Advanced Time Series Data Analysis

7Forecasting Based on Time Series by States

7.1 Introduction

In this chapter, the panel data considered is unstacked panel data, namely the annual time series by states, where the units of the analysis are the time observations. So that the sets or multidimensional of endogenous, exogenous, and environmental variables, respectively, for the state i can be presented using the symbols Y_i_t = (Y1_i,…,Yg_{_i},…)_t, X_i_t = (X1_i,…,Xk_i,…)_t, and Z_t = (Z1,…,Zm,…)_t for i = 1,…,N; and t = 1,…,T. Note that the scores of the environmental variables are constant for all states or individuals. Using these symbols, the panel data is considered the data of multivariate time series by states (countries, regions, agencies, firms, industries, households, or individuals).

Agung (2014) has presented various models, such as the VAR and System Equation Models (or SCM = Seemingly Causal Models) based on unstacked panel data with a small number of N. Referring to the multiple OLS regression analyses presented in previous chapters, then all data analyses using the VAR and SCM models presented in Agung (2014), can be reanalyzed using sets of equation specifications in order to compute the in‐sample forecast values of each of their dependent variables. Do these as exercises. However, this chapter presents alternative models as their modifications or extended time series models.

However, for panel data with a large number of firms, the time series models can be applied by a few selected firms or by means of ...