Economics 82400 Prof. Merih Uctum
Midterm
Spring 2007
Question I
1. Explain the difference between a difference stationary series and a trend stationary series. In your answer distinguish between random walk with and without drift.
2. How can you make each type of series stationary?
3. Suppose that you incorrectly assume that
i. a difference-stationary series is trend stationary,
ii. a trend-stationary series is difference stationary.
Suppose that based on your assumptions above, you proceed to make the series non-stationary using the appropriate transformation you discussed in part 2 above. Show that the resulting series are still non-stationary.
Question II
1. Consider an AR(1) process:
i. Find the transitory and the permanent components using the Beveridge-Nelson (BN) decomposition.
ii. Show that the permanent component’s effect on the process is higher, the longer is the memory.
iii. When the transitory component is measured by the BN decomposition, and the growth rate is AR(1), show that the transitory component is proportional to the growth rate in x.
2. Describe another decomposition method and explain the advantage and the disadvantage of each approach.
Question III
Suppose you estimate the following standard VAR
and .
1. Is this system stable?
2. What is a Cholesky decomposition and why is it used?
3. Calculate the impulse response functions for three periods on , of a unit change in , the structural innovation in the y equation, assuming . Interpret your findings.
Question IV
Suppose you want to test the purchasing power parity (PPP) between the US and the UK. This theory says that the price of the traded good should be the same when converted to the same currency: where E is the $ price of the UK pound, P and P* are the domestic and foreign prices, respectively.
1. You are applying the ADF test to test the PPP between the US and the UK. Explain the test (the definition, the null and the alternative hypotheses, which are appropriate for this question and the small sample properties compared with the Phillips-Perron test. If the test statistics takes the value of -2.93 do you reject the null hypothesis at the 5% level? What if the value is -2.67? Critical values are given in:
p is the order of time polynomial included in the regression.
2. Suppose you want to examine the short-run dynamics of the model with an ECM.
i. Explain briefly how you would proceed.
ii. What is the long-run equilibrium value? the long-run multiplier? the short-run multiplier?
Bonus Question
1. Suppose you are estimating a univariate model.
i. Sketch the steps you would follow to identify a model.
ii. Consider the following ARMA(2,2) model:
a. State the conditions needed for this model to be stationary and invertible.
b. Show whether the model is stationary.
c. Show whether the model is invertible.