Some Advances in Restricted Forecasting Theory for Multiple Time Series

Abstract

When forecasting time series variables, it is usual to use only the information provided by past observations to foresee potential future developments. However, if available, additional information should be taken into account to get the forecast. For example, let us consider a case where the Government announces an economic target for next year. Since the Government has the empowerment to implement the economic or social policies to approach the target, an analyst that does not consider this information to get the forecast and makes use only of the historical record of the variables, will not anticipate the change on the economic system. In fact, if predictions based on historical data would be invalid when a policy change affects the economy, the economic agents are forward rather than backward-looking and adapt their expectations and behavior to the new policy stance. Thus, given some targets for the variables under study it is important to know the simultaneous future path that will lead to achieving those targets. Here it is considered the case in which a system of variables are to be forecasted with the aid of a VAR model with a cointegration relationship. The paths projected forward into the future as a combination of the model-based forecasts and the additional information provides what is known as a restricted forecast.<br/>This work is an attempt to contribute to the literature on Restricted Forecasting Theory for Multiple Time Series within the VAR framework. Specifically, Chapter 2 decomposes the JCT into single tests by a variance-covariance matrix associated with the restrictions and derives the formulas of a feasible JCT that accounts for estimated parameters. Chapter 3 develops, by Lagrangian optimization, the restricted forecasts of the multiple time series process with structural change, as well as its mean squared error. In addition, the univariate time series types of changes are considered here in a multivariate setting. Finally, Chapter 4 derives a methodology for forecasting multivariate time series that satisfy a contemporaneous binding constraint for which there exists a future target. A Monte Carlo study of a VEC model with one unit root shows that, for a forecast horizon large enough, the forecasts obtained with the proposed methodology are more efficient. A more detailed account of these contributions is provided below.