## (solution) CASE STUDY TWO - continued Returning to the Case Study Two, you

CASE STUDY TWO - continued Returning to the Case Study Two, you will investigate if there have been any significant changes in the market models. To do this, you should first generate some dummy variables.  The first additive dummy variable, DA1, should equal zero up until November, 2007, one between December 2007 and June 2009, and zero from July 2009 onwards.  This period corresponds to when the GFC and the Great Recessions is considered to have officially begun, and when the NBER declared that the GFC and the Great Recession had ended. The second additive dummy variable, DA2, should equal zero up until November, 2007, and then one from December 2007 onwards.  This period corresponds to the onset and continuance of the GFC and the Great Recession, according to commentators like Robert J. Gordon and John B. Taylor. The first event dummy variable, DE1, should have a value of zero, except for September 2008, when it will have the value of one, and zero elsewhere.  This corresponds to the month when the US Government allowed Lehman Brothers, an Investment Bank, to go bankrupt. The second event dummy variable, DE2 should have a value of zero, except for June 2009, when it will have the value of one, and zero elsewhere.  This corresponds to when the US Government officially declared that the GFC and the Great Recession had ?ended?.

Estimate a market model for the entirety of the sample period.  Include only the additive dummy variable DA1, and the event dummy, DE1.  What do you conclude?       (3 marks)

Now estimate a second market model for the entirety of the sample period, but this time include only DA2 and DE2.  What do you conclude?                         (3 marks)

(c) Test to see if the models estimated in parts (a) and (b) contain any first-order autocorrelation. If they do, correct for it by including the appropriate number of ARMA terms.

(2 marks)

(d) Using the appropriate t and F-tests, see if there are any differences in the models, as a result of the GFC and the Great Recession.                                 (2 marks)

(e) Using your answers to the above questions, and the notes from the previous tutorials, briefly discuss whether the GFC and the Great Recession had any effect on the performance of Apple?s share price (Do this in a couple of paragraphs).                                      (2 marks)

RMIT Assignment 3

Basic Econometrics Group:

Daniel Reaper - s3545463

Jackson Kurz - s3544185

Tutor: Rami Osman, rami.osman@rmit.edu.au

Tutorial: Wednesday, 17:30 ? 18:30, 080.10.011 Faculty of Business Assignment 1 SCHOOL OF ECONOMICS, FINANCE &amp; MARKETING

ECON 1066 - BASIC ECONOMETRICS

SUBMISSION DATE - October 10th, 2016

___________________________________________________________________

CASE STUDY ONE - continued

Consider the model you fitted in Assignment Two, Case Study One, part (b).

(a) Test to see if the errors are auto correlated. If autocorrelation is present, suggest possible reasons why. Try to correct it by including the appropriate number of autoregressive moving average (ARMA) terms. Use the critical Durbin-Watson values at the 5 per cent

level of significance from the following website:

http://web.stanford.edu/~clint/bench/dw05b.htm (3 marks) We are testing whether the errors are serially correlated in this model: Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 1 Assignment 1 H 0 : ?=0

H1: ? ? 0 - ? =0.05, n=128, k =2, DW L=1.69568, DW U =1.72714

Since 0.2565 is between 0 and DW L =1.69568 , we reject the null and assume that there is some positive serial correlation.

We can correct for autocorrelation by including the ARMA model (Auto-regressive model,

moving average model). Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 2 Assignment 1 As we can see above, since the residuals are exponentially decreasing, we can use an AR term

at level 1 (AR (1)). Since the DW stat does not

AR(3), 125 5 Durbin table. However, it should be noted that since the model is very insignificant, the ARMA model may

make the model appear significant when it may not be, especially if the autocorrelation is not

pure.

(b) Test to see if the errors are heteroscedastic. If it is present, obtain an improved set of estimates for the t-statistics.

- (2 marks) We can conduct a heteroscedastic test using the white test: As 0.0121&lt;0.05, we can conclude that the errors are heteroscedastic, and that the standard

errors are incorrect. Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 3 Assignment 1 Corrected white stats: (c) Test to see if the errors are normally distributed. Based on the results of the three tests you have carried out, how reliable do you think the estimation and test statistics are? (2

marks)

- H 0 : P&gt; 0.05 , Normal errors H 1 : P&lt;0.05 , Abnormal errors Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 4 Assignment 1 - As P = 0.389, the errors are normally distributed and we do not reject H0 . (d) Now estimate a new Multiple Regression Model that uses all of the variables, as well as your original PREDICTOR variable, but excludes the ARMA terms. That is

st 0 1mt 2 PREDICTOR t 3 yt 4 y*t 5it 6it* ut (2 marks) - (e) Identify the coefficients with large p-values. Eliminate the variable with the largest p- value, and re-estimate the new equation. Repeat this procedure until the only variables

left in the model have coefficients for which the p-value is less than = 0.05. Show the

output for this final model (This is called the ?top-down? approach).

(3 marks) - The New Zealand interest rate (nz_ir) has the highest p-value Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 5 Assignment 1 - Afterwards, the Australian Interest rate has a high p-value, so we remove it. The final form: (f) Use the F-test for redundant variables to determine whether the joint impact of all the variables that you have excluded is significant. (2 marks) So we are testing if this model has:

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 6 Assignment 1 - Null hypothesis: Beta nz-ir = beta aust-ir = 0 - Alternative hypothesis: at least one is not = 0 We can see here: Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 7 Assignment 1 (g) Based on the results of part (f), and any other tests you think are necessary, choose a model you think contains all the relevant variables.

- (1 marks) So we have to test again and again until we are free of correlation and test for

homoscedasticity then test for normal errors, this will leave us with a final model. (h) Obtain a set of (static) forecasts (that excludes the ARMA terms) for the Australian dollar exchange rate. Asses the quality of your forecasts using the various error measures

generated internally by EViews, when you made your forecasts. Write a brief report

discussing your results. You should comment on the reliability of your estimation and test

procedures, the variables that are most important in explaining the exchange rate, and

how well your model predicts the exchange rate. (3 marks) - Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 8 Assignment 1 CASE STUDY TWO - continued

Returning to the Case Study Two, you will investigate if there have been any significant

changes in the market models. To do this, you should first generate some dummy variables.

The first additive dummy variable, DA1, should equal zero up until November, 2007, one

between December 2007 and June 2009, and zero from July 2009 onwards. This period

corresponds to when the GFC and the Great Recessions is considered to have officially

begun, and when the NBER declared that the GFC and the Great Recession had ended.

The second additive dummy variable, DA2, should equal zero up until November, 2007, and

then one from December 2007 onwards. This period corresponds to the onset and continuance of the GFC and the Great Recession, according to commentators like Robert J.

Gordon and John B. Taylor.

The first event dummy variable, DE1, should have a value of zero, except for September

2008, when it will have the value of one, and zero elsewhere. This corresponds to the month

when the US Government allowed Lehman Brothers, an Investment Bank, to go bankrupt.

The second event dummy variable, DE2 should have a value of zero, except for June 2009,

when it will have the value of one, and zero elsewhere. This corresponds to when the US

Government officially declared that the GFC and the Great Recession had ?ended?. (a) Estimate a market model for the entirety of the sample period. Include only the additive dummy variable DA1, and the event dummy, DE1. What do you conclude? (3 marks) (b) Now estimate a second market model for the entirety of the sample period, but this time include only DA2 and DE2. What do you conclude? (3 marks) Bachelor of Business

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 9 Assignment 1 (c) Test to see if the models estimated in parts (a) and (b) contain any first-order

autocorrelation. If they do, correct for it by including the appropriate number of ARMA

terms.

(2 marks)

(d) Using the appropriate t and F-tests, see if there are any differences in the models, as a

result of the GFC and the Great Recession. (2 marks) - (e) Using your answers to the above questions, and the notes from the previous tutorials,

briefly discuss whether the GFC and the Great Recession had any effect on the

performance of Apple?s share price (Do this in a couple of paragraphs).

(2 marks)

RMIT Economics, Finance &amp; Marketing

ECON1066 Basic Econometrics 10

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