Your report should provide concise and relevant answers to all questions with questio numbers, e.g. Q1 i) your answer, ii) your answer, and etc. The computer outputs should be attached as an appendix to your report or copy and pasted to the main report.
In conducting statistical tests throughout, clearly state all relevant information, such as the null and alternative hypotheses, the distribution you use, the level of significance, and the decision rule (critical value or p-value), and the decision you make. Graphs and Tables should be self-explanatory, i.e. have titles and properly labeled axes.
Your report may be typed or clearly hand-written on A4 pages, double-spaced (unclear handwriting may be unintentionally disadvantaged). Your report should not exceed 6 A4 Pages (excluding the appendix). You may shrink the size of graphs and tables but they should be legible. Note that “explain” or “discuss” type questions require concise and to-the-point answers (about 1/2 A4 double-spaced page maximum).
Q1. The file data2a.xls contains monthly time observations for the stock price (P) and output (Y), from January 1976 to June 2013. The total number of observations is 558. Using data2.xls, we perform tests for unit root and cointegration.
i) Generate two new variables, log of stock price, log(Pt), and log of production, log(Yt). Draw line plots for the time series variables, log(Pt) and log(Yt) separately.
ii) Perform Augmented Dickey-Fuller (ADF) test for log(Pt):
– with three lagged changes and intercept
– with three lagged changes, intercept and trend and interpret the result.
iii) Repeat (ii) for log(Yt).
iv) Run the following simple regression,
log(Pt) = ß0 + ß1log(Yt) + ut
and discuss the result in relation with (ii) and (iii).
v) Use the residuals from the regression in (iv) to test whether log(Pt) and log(Yt) are cointegrated. Use the ADF with two lags and intercept. What do you conclude?
vi) Run the following simple regression with a linear time trend t,
log(Pt) = ß0 + ß1log(Yt) + ß2t +ut
and test for cointegration using the same tests from (v). What do you conclude?
Q2. The file data2b.xls contains quarterly time observations for the price (P) and the money supply (M), from January 1961:1 to 2005:4. The total number of observations is 180. Using
data2b.xls, we perform tests for unit root and cointegration.
i) Draw line plots for the price (ΔPt) and the first difference of the price (ΔPt) over time. Perform the ADF test for the price (Pt) and the first difference of the price (ΔPt) with intercept. (Choose the automatic selection option for the lag length of the augmented term based on the Schwarz Information Criterion.) Interpret the results.
ii) Repeat (i) for the money supply (Mt) and the first difference of the money supply (ΔMt).
iii) Run the following regression model
Pt = ß0 + ß1Mt + ut
and report the estimation result.
iv) Test for cointegration in regression (residual based approach cointegration test) using the regression model in (iii). Clearly state the hull and alternative hypotheses and explain the result. (Use 5% significance level) Are they cointegrated?
v) Estimate the ECM using the cointegrating residuals, explain the results and discuss short run dynamics.