Econometric Principles and Data Analysis - Lagged Dependent Variables and Autocorrelation - Econometric Assignment Help

Assignment Task

Econometric Principles and Data Analysis -  Lagged Dependent Variables and Autocorrelation - Econometric Assignment Help

1) a) Explain carefully in words what is meant by the first-order autocorrelation.
    b) Draw diagrams to illustrate (i) positive autocorrelation and  (ii) negative autocorrelation.
    c) What are the consequences of autocorrelation for the OLS estimator of regression coefficients?
2) For each of the following statements, state whether it is true or false and explain briefly why.
a) Using the runs test, a large number of runs suggests positive autocorrelation.
b) The Durbin–Watson d test assumes an AR(1) autoregressive scheme and the lagged value of the dependent variable is not a regressor.
c) If the error term is autocorrelated, conventional t and F tests are misleading.
3) The text file M430_U6_Q3.txt contains the data used in the Example in Section 6.3. You have used this data in Unit 1 and Unit 2. Replicate the results in Section 6.3.
4) In the text file M430_U6_Q4.txt, you will find monthly data on the spot exchange rate (S) between the US dollar and sterling and the one-month ahead forward exchange rate (F), from January 1982 to January 2012, expressed as dollars per pound. The source is www.bankofengland.co.uk  (Bank of England, nd accessed July 2019). You used this data in Unit 1 and Unit 3.
 b) Plot the residuals over time, and comment on the plot.
c) Obtain a scatter plot of the residual in period t against the residual in period t − 1. Comment on the scatter plot.
d) Obtain the autocorrelation function of the residuals, up to lag length 12, and comment on the graph.
e) Use the Durbin–Watson statistic to test the hypothesis that the disturbances in the regression equation in part a) are not autocorrelated.
f) Use the LM test to test the hypothesis that the disturbances in the regression equation in part a) are not autocorrelated.
5)  A disturbance associated with one observation is influenced by a disturbance associated with the immediately preceding observation. A first-order autoregressive scheme, AR(1), can be written as 1 11 t t t uuv ρρ − =+− ≤ ≤  in which ρ is the first-order autoregressive parameter; ut, ut-1, and vt are disturbances; and vt has all of the desirable properties (zero mean, homoscedastic, non-autocorrelated).
b) For example for (i) positive autocorrelation see Gujarati and Porter Figure 10.2(a) p 316, Figure 10.3 p 318 and 10.4 p 320; for (ii) negative autocorrelation see Figure 10.2(b) on p 316 of Gujarati and Porter’s textbook.
c) The OLS estimator is unbiased and consistent but not efficient.
6) The analysis and discussion are presented in Example in Section 6.

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