2From the images‐method to a images‐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 images‐method, we focus on the general “signal + noise” model, whereas the original time series1 images is decomposed into a “trend” or “signal” or a slowly varying component denoted by images and a “noise” or “error” or “residual” component denoted by images. 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:


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 ...

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