Time series models

In the previous sections, we explored the basics behind time series. To perform correct predictions of future events based on what happened in the past, it is necessary to construct an appropriate numerical simulation model. Choosing an appropriate model is extremely important as it reflects the underlying structure of the series. In practice, two types of models are available: linear or non-linear (depending on whether the current value of the series is a linear or non-linear function of past observations).

The following are the most widely used models for forecasting time series data:

• AR
• MA
• ARMA
• ARIMA

Autoregressive models

AR models are a very useful tool to tackle the prediction problem in relation to a time series. A strong correlation between consecutive values of a series is often observed. In this case, we speak of autocorrelation of the first order when we consider adjacent values, of the second order if we refer to the relation between the values of the series after...