# 5Forecasting Based On (X1t,X2t,Yt)

## 5.1 Introduction

As the extension of all forecast models presented in previous chapters, especially the models based on the bivariate time series (Xt,Yt) presented in Chapter 4, this chapter presents various models based on trivariate or triple time series (X1t,X2t,Yt), and/or (Y1t,Y2t,Y3t). 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 (X1t,X2t,Y1t), 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) In addition, to compute the predicted ...

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