-438.
Jain, A. and S. Ghosh (2013). "Dynamics of global oil prices, exchange rate and precious metal prices in India." Resources Policy38(1): 88-93.
Jain, A. and P. Biswal (2016). "Dynamic linkages among oil price, gold price, exchange rate, and stock market in India." Resources Policy49: 179-185.
Joy, M. (2011). "Gold and the US dollar: Hedge or haven?" Finance Research Letters8(3): 120-131.
Jiménez-Rodríguez, R., & Morales-Zumaquero, A. (2016). A new look at exchange rate pass-through in the g-7 countries. Journal of Policy Modeling, 38(5), 985-1000.
Kurozumi, E. and T. Yamamoto (2000). "Modified lag augmented vector autoregressions." Econometric Reviews19(2): 207-231.
Khan, R. E. A., et al. (2012). "Effectiveness of exchange rate in Pakistan: Causality analysis." Pak. J. Commer. Soc. Sci6(1): 83-96.
Khan, H. H., Ghafoor, A., Qureshi, F., & Rehman, I. U. (2018). Bank competition, financial development and growth of financially dependent industries: Fresh evidence from china. Global Economic Review, 1-27.
Khan, H. H., Kutan, A. M., Naz, I., & Qureshi, F. (2017). Efficiency, growth and market power in the banking industry: New approach to efficient
35
structure hypothesis. The North American Journal of Economics and Finance, 42, 531-545.
Koopmans, L.H. (1995). The Spectral Analysis of Time Series, Probability and Mathematical Statistics 22, San Diego: Academic Press.
Le, T.-H. and Y. Chang (2011). "Dynamic relationships between the price of oil, gold and financial variables in Japan: a bounds testing approach."
Mahmood, I., et al. (2011). "Exchange rate volatility & macroeconomic variables in Pakistan." Business Management Dynamics, 1 (2): 11-22.
Mundell, R. (2000). Currency areas, volatility and intervention. Journal of Policy Modeling, 22(3), 281-299.
Mundell, R. (2007). Dollar standards in the dollar era. Journal of Policy Modeling, 29(5), 677-690.
Mundell, R. (2013). The shift from g7 to g20 increased swings in major exchange rates and worsened their options. Journal of Policy Modeling, 35(3), 412-415.
Peiers, B. (1997). Informed traders, intervention, and price leadership: A deeper view of the microstructure of the foreign exchange market.Journal of Finance, 52, 1589-1614.
Pershin, V., Molero, J. C., & de Gracia, F. P. (2016). Exploring the oil prices and exchange rates nexus in some african economies. Journal of Policy Modeling, 38(1), 166-180.
Pierce, D.A. (1979). R-squared measures for time series. Journal of the American Statistical Association, 74, 901-910.
Pierce, D.A., &Haugh, L.D. (1977). Causality in temporal systems.Journal of Econometrics, 5, 265-293.
Percival, D.B., Walden, A.T., (2000). Wavelet Methods for Time Series Analysis. Cambridge Press, Cambridge.
Pukthuanthong, K. and R. Roll (2011). "Gold and the Dollar (and the Euro, Pound, and Yen)." Journal of Banking & Finance35(8): 2070-2083.
Qureshi, F., Ismail, I., & Gee Chan, S. (2016). Mutual funds and market performance: New evidence from asean markets. Investment Analysts Journal, 1-19.
Qureshi, F., Kutan, A. M., Ismail, I., & Gee, C. S. (2017). Mutual funds and stock market volatility: An empirical analysis of asian emerging markets. Emerging Markets Review, 31, 176-192.
Reboredo, J. C. (2012). Modelling oil price and exchange rate co-movements. Journal of Policy Modeling, 34(3), 419-440.
Reboredo, J. C. (2013). Is gold a safe haven or a hedge for the us dollar? Implications for risk management. Journal of Banking & Finance, 37(8), 2665-2676.
Reboredo, J. C., & Rivera-Castro, M. A. (2014a). Can gold hedge and preserve value when the us dollar depreciates? Economic Modelling, 39, 168-173.
Reboredo, J. C., & Rivera-Castro, M. A. (2014b). Gold and exchange rates: Downside risk and hedging at different investment horizons. International Review of Economics & Finance, 34, 267-279.
36
Sjaastad, L. A. and F. Scacciavillani (1996). "The price of gold and the exchange rate." Journal of international Money and Finance15(6): 879-897.
Sari, R., et al. (2010). "Dynamics of oil price, precious metal prices, and exchange rate." Energy Economics32(2): 351-362.
Sujit, K. and B. R. Kumar (2011). "Study on dynamic relationship among gold price, oil price, exchange rate and stock market returns." International Journal of Applied Business and Economic Research9(2): 145-165.
Sujit, K. and B. R. Kumar (2011). "Study on dynamic relationship among gold price, oil price, exchange rate and stock market returns." International Journal of Applied Business and Economic Research9(2): 145-165.
Siddique, A., Selvanathan, E., & Selvanathan, S. (2016). The impact of external debt on growth: Evidence from highly indebted poor countries. Journal of Policy Modeling, 38(5), 874-894.
Toda, H. Y. and T. Yamamoto (1995). "Statistical inference in vector autoregressions with possibly integrated processes." Journal of econometrics66(1): 225-250.
Zagaglia, P., & Marzo, M. (2013). Gold and the us dollar: Tales from the turmoil. Quantitative Finance, 13(4), 571-582.
Zapata, H. O. and A. N. Rambaldi (1997)."Monte Carlo evidence on cointegration and causation."Oxford Bulletin of Economics and statistics59(2): 285-298.
Zhang, H. J., et al. (2016). "Exchange rates and commodity prices: measuring causality at multiple horizons." Journal of Empirical Finance36: 100-120.
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