Advanced Time Series Data Analysis

6Forecasting Quarterly Time Series

6.1 Introduction

I have found that all forecast models for the monthly time series, presented in the five previous chapters, can be used for the quarterly time series by replacing the time variable @Month = M with @Quarter = Q for all relevant models. For this reason, this chapter only presents selected illustrative examples. Referring to all possible models based on a single time series Y_t, bivariate time series (X_t,Y_t) or (Y1_t,Y2_t), and triple time series (X1_t,X2_t,Y_t) or (Y1_t,Y2_t,Y3_t,), which have been presented in Chapters 1–5 with a summary of alternative trends presented in Table 4.1, then based on a quarterly time series we have the summary of alternative trends as presented in Table 6.1.

Table 6.1 Forecast models with specific trends for all models based on a single quarterly time series, bivariate, and triple time series.

Continuous Regressions with Trend
Additional Time IV to insert	Forecast Model (FM) with
1. @Trend	Linear Trend
2. @Trend ^ 2 @trend	Quadratic Trend
3. @Trend ^ 3 @Trend ^ 2 @Trend	Cubic Trend
4. log(@Trend + 1) = log(t)	Logarithmic Trend
5. Exp(rt)	Exponential Trend, for a fixed selected r
Regressions with Heterogeneous Trends by @Year
6. aQ*@Expand(@Year) @Expand(@Year,@Droplast)
7. aQ*@Expand(@Year) aQ ^ 2*@Expand(@Year) @Expand(@Year,@Droplast)
8. aQ*@Expand(@Year) aQ ^ 2*@Expand(@Year)  Q ^ 3 a @Expand(@Year) @Expand(@Year,@Droplast)
Regressions with Heterogeneous Trends by ...