Classical approach to time series

So far we have dealt with time series according to a classic approach to the topic. In this perspective, the classic models that try to simulate the phenomenon can be of two types:

• Composition models: The elementary components are known, and, by assuming a certain form of aggregation, the resulting series is obtained
• Decomposition models: From an observed series is hypothesized the existence of some elementary trends of which we want to establish the characteristics

The decomposition models are the most used in practice, and, for this reason, we will analyze them in detail.

The components of a time series can be aggregated according to different types of methods:

• Additive method: Y(t) = τ(t) + C(t) + S(t) + r(t)
• Multiplicative method: Y(t) = τ(t) * C(t) * S(t) * r(t)
• Mixed method: Y(t) = τ(t) * C(t) + S(t) * r(t)

In these...