Forecasting With The Theta Method

2From the ‐method to a ‐model

By Dimitrios D. Thomakos and Kostas I. Nikolopoulos

2.1 Stochastic and Deterministic Trends and their DGPs

In our analysis of the properties of the ‐method, we focus on the general “signal + noise” model, whereas the original time series¹ is decomposed into a “trend” or “signal” or a slowly varying component denoted by and a “noise” or “error” or “residual” component denoted by . This class of models is very broad and allows for great flexibility in specifying various data‐generating processes (DGPs) on it. Therefore, we start with the following representation:

(2.1)

The particular context of analysis will shape the form that the trend/signal component will take and whether we would be interested in accurately extracting this component or just using a particular ...