Essays on Alternative Methods of Identification and Estimation of Vector Autoregressive Moving Average Models
George Athanasopoulos (Awarded PhD in February 2007)
Department of Econometrics and Business Statistics,Monash University, VIC 3800, Australia.
Abstract
This thesis is concerned with the identification, estimation and forecasting performance of vector autoregressive moving average (VARMA) models. The theoretical advantages in employing VARMA models over univariate autoregressive integrated moving average (ARIMA) models or the restrictive vector autoregressive (VAR) models, have been acknowledged by the statistical literature a long time ago. Despite this, the application of VARMA modelling in the field of applied macroeconomic research is at best very limited and arguably non-existent. The aim of this thesis is to provide to the literature further theoretical, experimental and most importantly practical motivation, for employing VARMA models.
The background information of Chapter (2) exposes the roots of the identification problem involved with VARMA modelling. Furthermore, the literature review of this chapter draws attention to methodologies that attempt to identify and estimate VARMA models. Finally the chapter reviews the role of VARMA models in other multivariate time series fields such as cointegration and causality.
Chapter (3) extends the Tiao and Tsay (1989) scalar component model (SCM) methodology and proposes a complete methodology for identifying and estimating canonical VARMA models. Monte-Carlo simulations verify that the proposed methodology performs well in identifying some pre-specified VARMA processes. Two examples demonstrate the practical application of the proposed methodology. The first example highlights the improved within sample fit of the canonical VARMA model specified by the proposed methodology when compared to VARMA models identified by previous studies, although requiring less number of parameters to be estimated. The second example illustrates the competitive out-of-sample forecasting performance of the identified VARMA model over a VAR model selected by AIC.
In an extensive forecasting exercise, Chapter (4) evaluates the performance of the VARMA model when forecasting macroeconomic variables, versus the forecasting performance of arguably the most popular multivariate macro-econometric model, the VAR. The results highlight the superior forecasting performance of the VARMA models over all forecast horizons considered, and for all forecast error measures.
Chapter (5) considers the specification of canonical Echelon form VARMA models, as an alternative modelling procedure to the SCM methodology. On a theoretical level, the SCM methodology is shown to be more flexible in specifying separate orders for the autoregressive and the moving average components of the VARMA(p,q) model. This advantage is reflected in the Monte-Carlo simulations where both methodologies perform well in identifying the Kronecker indices of some pre-specified VARMA processes, however, the SCM methodology returns that extra information. On a practical level, the out-of-sample forecast results indicate that the SCMs outperform the Echelon form models, in forecasting macroeconomic variables.
Chapter (6) studies models that contain both short-run restrictions, as studied by the literature on serial correlation common features (SCCFs), and long-run restrictions, as studied by the literature on cointegration. A new estimation algorithm, where short-run and long-run restrictions interact to estimate the cointegrating and the cofeature spaces, is proposed. The results from this chapter are threefold. Firstly the proposed algorithm performs well in estimating both the short-run and long-run coefficients. Secondly, the traditional model selection criteria that ignore SCCFs, frequently select under-parameterised models, therefore modified model selection criteria that simultaneously select lag length and rank order should be employed. Finally, the rank reduced vector error correction models (VECMs) selected by the modified criteria, outperform the unrestricted VECMs in out-of-sample forecasting with improvements in forecast accuracy being substantial in many cases.