Sample Statistics Assignment

8/3/2019 Sample Statistics Assignment

1/22

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.aspx


2/22

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


3/22

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


4/22

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


5/22


6/22

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


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



We compute multiple regression model for before earthquake and after

earthqauake

Dependent Variable: LOG(BNZ50CAP)


Date: 10/20/11 Time: 11:54

Sample: 1/01/2009 2/24/2011



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



S.E. of regression 8.72E-07 Akaike info criterion -25.06082

Sum squared resid 4.23E-10 Schwarz criterion -25.02995


7/22


F-statistic 7.90E+11 Durbin-Watson stat 0.080962


Dependent Variable: LOG(ANZ50CAP)


Date: 10/20/11 Time: 11:59

Sample: 2/25/2011 6/15/2011



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



S.E. of regression 8.10E-08 Akaike info criterion -29.77161

Sum squared resid 4.92E-13 Schwarz criterion -29.65164


F-statistic 1.12E+12 Durbin-Watson stat 0.224642


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:


8/22

Dependent Variable: WGT_RESID^2


Date: 10/21/11 Time: 17:26

Sample (adjusted): 1/05/2009 2/24/2011

Included observations: 559 after adjustments


C 0.971745 0.078471 12.38345 0.0000

WGT_RESID^2(-1) 0.005854 0.042369 0.138166 0.8902


Adjusted R-squared -0.001761 S.D. dependent var 1.574581


Sum squared resid 1383.404 Schwarz criterion 3.766664




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


Date: 10/21/11 Time: 17:48

Sample (adjusted): 3/01/2011 6/15/2011



C 1.152209 0.218417 5.275285 0.0000


9/22

WGT_RESID^2(-1) -0.072479 0.114913 -0.630728 0.5301








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.


10/22

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


11/22

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


12/22

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



13/22

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


S.E. of regression 0.144894 Akaike info criterion -3.133641



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


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


14/22

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





Durbin-Watson stat 1.923753

(c) regression model to predict stock market (before and after

earthquake)Dependent Variable: DLOG(BD2NZS2L)


Date: 10/20/11 Time: 15:05

Sample (adjusted): 1/02/2009 2/24/2011



C -0.023477 0.025782 -0.910575 0.3629

LOG(BF3NZS3L) 0.004853 0.005170 0.938724 0.3483








Dependent Variable: DLOG(AD2NZS2L)



15/22

Date: 10/20/11 Time: 15:01

Sample (adjusted): 2/28/2011 6/15/2011



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







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


16/22

-.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


Date: 10/20/11 Time: 15:24

Sample: 1/01/2009 2/24/2011


BCODE= C(1)+ C(2) *BD2NZS2L


C(1) 732397.9 55.83859 13116.34 0.0000

C(2) 6.777353 0.268168 25.27277 0.0000




Sum squared resid 13459489 Schwarz criterion 12.94592




17/22




Date: 10/20/11 Time: 15:29

Sample: 1/01/2009 2/24/2011


BCODE= C(1)+ C(2) *BF3NZS3L


C(1) 732397.7 55.83499 13117.18 0.0000

C(2) 9.512452 0.376294 25.27930 0.0000








After earthquake taken both the FTSE index and Dow Jones index as

independent variable



Date: 10/20/11 Time: 15:24

Sample: 1/01/2009 2/24/2011


BCODE= C(1)+ C(2) *BD2NZS2L


C(1) 732397.9 55.83859 13116.34 0.0000


18/22

C(2) 6.777353 0.268168 25.27277 0.0000R-squared 0.533277 Mean

dependent var 733799.4







Dependent Variable: ACODE


Date: 10/20/11 Time: 15:28

Sample: 2/25/2011 6/15/2011


ACODE=C(1)+C(2)*AD2NZS2L


C(1) 734250.8 142.5271 5151.658 0.0000

C(2) -0.013538 0.575791 -0.023512 0.9813








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


19/22

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)



20/22

Date: 10/20/11 Time: 11:19

Sample: 1/01/2009 2/24/2011



C 7.831009 0.022368 350.0963 0.0000

LOG(BNZBB90D) -0.201713 0.020175 -9.998095 0.0000








After Earthquake

Dependent Variable: LOG(ANZ50CAP)Method: Least Squares

Date: 10/20/11 Time: 11:15

Sample (adjusted): 1/01/2009 4/21/2009



C 7.729971 0.080806 95.66138 0.0000

LOG(ANZBB90D) -0.058530 0.082248 -0.711627 0.4788








21/22


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


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.

Refer: http://www.expertsmind.com/statistics-homework-assignment-help.aspx

Website: http://www.expertsmind.com/
http://www.expertsmind.com/statistics-homework-assignment-help.aspxhttp://www.expertsmind.com/http://www.expertsmind.com/statistics-homework-assignment-help.aspxhttp://www.expertsmind.com/

Sample Statistics Assignment

Documents

Transcript of Sample Statistics Assignment