Forecasting With The Theta Method

3The Multivariate ‐method

By Dimitrios D. Thomakos and Kostas I. Nikolopoulos

3.1 The Bivariate ‐method for the Unit Root DGP

In this chapter, we explore the extensions of the univariate ‐method to the case where we have more than one time series under study. One would not be amiss in thinking that the initial conceptual simplicity of the method will lend itself to a straightforward multivariate extension. It turns out that there are some useful implications to be discovered when dealing with the multivariate case. We explore these implications in what follows.

We start with the basics and the vector of time series . The properties of the individual series are yet left unspecified and we write the multivariate ‐line as in

(3.1)

where is the matrix of the ‐parameters and is the vector ...