Non-stationarity, forecast performance and fluctuations in macroeconomic series: Experience with United States seasonal data and simulations

Abstract

An important issue in macroeconomic modelling using times series data centers around the question of whether the observed series is generated by a stationary or a non-stationary process. Recent research has shown that there is a seasonal cycle in the US economy that closely mirrors business cycles (Barsky and Miron, 1989). It is thus important to apply the seasonal unit root tests to investigate the question of seasonal non-stationarity in the data generating process (DGP) and examine the properties of such series. This dissertation undertakes such an exercise using seasonally unadjusted US data.

The thesis examines four interrelated questions which have frequently been examined independently. The questions are: (i) Is there a seasonal cycle in the US economy? (ii) Are the macroeconomic series seasonally non-stationary? (iii) Does non-stationarity affect forecast performance? An finally, (iv) How the presence of substantial moving average (MA) component in the DGP interferes with the outcome of the test for non-stationarity?

The thrust of research is empirical and centers around the degree of differencing needed to induce stationarity, within the Box-Jenkins ARIMA framework. Models with various degrees of differencing are fitted through the AIC and SBC criterion. In addition, various tests for seasonal and regular unit roots are applied, and the properties of these tests are investigated in the context of the fitted models. The tests for unit roots at seasonal frequencies are performed by using all the four major approaches proposed by Dickey, Hasza and Fuller (1984), Hasza and Fuller (1982), Osborn, Chui, Smith and Birchenhall (1988) and Hylleberg, Engle, Granger and Yoo (1990).

Forecast performance of the fitted models is investigated, and statistical comparisons made. These are related to the structures of the fitted models and to the outcomes of the unit root tests. If non-stationarity is present in the series then this framework also enables us to assess the value of the test in the conduct of a forecasting exercise. It is generally agreed that most economic time series contains substantial MA component in the DGP. Recent research shows that the power of the unit root test for annual data is significantly affected by such MA components. This thesis performs some simulation exercises using seasonal data to examine the properties of the unit root test under such situations.