QUESTION 1 (25 MARKS)
a) What is the difference between time-series and cross-sectional data?
[5]
b) Explain the purpose of the following diagnostic tests, and also state their hypotheses
and decision rules
1. Normality
[3]
ll. Autocorrelation
[3]
lll. Heteroscedasticity
[3]
IV. Ramsey RESET
[3]
V. CUSUM
[3]
c) Given the following unrestricted OLS regression equation
Yt = B0 + B1Xu + B2Xu + B3X3t + B4X4t + B5Xst + et
1. State the hypothesis and decision rule used to test whether X2, X3 and X4 are
redundant variables.
[4]
11. If the variables in question c) i. are redundant, how would the adjusted
coefficient of determination be affected?
[1]
QUESTION 2 (25 MARKS)
a) What properties of time series data would make Ordinary Least Squares (OLS) results
spurious?
[2]
b) State the four characteristics of the spurious OLS regression equation. [4]
c) Why should one conduct the unit-roots tests?
[4]
d) State the Augmented Dickey-Fuller (ADF) and Phillips Peron equations used to test for
unit roots.
[10]
e) Fully interpret the unit root test results for the Exports (EXP) variable in Tables 1-4
below.
[5]
Table 1
Null Hypothesis: EXP has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=7)
Augmented Dickey-Fuller test statistic
Test critical values:
1% level
5% level
10% level
*MacKinnon (1996) one-sided p-values.
~-Statistic
-1.277610
-3.679322
-2.967767
-2.622989
Prob.*
0.6261
Table 2
Null Hypothesis: EXP has a unit root
Exogenous: Constant, Linear Trend
lag Length: 1 (Automatic - based on SIC, maxlag=7)
I
I
!Augmented Dickey-Fuller test statistic
[est critical values:
11% level
I
~-Statistic
-1.271960
-4.309824
Prob.*
0.8750
2