# WORD ```Economics 674
Fall 2006
Project 3
(Due: Friday, December 1)
Let πt denote the inflation rate in period t. In the following problems, use the same inflation rate
data you used in Projects 1 and 2 and the sample period 1960:I-2006:I. Report all pertinent results
and accompany results with clear explanations and discussion.
1. Base Model
Fit the inflation rate to an AR(p) model, where p is selected by applying the AIC with
pmax = 4.
2. Test for Structural Change with an Unknown Breakpoint
Test whether the parameters of the AR(p) model are constant over time by computing
Quandt’s Likelihood Ratio (QLR) statistic and comparing it to the appropriate limiting
distribution provided in Andrews (1993). (Set r min = 0.1and rmax=0.9.)
3. Fit the Inflation Rate to a Threshold Model
Fit πt to a two-regime self-exciting threshold model, assuming that the threshold is equal
to the inflation rate’s sample mean. (Use the same p you selected for the base model.
Choose the delay parameter, d, to minimize the SSR.)
4. Testing for ARCH Effects
Apply Engle’s LM test to the residuals from the AR(p) model you fit in (1) to test the null
hypothesis that the inflation rate is homoskedastic. (Choose the order of the AR
regression for the squared residuals by applying the AIC with a maximum lag length of
4.)
5. Testing for a Unit Root
Apply the ADF test to test the null hypothesis that there is a unit root in the inflation rate
under each of the following assumptions:
i.
ii.
Under H0, the inflation rate is an I(1) process without drift. Under HA, the
inflation rate is I(0) without any restriction on its mean.
Under H0, the inflation rate is an I(1) process with drift. Under HA, the
inflation rate is trend stationary.
Use the same p you selected in (1).
6.
Cointegration
Let it denote the nominal interest rate in period t. Using the same interest rate data you
used in Projects 1 and 2 and use the sample period 1960:I-2006:I .
Assume that πt and it are I(1) processes.
i.
ii.
Test the null hypothesis that that the real interest rate is I(1), with no drift,
applying the ADF test. Select the lag length for the ADF regression by
applying the AIC with pmax = 4.
Test the null hypothesis that πt and it are cointegrated by applying the EngleGranger residual-based ADF test using a lag length of four in the secondstage regression.
```