ISSN 1977-3331 EWP 2011/030

Malaysian Economic Time Series DataNon-Fixed Seasonal Effect: A Case Study of

Norhayati Shuja´Mohd.Alias LazimYap Bee Wah

Improving Trend-Cycle Forecast by Eliminating

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1

Improving Trend-Cycle Forecast by Eliminating Non-Fixed Seasonal Effect: A Case Study of Malaysian Economic Time Series Data

Norhayati Shuja’1

yatishuja@stats.gov.my. Department of Statistics, Malaysia.

Mohd. Alias Lazim. Universiti Teknologi MARA, Malaysia. dralias@tmsk.uitm.edu.my Yap Bee Wah. Universiti Teknologi MARA, Malaysia. beewah@tmsk.uitm.edu.my

Abstract

The major festival celebrations in Malaysia are usually related to religious activities and as such, the

dates are determined based on the lunar calendar. As a result, the dates of these holidays do not

move in accordance to the Gregorian calendar. When these holidays take place, they tend to affect the

economic activities for the periods in the vicinity of the holiday dates and may mask the underlying

trend movements and thus provide inaccurate signals for decision making. The impact of non-fixed

holidays on the time series need to be taken into account when performing seasonal adjustment so as

to avoid misleading interpretations on the seasonally adjusted and trend estimates. In this study, two

approaches, the SEAM (Seasonal Adjustment for Malaysia) and Regression-ARIMA (Reg-ARIMA)

were developed for eliminating the non-fixed holiday effects on five selected Malaysian economic time

series. The results show that the SEAM and Reg-ARIMA procedure were able to remove non-fixed

holiday effect. Furthermore, the forecast performances of these models were subsequently evaluated

based on out-of-sample forecasts procedure using two error measures, the RMSE and MAPE. Though

both methods gave equally good results, however, the overall results show that the SEAM method out-

performs the Reg-ARIMA procedure.

Keywords: Non-fixed Seasonal Effect, Seasonal Adjustment, Trend-Cycle Forecast JEL codes: C22, E32, E37

1 Correspondence Address: Norhayati Shuja’. Economic Indicators Division, Department of Statistics, Malaysia.

2

1. Introduction

The desire for time series data that accurately portray economic growth and decline is usually

being complicated by factors unrelated to the trend of the data but nevertheless do influence

the level of data, thus obscuring accurate interpretation. Seasonal variation is the most

common and important source of noise influencing the monthly or quarterly economic data

series. Seasonal variation includes the recurring calendar-related effects caused by economic

and non-economic factors, such as weather conditions, school holidays, festival holidays,

trading days and etc. Findley and Soukup (2000) pointed out that certain kinds of economic

activities and their associated time series are affected significantly by holidays. When these

holidays take place they tend to affect or influence the economic activities for the periods in

the vicinity of the holiday dates. Incidentally, there are some holidays whose event dates are

not fixed at any specific location within a year period but move from one point to the next,

some within a certain time intervals whilst others are not. For such moving holiday effects,

they need to be taken into account in the seasonal process to avoid biased seasonally adjusted

and trend estimates which can lead to wrong decision making by policy makers (Zhang et al.,

2001).

Many researchers have shown interest in undertaking such studies with the aim of achieving

more reliable methods of seasonal adjustment (Hilmer et al, 1983; McKenzie, 1984; Dagum

et al, 1988; Bell & Hilmer, 2002; Matas-Mir et al, 2008; Koopman & Lee, 2009). For

example, Findley et al. (1998) developed a method to remove Easter holiday effect, Labour

Day effect and Thankgiving effect based on a North American holiday period. While, for

Australian Easter, Zhang et al. (2001) developed a method to remove the Easter effect on the

Australian data series. Lin & Liu (2002) also studied the impact of Chinese New Year, the

Dragon boat festival and Mid Autumn holiday on Taiwan time series data. Similarly for

3

Turkey, the Islamic festivals occur according to the Hegirian calendar (Lunar calendar), that

is the Holy month of Ramadhan, the Feast of Ramadhan (Eid-ul Fitr) and the Feast of

Sacrifice (Eid-ul Adha). Therefore, Alper and Aruoba (2001) proposed the method which

eliminates the festivals’ effect by using dummy variables for religious events which are tied

to the lunar calendar in the regression method. These are some of the major works that have

been performed by researchers.

In the context of Malaysia, Malaysian economic time series data are affected by the major

religious festivals such as the Eid-ul Fitr of the Muslims, the Chinese New Year of the

Chinese and the Deepavali of the Indian. Since the major festivals in this country are usually

related to the religious activities and as such, the dates are determined by the respective

religious calendar. The Eid-ul Fitr is based on the Islamic calendar in which the date is

determined upon the sighting of the new moon. The difference in the method of determining

the date has caused the Eid-ul Fitr to move forward from one period to the next in the interval

of eleven or twelve days earlier each year. The date of Chinese New Year is determined on

the first full moon of the Chinese lunar calendar. It usually moves between 21st January and

21st February, whilst the date of Deepavali is determined by the Indian lunar calendar which

usually moves between 15th October and 15th November. The date of the three major

festivals in Malaysia, i.e. the Eid-ul Fitr, Chinese New Year and Deepavali is shown in

Appendix 1.

As a result, the dates of these holidays are not in alignment with the Gregorian calendar.

Hence, they tend to move along the Gregorian calendar and along the way discharge strong

seasonal influence on many economic time series data. Since these non-fixed holiday

impacts on the time series data are large, therefore, they need to be taken into account when

performing seasonal adjustment process so as to avoid misleading seasonally adjusted and

4

trend estimates. Furthermore, the presence of non-fixed holiday effects may complicate the

interpretation of the data, for example when comparing over a short time frame such as

month to month or quarter to quarter (Department of Statistics, Singapore, 1992). Ashley

(2001) concluded that by removing the non-fixed seasonality effect, the important features of

economic series such as direction, turning points and consistency between other economic

indicators can be easily identified. Deutsche Bundesbank (1999) had earlier stated that

seasonally adjusted data are also better suited for the analysis of current business cycle whilst

(Burck et al., 2004) considered it as important for early detection of turning points and

directional change of the socio-economic activities.

In view of the importance of eliminating the non-fixed holiday effects on time series data,

this paper explores a different procedure for eliminating non-fixed seasonal effect with the

aim of achieving more reliable methods in improving trend-cycle forecast. The paper

comprised of four parts. Section 2 explains the methodology for Seasonal Adjustment for

Malaysia which has been named SEAM, the RegARIMA (adjusted for Malaysia) and the

regressors for measuring the holiday effects. Section 3 presents the findings and Section 4

concludes this paper.

2. Methodology

There are many different approaches to seasonal adjustment used by practitioners and

academicians such as the X-11 family or TRAMO/SEATS. The X-11 family is the most

common method used by many statistical agencies throughout the world, such as the U.S.

Census Bureau and Statistics Canada. In this study, two approaches, the Seasonal

Adjustment for Malaysia (SEAM) and Regression-ARIMA (Reg-ARIMA) were developed

for eliminating the non-fixed holiday effects on selected Malaysian economic time series

5

data. This is done by using two different regressors called REG1 and REG3 to measure the

Eid-ul Fitr, Chinese New Year and Deepavali effect.

2.1 Regressors

In the proposed procedures, the numbers of holidays before, during and after the festivals

were taken into account in the construction of the regressors. This is because the change in

activities caused by the non-fixed holiday may affect the prior or the following month’s level.

This type of effect is referred to as proximity effect and it has different impact both before and

after the date of the festival. In the conduct of these procedures, the number of holidays

taken before, during and after the Eid-ul Fitr, Chinese New Year and Deepavali festivals were

used to construct the regressors. To determine the numbers of holidays a term called

‘Window Length’ will be used as explanatory variable. A sample survey was conducted on

350 individuals primarily to collect the information pertaining to the behavioural pattern of

the Malaysia public with respect to the number of holidays they normally take to celebrate

these festivals (Norhayati et al, 2007). The holiday weights used in constructing the

regressors can also vary depending on the characteristics of the time series data. Table 1

shows the various ‘Window Length’ for each of the festivals.

Table 1: The Number of Window Length

Festival Before During & After Total

1w 2w w Eid-ul Fitr

Chinese New Year

Deepavali

2

2

1

5

6

3

7

8

4

REG1 uses the weight comprising of the combination of the three festivals, namely the

Chinese New Year, Eid-ul Fitr and Deepavali. For example, the Eid-ul Fitr has a total

6

window length of seven-days, two-days to model the effect prior and five-days during & after

the holiday. Similar procedure was also used for the Chinese New Year and Deepavali.

However, if two festivals fall in the same month, then the number of holidays for the two

festivals is combined. The weight variable is defined as follows;

Case 1 : When the festival fall in the beginning of the month (1st-15th)

wn1 in the respective festive month

wn2 before the respective festive month

0 Otherwise

Case 2 : When the festival fall at the end of the month (16th-31st)

wn1 in the respective festive month

wn2 during & after the respective festive month

1 otherwise

where, w is the total number of window lengths, w=8 for Chinese New Year, w=7

for Eid-ul Fitr, w=4 for Deepavali,

1n is the number of holidays fall in the festive month

2n is the number of holidays fall before or after the festive month.

The REG3 on the other hand, uses three separate weight variable, each representing the Eid-

ul Fitr, Chinese New Year and Deepavali festivals. In this method, the weight variables used

are similar to that of REG1, except in this case the value of (-1) is assigned so that the weight

variable for any one year sums up to zero. This is defined as follows:

Reg1 =

Reg1 =

7

Case 1 : When the festival fall in the beginning of the month (1st-15th)

wn1 in the respective festive month

wn2 before the respective festive month

-1 after the respective festive month

0 otherwise

Case 2 : when the festival fall at the end of the month (16th-31st)

wn1 in the respective festive month

wn2 after the respective festive month

-1 before the respective festive month

0 otherwise

where, w is the total number of window lengths, w=8 for Chinese New Year, w=7

for Eid-ul Fitr, w=4 for Deepavali,

1n is the number of holidays fall in the festive month

2n is the number of holidays fall before or after the festive month.

2.2 Seasonal Adjustment for Malaysia (SEAM)

The application of the proposed SEAM procedure requires the support of X-12 ARIMA

program. The SEAM procedure is based on the use of irregular values obtained after

performing an initial seasonal adjustment with the assumption that the moving holiday effect

resides in the irregular series and this series is used to derive correction factors. This is done

in two stages.

In stage one, the irregular ( tI ) estimate is obtained by running the X-12 ARIMA program

which is expected to also contain the irregular series. This series is then used to estimate the

Reg3 =

Reg3 =

8

‘true irregular’, ′tI which is free from moving holiday effect. This is done by using two

different regressors called REG1 and REG3, used to measure the Eid-ul Fitr, Chinese New

Year and Deepavali effect. Hence, the moving holiday effect correction is made after the

first seasonal adjustment run of the X-12 ARIMA. The seasonally adjusted time series data

without moving holiday effect is then obtained.

Initially, run the X-12 ARIMA program to obtain the two different components of the time

series called the ‘Final Trend-Cycle’, tT and the ‘Final Irregular’ , tI .

Consider a time series Yt , t=1,2,3,…,n which is represented (based on the multiplicative

assumption) as follows,

tttt ISTY ××=

[1]

where, tT = trend-cycle, tS = seasonal and tI = irregular.

tI is assumed to comprise of three distinct components, i.e.

′××= tttt IHEI [2]

where, tE = the extreme value which falls outside the sigma limit of 2.5, tH = the

moving holiday effect and ′tI = the true irregular assumed free of moving holiday

effect.

However, when the X-12 ARIMA was first run, the component tE [equation 2] was

automatically removed and thus leaving components tH and ′tI . To estimate the moving

holiday effect, fit a regression model to the irregular component ( tI ).

ttt hI εββ ++= 10 [3]

9

where, tI = irregular in time t, β 0 = the intercept term value, β1 = parameter for

festival holidays ( th ), th = the weight variable for the month t with the holiday effects

and tε iid with mean of tε is 0)( =tE ε and variance 2)( εσε =t

The estimated function of [3] is then,

tot hI 1ˆˆˆ ββ += [4]

where I tˆ = estimated irregular in time t, 0β = the estimated intercept term value, 1β =

estimated parameter for festival holidays ( th ), th = the weight variable for the month

t with the holiday effects for t= 1, 2, …, 12. The weight variable th is assigned using

REG1 and REG3.

The ‘moving holiday effect’, tH is then removed by dividing the value of the irregular

components ( tI ) obtained from X-12 ARIMA procedure by the estimated value of irregular

components ( tI ) as given in equation [4],

″= tt

t IIIˆ [5]

The resulting value, ″tI in equation 5 is therefore the “irregular” component which is

assumed to be free from the influence of ‘moving holiday’ component ( tH ).

A new set of time series data ′tY (seasonally adjusted for moving holiday effect), is then

generated as the product of tT and ″tI where tT is the “Final trend cycle” obtained from X-

12 ARIMA procedure. Thus,

″×=′ ttt ITY [6]

which is now a new seasonally adjusted series with the seasonal and moving holiday effects

removed.

10

2.3 RegARIMA (Adjusted for Malaysia)

The RegARIMA procedure (Findley et al.,(1998) employs the RegARIMA model which is

part of X12-ARIMA modeling capabilities. This method uses a regression model with

ARIMA error term to derive the correction factors and adjust the original data. A correction

to the original data is done before performing any seasonal adjustment. A regressor is used to

estimate the moving holiday effect and is a predictor variable in the regression model. It is

assumed that the festival holidays have an effect of decreasing or increasing the activities

before, during and after a festival. This study proposed two types of regressors, REG1 and

REG3 that are being used in the X-12 ARIMA program as available from SEASABS

(SEASonal Analysis, Australia Bureau of Statistics Standards). SEASABS is a “knowledge-

based” seasonal analysis and adjustment system used by the Australian Bureau of Statistics to

seasonally adjust time series data.

2.4 Forecast Evaluation

A common criteria used to compare the superiority of one model against the other is to

evaluate their out-of-sample forecasting performance. For this study the Box-Jenkins

methodology was used as the basis of comparison to determine which method, SEAM or

RegARIMA perform better at deseasonalising the data series. The accuracy of model’s

forecast performance is determined by measuring the size of the forecast errors, for both the

within-sample and out-of-sample data. To identify whether the SEAM or RegARIMA gives

a better result in forecasting the trend, a fair comparison is made using the same ARIMA

model. Hence, the levels of adequacy for some models may be lower and some may be

higher. The best ARIMA models that have been identified were applied to the five economic

series which was seasonally adjusted using the two seasonal adjustment methods, the SEAM

and RegARIMA with two different regressors, REG1 and REG3. To determine which

11

seasonal adjustment method performs better in removing non-fixed seasonal effect, the

evaluation of forecast accuracy is performed using out-of-sample test rather than within

sample tests. Lettau & Ludvigson (2000), Chatfield (2001) suggested that when assessing

forecast, it is best to look at the model that minimises out-of-sample forecast errors.

3. Results and Findings

The test for the presence of stable (fixed) and moving seasonality (non-fixed) using X-12

ARIMA program was carried out for five selected Malaysian economic time series data

which represent several industries. For analytical purposes these series are assigned special

name as given in brackets.

i) Monthly Total Imports (IMPORT)

ii) Monthly Total Exports (EXPORT)

iii) Monthly Sales Value of Own Manufactured Products (Ex-factory) (OMP)

iv) Monthly Production of Crude Palm Oil (PALM)

v) Monthly Manufacture & Assembly of Motor Vehicle (1600 cc & below)

(VEHICLE)

The Fs-test was observed at the 0.1% and Fm-test was observed at the 5% level of

significance. These two tests are combined to determine whether the seasonality of the series

is ‘identifiable’ or not. If the Fm-test fails, then the two T’s is calculated and if these averages

are less than one, then the seasonality is ‘identifiable’. The results are as given in Table 2,

which indicates that the all the series were found to have significant presence of seasonality

effect.

12

Table 2: Test for presence of seasonality results using X-12 ARIMA

ORIGINAL DATA SERIES

STABLE SEASONALITY (test at 0.1%)

MOVING SEASONALITY (test at 1%)

COMBINED TEST

F-value p-value Presence F-value p-value Presence SEASONALITY

PRESENCE

1 EXPORT 16.391 0.00 YES 4.972 0.00 YES YES 2 IMPORT 12.452 0.00 YES 3.719 0.00 YES YES 3 PALM 19.283 0.00 YES 9.341 0.0002 YES YES 4 OMP 3.523 0.00 YES 5.161 0.001 YES YES 5 VEHICLE 11.371 0.99 YES 1.889 0.00 YES YES

Having confirmed that the seasonality effect is present in the data series tested, the next step

is to specifically determine whether moving holiday is also present. The F-test at 5% level of

significance was then performed. The results are summarised in Table 3. For all data series,

the effects of moving holidays were significant at 5% level of significance.

Table 3: Test for Moving Holiday Effects results

REGRESSOR TIME SERIES DATA

TEST FOR MOVING HOLIDAY EFFECT (α =0.05)

F-value p-value Presence

REG1 IMPORT 28.677 0.000 YES EXPORT 44.492 0.000 YES OMP 26.204 0.000 YES PALM 16.724 0.000 YES MACHINE 29.711 0.000 YES REG3 IMPORT 13.881 0.000 YES EXPORT 23.993 0.000 YES OMP 14.356 0.000 YES PALM 12.678 0.000 YES MACHINE 10.823 0.000 YES

To test for the effectiveness of the application of those methodologies, the seasonally

adjusted data series were then tested to determine the presence of seasonality again by

running the X-12 ARIMA program. The results are presented in Table 4. Both methods, the

SEAM and RegARIMA were found to be able to remove the non-fixed seasonal effects.

However, when combined tests were performed, the overall results were much more

conclusive in which all series show absence of any seasonality effect.

13

Table 4: Test of seasonality for seasonally adjusted data

SEASONALLY ADJUSTED TIME SERIES DATA M

ETH

OD

REG

RES

SOR

TEST FOR PRESENCE OF SEASONALITY COMBINED

TEST STABLE SEASONALITY

(test at 0.01%) MOVING SEASONALITY (test at 5%) ( * test at 1%) SEASONALITY

F-value p-value Presence F-value p-value Presence Presence

IMPORT

SEAM REG1 0.802 0.64 NO 1.267 0.20 NO NO

REG3 0.740 0.70 NO 0.939 0.54 NO NO

Reg-ARIMA

REG1 0.541 0.87 NO 1.260 0.20 NO NO

REG3 0.531 0.88 NO 1.304 0.17 NO NO

EXPORT

SEAM REG1 0.545 0.87 NO 0.874 0.63 NO NO

REG3 0.355 0.97 NO 0.827 0.69 NO NO

Reg-ARIMA

REG1 0.652 0.78 NO 1.025 0.43 NO NO

REG3 0.720 0.72 NO 1.053 0.40 NO NO

OMP

SEAM REG1 1.000 0.45 NO 1.931 0.01 YES NO

REG3 0.943 0.50 NO 1.960 0.009 * YES NO

Reg-ARIMA

REG1 1.558 0.11 NO 4.883 0.00 * YES NO

REG3 1.482 0.14 NO 4.281 0.00 * YES NO

PALM

SEAM REG1 0.646 0.79 NO 1.045 0.41 NO NO

REG3 0.456 0.93 NO 1.190 0.26 NO NO

Reg-ARIMA

REG1 1.165 0.31 NO 2.527 0.00 * YES NO

REG3 0.354 0.97 NO 1.832 0.02 YES NO

VEHICLE

SEAM REG1 2.230 0.01 NO 1.240 0.22 NO NO

REG3 1.984 0.03 NO 1.119 0.33 NO NO

Reg-ARIMA

REG1 2.127 0.02 NO 2.413 0.001 YES NO

REG3 0.297 0.99 NO 1.596 0.05 NO NO

Since both procedures were effective in removing the moving holiday effect, the next stage is

to determine which procedure performs better. A comparison was made on each of the series

by ranking the probability values of moving seasonality based on the types of regressors

used. For example, IMPORT series, where REG1 for SEAM was compared against REG1

for RegARIMA and rank 1 is given to biggest p-value. When the probability values are equal

as in this case, then the corresponding F-values will be used. Hence, for IMPORT series,

rank 1 is given to REG1 of RegARIMA and rank 2 to REG1 of SEAM. These ranks are then

summed across all data series and the results of ranking are shown in Table 5.

14

Table 5: The Results of Ranking the p-value based on Regressors SEASONALLY ADJUSTED TIME SERIES DATA M

ETH

OD

REG

RES

SOR

MOVING SEASONALITY (test at 5%) ( * test at 1%)

RANKING

F-value p-value Presence REG1 REG3

IMPORT

SEAM REG1 1.267 0.20 NO 2

REG3 0.939 0.54 NO 1

Reg-ARIMA

REG1 1.260 0.20 NO 1

REG3 1.304 0.17 NO 2

EXPORT

SEAM REG1 0.874 0.63 NO 1

REG3 0.827 0.69 NO 1

Reg-ARIMA

REG1 1.025 0.43 NO 2

REG3 1.053 0.40 NO 2

OMP

SEAM REG1 1.931 0.01 YES 1

REG3 1.960 0.009 * YES 1

Reg-ARIMA

REG1 4.883 0.00 * YES 2

REG3 4.281 0.00 * YES 2

PALM

SEAM REG1 1.045 0.41 NO 1

REG3 1.190 0.26 NO 1

Reg-ARIMA

REG1 2.527 0.00 * YES 2

REG3 1.832 0.02 YES 2

VEHICLE

SEAM REG1 1.240 0.22 NO 1

REG3 1.119 0.33 NO 1

Reg-ARIMA

REG1 2.413 0.001 YES 2

REG3 1.596 0.05 NO 2

Table 6 summarizes the results of the total rank of p-values associated with each of the

regressor REG1 and REG3 as applied to the two competing methods, SEAM and

RegARIMA. The method that has the smallest total rank values will be considered the more

effective procedure. From the results in Tables 5 and 6, we can conclude that the SEAM

method is more effective than the RegARIMA method when used for removing holiday

effect.

Table 6: Summary of Total Rank for SEAM and RegARIMA

METHOD REG1 REG3 TOTAL

SEAM RegARIMA

6 9

5 10

11 19

15

3.1 Forecast Performance

Although the SEAM method fared better at removing holiday effect than Reg-ARIMA but

more importantly is to determine which procedure performs better in trend forecasting for

seasonally adjusted time series. A comparison of models’ performance, in particular for short

term forecasting of the underlying trend was done for the two types of seasonally adjusted

data. The type 1 was seasonally adjusted using SEAM while the type 2 was seasonally

adjusted using RegARIMA. The ARIMA models were then fitted to the data series. The

models were identified based on the ACF and PACF. The selection of the best model was

carried out using the Akaike Information Criterion (AIC) goodness-of-fit statistics. The

decision rule is to select a model with the smallest AIC which is said to fit the data better. At

the same time the adequacy of the competing models (diagnostic checking) was determined

using the Ljung-Box portmanteau test ( Q* -statistics). Lastly, the models were evaluated

using two error measures, that is, Relative Mean Squared Error (RMSE).

Table 7 : Ljung-Box, AIC, RMSE and Best ARIMA Model

Data Series ARIMA Model Ljung-Box

AIC RMSE Best ARIMA

Model d.f )(2

][ pnK −αχ

p-value

IMPORT (5,1,1)(1,0,0)12 4 7.8 0.101 3989.94 704.30 (5,1,1)(1,0,0)12

(5,1,2)(1,0,0)12 4 4.6 0.329 3991.63 707.24

(5,1,2)(1,0,1)12 3 4.3 0.233 3992.88 704.74

EXPORT (3,1,0)(1,0,0)12 8 7.0 0.533 3942.52 786.05

(4,1,0)(1,0,0)12 7 7.5 0.381 3944.51 787.41

(5,1,0)(1,0,0)12 6 2.5 0.870 3941.88 779.27 (5,1,0)(1,0,0)12

OMP (4,1,0)(1,0,0)12 7 6.5 0.488 7396.24 421688.42

(4,1,0)(1,0,1)12 6 6.5 0.374 7397.83 422466.82

(5,1,0)(1,0,0)12 6 2.3 0.888 7377.45 419533.64 (5,1,0)(1,0,0)12

RPV (3,1,1)(1,0,0)12 7 7.7 0.355 4930.36 3377.04 (3,1,1)(1,0,0)12

(4,1,0)(1,0,0)12 7 7.8 0.355 4931.86 3377.05

(4,1,1)(1,0,0)12 6 7.6 0.270 4931.52 3382.15

VEHICLE (1,1,2)(1,0,0)12 8 16.6 0.034 4624.21 1709.31

(5,1,3)(1,0,0)12 3 6.3 0.099 4624.87 1678.25 (5,1,3)(1,0,0)12

(5,1,3)(1,0,1)12 2 506 0.061 4625.88 1690.17

16

The RMSE within sample for the data series were calculated by using the SAS software and

the results are shown in Table 7. In order to select the best model, the smallest RMSE is

considered. Therefore, among the three models for each series, the best model selected

contains the smallest AIC and RMSE. The best ARIMA models were then applied to the

deseasonalised data which used REG1 and REG3. The test statistics, such as the Ljung –Box

statistics, the AIC and the RMSE were performed and shown in Table 8.

Table 8 : The Summary Statistics for All Seasonally Adjusted Series SEASONALLY ADJUSTED TIME SERIES DATA

ARIMA MODELS

NA

L

AD

JUS

TM

EN

T

PRO

CE

RE

GR

ESS

OR

S Ljung-Box

(Q* statistics) AIC

WITHIN SAMPLE

df 2χ p-value RMSE

IMPORT (5,1,1)(1,0,0)12

SEAM REG1 4 18.9 *0.001 3997.85 697.47

REG3 4 7.8 0.101 3989.94 704.30

Reg- ARIMA

REG1 4 3.7 0.454 3909.40 576.42

REG3 4 5.3 0.260 3914.79 578.49

EXPORT (5,1,0)(1,0,0)12

SEAM REG1 6 5.3 0.504 3951.36 780.27

REG3 6 2.5 0.870 3941.88 779.27

Reg- ARIMA

REG1 6 9.0 0.171 3859.09 577.30

REG3 6 6.4 0.377 3862.64 578.62

OMP (5,1,0)(1,0,0)12

SEAM REG1 6 10.1 0.120 7381.80 444279.51

REG3 6 2.3 0.888 7377.45 419533.64

Reg- ARIMA

REG1 6 13.6 *0.034 7301.18 369081.79

REG3 6 12.9 *0.045 7300.84 363838.17

RPV (3,1,1)(1,0,0)12

SEAM REG1 7 16.7 *0.019 4948.91 3510.90

REG3 7 7.7 0.355 4930.36 3377.04

Reg- ARIMA

REG1 7 10.4 0.165 4915.18 3306.32

REG3 7 10.7 0.150 4900.90 3219.94

VEHICLE (5,1,3)(1,0,0)12

SEAM REG1 3 6.6 0.086 4639.35 1808.87

REG3 3 6.3 0.099 4624.87 1678.25

Reg- ARIMA

REG1 3 5.7 0.126 4655.96 1889.98

REG3 3 6.3 0.099 4589.05 1678.25

* models are not adequate

3.2 Forecast Evaluation

The out-of-sample forecast starts in January 2002 – December 2002 and the first 21 years’

(1981-2001) data are used for model estimation. The results of out-of-sample error measures

17

for the seasonally adjusted time series data are shown in Table 9. Each economic series was

seasonally adjusted using the the SEAM and RegARIMA with two different regressors, that

is, REG1 and REG3. The series were evaluated and two error measures, RMSE and MAPE

were calculated. The results show that both the SEAM and RegARIMA seem to give similar

results. Therefore, it is difficult to identify which method performs better forecasting. For

some series, SEAM procedure is better than RegARIMA whilst for some other series

RegARIMA procedure is better than SEAM.

Therefore, to determine which method performed better forecasting of the trend, the values of

RMSE and MAPE were ranked according to the types of regressors. A comparison is made

on each of the series, e.g., for the import series, REG1 for SEAM is compared against REG1

of RegARIMA. Since the RMSE value of REG1 (SEAM) is smaller than REG1

(RegARIMA), therefore, rank 1 is given to REG1 of SEAM and rank 2 is given to REG1 of

RegARIMA. The same ranking is done for MAPE. Comparing SEAM and RegARIMA

method, the smaller value of MAPE is given rank 1 and subsequently the bigger value is

given rank 2. These ranks are then summed across all data series. The results of ranking are

as shown in Table 9 and the summary of ranking the RMSE and MAPE are shown in Table

10. From the results of ranking the RMSE and MAPE, was found that the SEAM method has

smaller total rank for REG1 and REG3 while the RegARIMA method has smaller total rank

for REG2. Therefore, we can conclude that the SEAM method is more effective in

deseasonalising using REG1 and REG3. As an overall conclusion, the SEAM method

provides better forecasts of the underlying trend.

18

Table 9 : The Results of Out-of-sample Evaluation SEASONALLY ADJUSTED TIME SERIES DATA

ARIMA MODELS

SEA

SON

AL

A

DJU

STM

EN

T

PRO

CE

DU

RE

S

RE

GR

ES

SOR

S

OUT-Of-SAMPLE RANKING

RMSE MAPE RMSE MAPE

IMPORT (5,1,1)(1,0,0)12

SEAM REG1 887.2 2.8 1 1

REG3 1225.6 4.2 1 1

Reg-ARIMA

REG1 956.1 3.2 2 2

REG3 1353.8 4.6 2 2

EXPORT (5,1,0)(1,0,0)12

SEAM REG1 1756.8 5.3 2 2

REG3 2149.7 6.8 2 2

Reg-ARIMA

REG1 1312.7 4.0 1 1

REG3 1545.4 4.7 1 1

OMP (5,1,0)(1,0,0)12

SEAM REG1 1585860.9 5.8 1 1

REG3 1783056.3 6.4 1 1

Reg-ARIMA

REG1 2120293.5 6.9 2 2

REG3 1783283.7 6.4 2 2

PALM (4,1,0)(1,0,0)12

SEAM REG1 46.2 4.1 1 1

REG3 46.0 4.0 1 1

Reg-ARIMA

REG1 58.9 4.5 2 2

REG3 60.3 4.8 2 2

VEHICLE (5,1,3)(1,0,0)12

SEAM REG1 2991.6 10.9 1 1

REG3 3213.5 11.3 1 1

Reg-ARIMA

REG1 4539.9 14.9 2 2

REG3 3364.8 11.8 2 2

Table 10 : Summary of Ranking the RMSE and MAPE

RMSE MAPE TOTAL

SEAM

Reg- ARIMA

SEAM Reg-

ARIMA SEAM

Reg- ARIMA

REG1 6 9 6 9 12 18

REG3 6 9 6 9 12 18

4. Conclusion

This study shows that the festivals such as Eid-ul Fitr, Chinese New Year and Deepavali

celebration that fall on different dates and hence do not follow the Gregorian calendar

significantly affect the eight time series data. These three major festivals have the effect of

either stimulating or reducing activities for the periods in the vicinity of the holiday dates.

19

The application of the seasonal adjustment procedures using SEAM (Seasonal Adjustment

for Malaysia) and RegARIMA (adjusted for Malaysia) can significantly eliminate the

presence of the moving holiday effects. Therefore, the proposed methods, SEAM and

RegARIMA are able to remove moving holiday effects and seasonally adjust the data series.

Although, RegARIMA is a standard program for removing holiday effects, results show that

overall SEAM performs better than the RegARIMA in removing the Malaysian moving

holiday effect.

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Appendix 1: The Dates of Major Festivals in Malaysia, 1981-2010

Year Eid-ul Fitr Chinese New Year Deepavali

1981 1-Aug 5-Feb 26-Oct 1982 22-Jul 25-Jan 14-Nov 1983 12-Jul 13-Feb 4-Nov 1984 30-Jun 2-Feb 23-Oct 1985 20-Jun 20-Feb 11-Nov 1986 9-Jun 9-Feb 1-Nov 1987 29-May 29-Jan 4-Nov 1988 17-May 17-Feb 8-Nov 1989 7-May 6-Feb 29-Oct 1990 26-Apr 27-Jan 17-Oct 1991 16-Apr 15-Feb 5-Nov 1992 4-Apr 4-Feb 26-Oct 1993 25-Mar 23-Jan 13-Nov 1994 14-Mar 10-Feb 3-Nov 1995 3-Mar 31-Jan 23-Oct 1996 20-Feb 19-Feb 10-Nov 1997 9-Feb 7-Feb 30-Oct 1998 30-Jan 28-Jan 19-Oct 1999 19-Jan 16-Feb 7-Nov 2000 8-Jan & 27-Dec 5-Feb 26-Oct 2001 16-Dec 24-Jan 14-Nov 2002 6-Dec 12-Feb 4-Nov 2003 26-Nov 1-Feb 23-Oct 2004 14-Nov 22-Jan 11-Nov 2005 3-Nov 9-Feb 1-Nov 2006 24-Oct 30-Jan 21-Oct 2007 13-Oct 19-Feb 9-Nov 2008 2-Oct 7-Feb 28-Oct 2009 21-Sep 26-Jan 16-Nov 2010 10-Sep 1-Jan 5-Nov