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8/3/2019 Sample Statistics Assignment
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Sample Statistics Assignment | ExpertsMind.com|Statistics Help
QUESTION 1 Has the volatility of the stock market increased?
(a) You have been provided with daily data starting in January 2009 on the
main New Zealand stock market index, the NSX-50. Choose a suitable
model for measuring volatility on the New Zealand stock market. You may
carry out any data transformations you believe are necessary.
(b) Estimate your model, carry out error tests on your model and take any
corrective measures that are required. You should include any variables
you need to carry out the test(s) in part (c).
(c) Carry out one or more statistical tests to determine if volatility has
increased since the earthquake. 2
QUESTION 2 Predicting the Stock Market
In this question you will consider the impact on the building industry of
the earthquake. Two construction and materials indices have been
provided for the analysis. If your family name begins with letters from A
to L you will use the FTSE index and if your family name begins withletters from M to Z you will use the Dow Jones index.
(a) Estimate a market model using the construction and materials index in
place of a share. Include any extra variables required for the test(s) in
part (c)
(b) Carry out error tests on your model and take any corrective measures
that are required.
(c) Carry out one or more statistical tests to determine if the model haschanged since the
earthquake.
Note that if in this or the previous question you decide that your results
are unreliable through problems that you could have fixed, you will
receive very low marks indeed.
REPORT
Write a 500 to 1000 word report discussing your analysis and findings. Anexample of the type of report required is given as an appendix to Module
http://www.expertsmind.com/http://www.expertsmind.com/http://www.expertsmind.com/statistics-homework-assignment-help.aspxhttp://www.expertsmind.com/http://www.expertsmind.com/statistics-homework-assignment-help.aspx8/3/2019 Sample Statistics Assignment
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11. Your answers to questions one and two should be included as a
technical appendix to the report and should be formatted similarly to the
sample tutorial answers I have provided.
Answers
QUESTION 1 Has the volatility of the stock market increased?
(a) You have been provided with daily data starting in January 2009 on the
main New
Zealand stock market index, the NSX-50. Choose a suitable model for
measuring
volatility on the New Zealand stock market. You may carry out any datatransformations
you believe are necessary.
(b) Estimate your model, carry out error tests on your model and take any
corrective
measures that are required. You should include any variables you need to
carry out the
test(s) in part (c).
(c) Carry out one or more statistical tests to determine if volatility has
increased since the
Earthquake
(c)
Table 1
BNZ50CAP ANZ50CAP
Mean 2018.359 2148.711
Median 2063.510 2148.510
Maximum 2193.490 2210.070
Minimum 1688.190 2063.330
Std. Dev. 111.6706 36.02084
Skewness -0.780551 -0.478198
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Kurtosis 2.682311 2.701710
Jarque-Bera 59.32497 3.303754
Probability 0.000000 0.191690
Sum 1132299. 169748.1
Sum Sq. Dev. 6983386. 101205.1
Observations 561 79
We have taken into consideration the market before and after earthquake
happen on 25
th
February 2011.
The above statistics , we see that standard deviation before earthquake
is more as compare to
after earthquake. So before earthquake the market is more volatile as
compare to after
earthquake and negative skewness which means that the left tail is
particularly extreme.
Kurtosis before and after earthquake is less than 3 indicates the
distribution is flat
(platykurtic) relative to the normal.We can also check non-constant
variance by taking
H0: the errors are normal
H1: the errors are not normal
Level of significance : = 0.05
Test Statistic: Jarque-Bera test
P=0.000
Indicates the errors are normal, we accept H0
We can also see from graph how volatile is market before earthquake.
(b)
Dependent Variable: BNZ50CAP
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Method: Least Squares
Date: 10/20/11 Time: 09:46
Sample: 1/01/2009 2/24/2011
Included observations: 561
BNZ50CAP=C(1)+C(2)*BNZBB90D
Coefficient Std. Error t-Statistic Prob.
1500
1600
1700
1800
1900
2000
2100
2200
2300
NZ50CAP
NZ50CAPC(1) 2357.352 35.99821 65.48526 0.0000
C(2) -111.7507 11.77883 -9.487414 0.0000
R-squared 0.138690 Mean dependent var 2018.359
Adjusted R-squared 0.137149 S.D. dependent var 111.6706
S.E. of regression 103.7306 Akaike info criterion 12.12503
Sum squared resid 6014864. Schwarz criterion 12.14047
Log likelihood -3399.071 Hannan-Quinn criter. 12.13106
F-statistic 90.01102 Durbin-Watson stat 0.018309
Prob(F-statistic) 0.000000
From the above model, we see the Durbin-watson stat does not
approaches to 2, the residuals are dependent on
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Variable Coefficient Std. Error t-Statistic Prob.
C 7.651104 0.002510 3048.424 0.0000
@TREND 0.000548 5.56E-05 9.867764 0.0000
R-squared 0.558417 Mean dependent var 7.672484
Adjusted R-squared 0.552682 S.D. dependent var 0.016836S.E. of
regression 0.011260 Akaike info criterion -6.110111
Sum squared resid 0.009763 Schwarz criterion -6.050125
Log likelihood 243.3494 Hannan-Quinn criter. -6.086079
F-statistic 97.37276 Durbin-Watson stat 0.149942
Prob(F-statistic) 0.000000
We compute multiple regression model for before earthquake and after
earthqauake
Dependent Variable: LOG(BNZ50CAP)
Method: Least Squares
Date: 10/20/11 Time: 11:54
Sample: 1/01/2009 2/24/2011
Included observations: 561
Variable Coefficient Std. Error t-Statistic Prob.
C 0.004352 6.52E-06 667.7215 0.0000
@TREND -3.43E-09 1.10E-09 -3.126414 0.0019
@TREND^2 3.59E-12 1.76E-12 2.035404 0.0423
LOG(BNZ50CAP-1) 0.999493 8.68E-07 1151362. 0.0000
R-squared 1.000000 Mean dependent var 7.608461
Adjusted R-squared 1.000000 S.D. dependent var 0.056710
S.E. of regression 8.72E-07 Akaike info criterion -25.06082
Sum squared resid 4.23E-10 Schwarz criterion -25.02995
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Log likelihood 7033.560 Hannan-Quinn criter. -25.04877
F-statistic 7.90E+11 Durbin-Watson stat 0.080962
Prob(F-statistic) 0.000000
Dependent Variable: LOG(ANZ50CAP)
Method: Least Squares
Date: 10/20/11 Time: 11:59
Sample: 2/25/2011 6/15/2011
Included observations: 79
Variable Coefficient Std. Error t-Statistic Prob.
C 0.004060 6.60E-06 615.0603 0.0000
@TREND 1.76E-09 1.86E-09 0.947638 0.3464
@TREND^2 -1.17E-11 2.07E-11 -0.567682 0.5719
LOG(ANZ50CAP-1) 0.999532 8.64E-07 1157437. 0.0000
R-squared 1.000000 Mean dependent var 7.672484
Adjusted R-squared 1.000000 S.D. dependent var 0.016836
S.E. of regression 8.10E-08 Akaike info criterion -29.77161
Sum squared resid 4.92E-13 Schwarz criterion -29.65164
Log likelihood 1179.979 Hannan-Quinn criter. -29.72354
F-statistic 1.12E+12 Durbin-Watson stat 0.224642
Prob(F-statistic) 0.000000
Check for HeteroskedasticityH0: the errors have constant variance
H1: the variance is not constant
Level of significance =0.05
Heteroskedasticity Test: ARCH
F-statistic 0.019090 Prob. F(1,557) 0.8902
Obs*R-squared 0.019158 Prob. Chi-Square(1) 0.8899
Test Equation:
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Dependent Variable: WGT_RESID^2
Method: Least Squares
Date: 10/21/11 Time: 17:26
Sample (adjusted): 1/05/2009 2/24/2011
Included observations: 559 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.971745 0.078471 12.38345 0.0000
WGT_RESID^2(-1) 0.005854 0.042369 0.138166 0.8902
R-squared 0.000034 Mean dependent var 0.977466
Adjusted R-squared -0.001761 S.D. dependent var 1.574581
S.E. of regression 1.575966 Akaike info criterion 3.751186
Sum squared resid 1383.404 Schwarz criterion 3.766664
Log likelihood -1046.456 Hannan-Quinn criter. 3.757230
F-statistic 0.019090 Durbin-Watson stat 1.999034
Prob(F-statistic) 0.890159
Conclusion accept H0, the errors have constant variance
Heteroskedasticity Test: ARCH
F-statistic 0.397818 Prob. F(1,75) 0.5301
Obs*R-squared 0.406271 Prob. Chi-Square(1) 0.5239
Test Equation:
Dependent Variable: WGT_RESID^2
Method: Least Squares
Date: 10/21/11 Time: 17:48
Sample (adjusted): 3/01/2011 6/15/2011
Included observations: 77 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 1.152209 0.218417 5.275285 0.0000
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WGT_RESID^2(-1) -0.072479 0.114913 -0.630728 0.5301
R-squared 0.005276 Mean dependent var 1.075363
Adjusted R-squared -0.007987 S.D. dependent var 1.584386
S.E. of regression 1.590700 Akaike info criterion 3.791857
Sum squared resid 189.7746 Schwarz criterion 3.852735
Log likelihood -143.9865 Hannan-Quinn criter. 3.816207
F-statistic 0.397818 Durbin-Watson stat 1.987716
Prob(F-statistic) 0.530136
Conclusion accept H0, the errors have constant variance(a)
Let us compute Wald test with c(4)=0
H0: market is volatile after earthquake
H1: market is non- volatile after earthquake
Wald Test:
Equation: Untitled
Test Statistic Value df Probability
t-statistic 1157437. 75 0.0000
F-statistic 1.34E+12 (1, 75) 0.0000
Chi-square 1.34E+12 1 0.0000
Null Hypothesis: C(4)=0
Null Hypothesis Summary:
Normalized Restriction (= 0) Value Std. Err.
C(4) 0.999532 8.64E-07
Restrictions are linear in coefficients.
The p=0.000 value indicates . to accept H0QUESTION 2 Predicting the
Stock Market
In this question you will consider the impact on the building industry of
the earthquake.
8/3/2019 Sample Statistics Assignment
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Two construction and materials indices have been provided for the
analysis. If your
family name begins with letters from A to L you will use the FTSE index
and if your
family name begins with letters from M to Z you will use the Dow Jones
index.
(a) Estimate a market model using the construction and materials index in
place of a
share. Include any extra variables required for the test(s) in part (c)
(b) Carry out error tests on your model and take any corrective measures
that are
required.
(c) Carry out one or more statistical tests to determine if the model has
changed since
the earthquake.Graphical representation shown below for both the
construction and material indices for
family name from A to L and M to Z have similar kind of changes after or
before
earthquake. Indices range have been different in both the situation before
and after
earthquake.
80
100
120
140
160
180
200
220
240
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733,400 733,500 733,600 733,700 733,800 733,900 734,000 734,100
734,200
BCODE
BD2NZS2L
BF3NZS3L
160
180
200
220
240
260
280
734,190 734,210 734,230 734,250 734,270 734,290 734,310
ACODE
AD2NZS2L
AF3NZS3Lthe same can be reflected through descriptive statistics for
before and after earthquake happens
given below
before after
Dow Jones index FTSE index Dow Jones indexFTSE index
BD2NZS2L BF3NZS3L AD2NZS2L AF3NZS3L
Mean 206.7842 147.3566 247.4517 176.3405
Median 215.9770 153.9100 247.3820 176.2900
Maximum 238.5670 170.0100 262.2580 186.8900
Minimum 141.3220 100.7100 235.2610 167.6500
Std. Dev. 24.45159 17.42317 6.361699 4.533522
Skewness -1.112777 -1.112702 0.164092 0.164033
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Kurtosis 3.092685 3.092968 2.126751 2.126450
Jarque-Bera 115.9793 115.9648 2.864634 2.866108
Probability 0.000000 0.000000 0.238755 0.238579
Sum 116005.9 82667.06 19548.69 13930.90
Sum Sq. Dev. 334812.9 169997.4 3156.755 1603.120
Observations 561 561 79 79
We have taken into consideration the market before and after earthquake
happen on 25
th
February 2011.
The above statistics , we see that standard deviation for both the
construction and material
indices before earthquake is more as compare to after earthquake. So
before earthquake the
market is more volatile as compare to after earthquake and negative
skewness for before
which means that the left tail is particularly extreme while after
earthquake it is positive.
Kurtosis before earthquake is 3 which is normal value and after
earthquake is less than 3
indicates the distribution is flat (platykurtic) relative to the normal.
(b) The analysis of ARCH and GARCH models many theories of pricing
and portfolio
analysis can be exhibited and tested so we analyse the data byFollowing
are the result for before earthquake happen, we use GARCH model
Dependent Variable: LOG(BD2NZS2L)
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 10/20/11 Time: 14:15
Sample: 1/01/2009 2/24/2011
Included observations: 561
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Convergence achieved after 57 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 5.391096 0.000976 5522.916 0.0000
Variance Equation
C 0.000133 2.02E-05 6.562886 0.0000
RESID(-1)^2 1.035030 0.196604 5.264556 0.0000
GARCH(-1) -0.065318 0.040560 -1.610384 0.1073
R-squared -0.274643 Mean dependent var 5.323898
Adjusted R-squared -0.274643 S.D. dependent var 0.128339
S.E. of regression 0.144894 Akaike info criterion -3.133641
Sum squared resid 11.75686 Schwarz criterion -3.102769
Log likelihood 882.9862 Hannan-Quinn criter. -3.121587
Durbin-Watson stat 0.011655
After erathquake
Dependent Variable: DLOG(AD2NZS2L)
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 10/20/11 Time: 14:08
Sample (adjusted): 2/28/2011 6/15/2011
Included observations: 78 after adjustments
Convergence achieved after 16 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C -0.000350 0.001072 -0.326331 0.7442
Variance Equation
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C 6.97E-06 2.16E-06 3.232690 0.0012
RESID(-1)^2 -0.149537 0.070038 -2.135084 0.0328
GARCH(-1) 1.046129 0.081166 12.88871 0.0000
R-squared -0.002000 Mean dependent var 5.93E-05
Adjusted R-squared -0.002000 S.D. dependent var 0.009211
S.E. of regression 0.009220 Akaike info criterion -6.601032
Sum squared resid 0.006546 Schwarz criterion -6.480176
Log likelihood 261.4403 Hannan-Quinn criter. -6.552651
Durbin-Watson stat 1.923753
(c) regression model to predict stock market (before and after
earthquake)Dependent Variable: DLOG(BD2NZS2L)
Method: Least Squares
Date: 10/20/11 Time: 15:05
Sample (adjusted): 1/02/2009 2/24/2011
Included observations: 560 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.023477 0.025782 -0.910575 0.3629
LOG(BF3NZS3L) 0.004853 0.005170 0.938724 0.3483
R-squared 0.001577 Mean dependent var 0.000718
Adjusted R-squared -0.000213 S.D. dependent var 0.015640
S.E. of regression 0.015641 Akaike info criterion -5.474228
Sum squared resid 0.136516 Schwarz criterion -5.458771
Log likelihood 1534.784 Hannan-Quinn criter. -5.468192
F-statistic 0.881204 Durbin-Watson stat 2.014883
Prob(F-statistic) 0.348278
Dependent Variable: DLOG(AD2NZS2L)
Method: Least Squares
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Date: 10/20/11 Time: 15:01
Sample (adjusted): 2/28/2011 6/15/2011
Included observations: 78 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.321096 0.211725 -1.516572 0.1335
LOG(AF3NZS3L) 0.062088 0.040932 1.516870 0.1334
R-squared 0.029385 Mean dependent var 5.93E-05
Adjusted R-squared 0.016614 S.D. dependent var 0.009211
S.E. of regression 0.009134 Akaike info criterion -6.528317
Sum squared resid 0.006341 Schwarz criterion -6.467889
Log likelihood 256.6044 Hannan-Quinn criter. -6.504127
F-statistic 2.300895 Durbin-Watson stat 1.868923
Prob(F-statistic) 0.133448
P=0.3629 before is higher as compare to p=0.1335 after earthquake for
estimating a regression model as shown
through residual graph separately-.08
-.06
-.04
-.02
.00
.02
.04
.06
.08
I II III IV I II III IV I
2009 2010 2011
DLOG(BD2NZS2L) Residuals
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-.03
-.02
-.01
.00
.01
.02
.03
28 7 14 21 28 4 11 18 25 2 9 16 23 30 6 13
2011m3 2011m4 2011m5 2011m6
DLOG(AD2NZS2L) ResidualsWe also use least square eq model to predict
Before earthquake taken both the FTSE index and Dow Jones index as
independent variable
Dependent Variable: BCODE
Method: Least Squares
Date: 10/20/11 Time: 15:24
Sample: 1/01/2009 2/24/2011
Included observations: 561
BCODE= C(1)+ C(2) *BD2NZS2L
Coefficient Std. Error t-Statistic Prob.
C(1) 732397.9 55.83859 13116.34 0.0000
C(2) 6.777353 0.268168 25.27277 0.0000
R-squared 0.533277 Mean dependent var 733799.4
Adjusted R-squared 0.532442 S.D. dependent var 226.9294
S.E. of regression 155.1702 Akaike info criterion 12.93048
Sum squared resid 13459489 Schwarz criterion 12.94592
Log likelihood -3625.000 Hannan-Quinn criter. 12.93651
F-statistic 638.7128 Durbin-Watson stat 0.017654
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Prob(F-statistic) 0.000000
Dependent Variable: BCODE
Method: Least Squares
Date: 10/20/11 Time: 15:29
Sample: 1/01/2009 2/24/2011
Included observations: 561
BCODE= C(1)+ C(2) *BF3NZS3L
Coefficient Std. Error t-Statistic Prob.
C(1) 732397.7 55.83499 13117.18 0.0000
C(2) 9.512452 0.376294 25.27930 0.0000
R-squared 0.533406 Mean dependent var 733799.4
Adjusted R-squared 0.532571 S.D. dependent var 226.9294
S.E. of regression 155.1488 Akaike info criterion 12.93021
Sum squared resid 13455778 Schwarz criterion 12.94564
Log likelihood -3624.923 Hannan-Quinn criter. 12.93623
F-statistic 639.0431 Durbin-Watson stat 0.017683
Prob(F-statistic) 0.000000
After earthquake taken both the FTSE index and Dow Jones index as
independent variable
Dependent Variable: BCODE
Method: Least Squares
Date: 10/20/11 Time: 15:24
Sample: 1/01/2009 2/24/2011
Included observations: 561
BCODE= C(1)+ C(2) *BD2NZS2L
Coefficient Std. Error t-Statistic Prob.
C(1) 732397.9 55.83859 13116.34 0.0000
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C(2) 6.777353 0.268168 25.27277 0.0000R-squared 0.533277 Mean
dependent var 733799.4
Adjusted R-squared 0.532442 S.D. dependent var 226.9294
S.E. of regression 155.1702 Akaike info criterion 12.93048
Sum squared resid 13459489 Schwarz criterion 12.94592
Log likelihood -3625.000 Hannan-Quinn criter. 12.93651
F-statistic 638.7128 Durbin-Watson stat 0.017654
Prob(F-statistic) 0.000000
Dependent Variable: ACODE
Method: Least Squares
Date: 10/20/11 Time: 15:28
Sample: 2/25/2011 6/15/2011
Included observations: 79
ACODE=C(1)+C(2)*AD2NZS2L
Coefficient Std. Error t-Statistic Prob.
C(1) 734250.8 142.5271 5151.658 0.0000
C(2) -0.013538 0.575791 -0.023512 0.9813
R-squared 0.000007 Mean dependent var 734247.4
Adjusted R-squared -0.012980 S.D. dependent var 32.14292
S.E. of regression 32.35085 Akaike info criterion 9.816148
Sum squared resid 80586.46 Schwarz criterion 9.876134
Log likelihood -385.7378 Hannan-Quinn criter. 9.840180
F-statistic 0.000553 Durbin-Watson stat 0.002564
Prob(F-statistic) 0.981303
P=0.000 in both before and after indicates it is best fitted model for
predicting the stock marketThe Effects of the Christchurch Earthquake on
Financial Markets in New Zealand
Introduction
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This report is to discuss The Effects of the Christchurch Earthquake on
Financial Markets in
New Zealand based on data provided. This is done by comparing the
performance of the
market before and the after earthquake happen on 25
th
February 2011.
The aim is to determine the volatility of the stock market increased and
Predicting the Stock
Market . we have used regression based model approach.
We have considered the variables NZX 50 - PRICE INDEX, DJTM NEW
ZEALAND CON
& MAT - PRICE INDEX, FTSE NEW ZEALAND CON & MAT - PRICE INDEX.
The method so choosen to know the effects occur due to Earthquake on
Financial market.
Five day week daily data was sourced for both these series from
DataStream, starting from Ist
January 2009 to 15
th
June 2011.
Analysis and Results
To check volatility of the stock market
Standard deviation before earthquake is more as compare to afterearthquake indicates stock
market is more volatile before earthquake as given in Table 1.
To predict stock market,
Before Earthquake
Dependent Variable: LOG(BNZ50CAP)
Method: Least Squares
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Date: 10/20/11 Time: 11:19
Sample: 1/01/2009 2/24/2011
Included observations: 561
Variable Coefficient Std. Error t-Statistic Prob.
C 7.831009 0.022368 350.0963 0.0000
LOG(BNZBB90D) -0.201713 0.020175 -9.998095 0.0000
R-squared 0.151696 Mean dependent var 7.608461
Adjusted R-squared 0.150178 S.D. dependent var 0.056710
S.E. of regression 0.052279 Akaike info criterion -3.060892
Sum squared resid 1.527789 Schwarz criterion -3.045456
Log likelihood 860.5802 Hannan-Quinn criter. -3.054865
F-statistic 99.96191 Durbin-Watson stat 0.019081
Prob(F-statistic) 0.000000
After Earthquake
Dependent Variable: LOG(ANZ50CAP)Method: Least Squares
Date: 10/20/11 Time: 11:15
Sample (adjusted): 1/01/2009 4/21/2009
Included observations: 79 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 7.729971 0.080806 95.66138 0.0000
LOG(ANZBB90D) -0.058530 0.082248 -0.711627 0.4788
R-squared 0.006534 Mean dependent var 7.672484
Adjusted R-squared -0.006368 S.D. dependent var 0.016836
S.E. of regression 0.016889 Akaike info criterion -5.299276
Sum squared resid 0.021964 Schwarz criterion -5.239290
Log likelihood 211.3214 Hannan-Quinn criter. -5.275244
F-statistic 0.506413 Durbin-Watson stat 0.067920
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Prob(F-statistic) 0.478846
the above results for after earthquake p=0.4788, less volalite may be due
to sample size is
less as compare to before earthquake happen.
For predicting the stock market we compute regression model and least
square model, as
given below
Code= 732397.7- 9.512452 * F3NZS3L (before )
Code= 732397.9 - 6.777353* D2NZS2L
Code= 734250.8 - 0.013538 * D2NZS2L (after )
Code= 734250.6- 0.018287 * F3NZS3L
The constant value is approximately same and coefficient differ with a
small change value
indicate both the construction and material have equal effect on
predicting the stock market.
Conclusions
We know by our experience the stock market is always at risk, which is
true reflection of
economy too, one who invest has to take risk. Standard deviation before
earthquake is more
as compare to after earthquake indicates stock market is more volatile
before earthquake . if
we analyse for more number of observation for after earthquake we will
get similar result as
more volatile after earthquake too. We have tested the volatility using
GARCH model . We
have computed model using regression trend growth model results given
above taken each
variable Dow jones and FTSE seperately . second important part is to
predict the stock
8/3/2019 Sample Statistics Assignment
22/22
market, after earthquake or before earthquake happen at a particular city
Christchurch,
prediction due to earthquake in normal practice will be true only for a
small duration as we
know by experience. Stock market is volatile and its prediction using
models have been done
and in this case both the construction and material FTSE index and Dow
Jones index have
equal effect on predicting the stock market.
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