Threshold Vector ARMA Forecasts under General Loss Functions

In linear time series analysis point forecasts are based on the minimization of a square loss function which allows to obtain the conditional expectation as optimal predictor. When the data generating process is nonlinear, the forecaster should use general loss functions that are able to take into account some features of the underlying process. The introduction of “general loss functions” has been widely investigated in univariate time series domain (see among the others Christoffersen and Diebold (1996, 1997), Granger (1999), Patton and Timmermann (2007a, 2007b, 2010)) whereas, in our knowledge, in multivariate domain the use of this kind of functions has been only marginally explored in Alp and Demetrescu (2010) and Komunjer and Owyang (2010). Starting from these results, in our contribution we present a new class of multivariate nonlinear time series models called Threshold Vector ARMA (TVARMA) that generalizes the Threshold ARMA model proposed in Tong (1983). After the presentation of some properties of the TVARMA model, we propose the use of asymmetric loss functions to generate forecasts. In more detail we show that these functions are able to catch some features of the model that are completely neglected by square loss functions