Advanced Time Series Data Analysis

5Forecasting Based On (X1_t,X2_t,Y_t)

5.1 Introduction

As the extension of all forecast models presented in previous chapters, especially the models based on the bivariate time series (X_t,Y_t) presented in Chapter 4, this chapter presents various models based on trivariate or triple time series (X1_t,X2_t,Y_t), and/or (Y1_t,Y2_t,Y3_t). However, I will start with various translog linear models as the extension of those presented in Section 4.7. The examples will be presented based on the GARCH.wf1. In order to be general, I select X1 = IP, X2 = PW, Y1 = FSPCOM, and Y2 = FSDXP.

5.2 Translog Linear Models Based on (X1,X2,Y1)

5.2.1 Basic Translog Linear Model

Based on the trivariate time series (X1_t,X2_t,Y1_t), I propose the following equation specifications (ESs) to present three basic translog linear LV(1) models, which are in fact the Cobb–Douglass production functions. Note that the models are additive models. However, I would recommend applying the first model, since we can be very confident that log(Y1(−1)), log(X(−1)), and log(X2(−1) are the cause, source, or upstream factors for Y1. These LV(1) models could easily be extended to LVARMA(p,q,r) models of Y1 for various p > 0, q ≥ 0, and r ≥ 0. Refer to Subsection 3.2.1 for illustrative examples. By using the log(Y1) as a dependent variable, we can forecast either Y1 or log(Y1).

(5.1)

(5.2)

(5.3)

In addition, to compute the predicted ...