Advanced Time Series Data Analysis

2Forecasting with Time Predictors

2.1 Introduction

Various models with the numerical time, t, or the time dummies as independent variables have been presented in Agung (2014, 2009a), Brooks (2008), Gujarati (2003), Wooldridge (2002), Hankle and Reitch (1992), and Wilson and Keating (1994), as well as the EViews User Guide. Now, referring to the forecast of a monthly time series, HS, presented in previous chapter, we have two additional time variables, namely YEAR and MONTH, which can be treated as additional numerical or ordinal variables in forecasting, as well as categorical variables. In general, for all monthly time series data, two time variables can easily be generated as the variables YEAR = @Year and MONTH = @Month, in addition to time t = @Trend, or t = (@Trend + 1). However, the functions @Year, @Month, and @Trend can in fact be used directly in presenting the equation specification (ES) of the corresponding models. See the following examples.

As the extension of all LVAR(p,q) models of HS previously presented, we can easily conduct the forecasting based on a lot of LVAR(p,q) models of HS on the numerical or categorical variables YEAR and MONTH, either a basic or common LVAR(p,q) model, or a special LVAR(p,q) model. Note that for q = 0, and p > 0, we would have various LV(p) models, and various AR(q) models for p = 0, and q > 0. However, this section presents only a few illustrative examples of LVAR(p,q) models.

2.2 Application of LV(p) Models of HS on MONTH by