Advanced Time Series Data Analysis

4Forecasting Based on (X_t,Y_t)

4.1 Introduction

As the extension of all forecast models presented in previous chapters, this chapter presents various models based on bivariate time series (X_t,Y_t). It is well‐known that the Y(−1) is one of the best predictor for any time series Y, in addition to a cause (exogenous, upstream, or source) factor or variable X. So the simplest model Y considered should use possible independent variables X or X(−1), and Y(−1) with the following alternative form of forecast models. Note that these models can be considered to be the modifications of all cross‐section GLMs (General Linear Models) based on a bivariate time series (X_i,Y_i) presented in Agung (2011a).

4.2 Forecast Models Based on (X_t,Y_t)

Figure 4.1 presents the graphs of three alternative simple relationships or up‐and‐down relationships between the variables X or X(−1), Y, and Y(−1). Based on these graphs, referring to the two‐way interaction model (3.1) with its possible reduced models, I propose the basic full models as follows:

1. Based on the graph in Figure 4.1a, the simplest LV(1) two‐way interaction full model can be presented using the following equation specification.
   (4.1)
2. Based on the graph in Figure 4.1b, the simplest LV(1) two‐way interaction full model can be presented using the following equation specification.
   (4.2)
3. The graph in Figure 4.1c is presented to forecast beyond ...