Introduction to Time Series Econometrics (ECM3ITE).

Assignment 2

This project is worth 30% of the total mark and should be handed in to me by 10am (in the

lecture) on Thursday, May 14th. Late submission will not be accepted and no extensions

will be given.

This is a project where students should solve the questions independently. I am not allowed to

help you on any aspect of the assignment, and I will not answer any questions directly related

to the assignment, unless they are related to clarification of the content.

Students can discuss the content of the project with their peers. However, the work on Eviews

and report writing should be done individually and independently. Any form of plagiarism

will be penalized according to the University policy.

Your report should provide concise and relevant answers to all questions with question

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 (Pt) and the first difference of the price (?Pt) over time.

Perform the ADF test for the price (Pt) and the first difference of the price (?Pt) 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 (?Mt).

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.