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ECON7350: Applied Econometrics for Macroeconomics and Finance

Tutorial 5: Trends and Cycles

At the end of this tutorial you should be able to:

❼ construct an adequate set of ADF specifications for unit root testing;

❼ carry out ADF tests for a unit root and interpret the results;

❼ construct an adequate set of general ARIMA(p,d,q) models.

Problems

The specification for a general ARIMA(p,d,q) model is

p                                   q

∆dyt  = δt +工 aj ∆dyt −j  +工 bj ϵt + ϵt ,

j=1                              j=1

where δt  is a general deterministic term.

❼ If the process has no deterministic terms, then δt  = 0.

❼ If the process includes a constant only, then δt  = a0 .

❼ If there is a constant and a trend, then δt  = a0 + δt.

The file usdata .csv contains 209 observations on:

❼ yt  ≡ log real per capita GDP (GDP); and

❼ rt  ≡ the overnight Federal Funds Rate for the US (FFR).

1. For yt :

(a) Plot the observed time series and comment on potential trends.

(b) Construct an adequate set of ADF regression models.

(c) Implement the ADF test for a stochastic trend and draw inference regarding the integration properties of yt .

(d) Repeat parts (a)-(c) for the differenced series ∆yt .

(e) Interpret the overall findings in parts (c) and (d).

(f) Construct an adequate set of ARIMA(p,d,q) models using information criteria and residuals analysis.

2. Repeat parts (a)-(e) of Question 1 for rt  (you do not need to do part (f)).