Theoretical Examination of Time Series Models

The theoretical examination of time series models considers the computation of theoretical properties and their interpretation. These results will allow us to develop different methods for modelling and understanding time series. 

For the analysis of time series models, two concepts need to be introduced causality and invertibility. A process is said to be causal, if and only if, the current value of the process can be determined solely using past or current values of the process. This means that no unavailable, future values of the process are required. A process is said to be causal if and only if all roots of the denominator (i.e. the A-polynomials) lie inside the unit circle in the complex domain, that is, z 1. Under such circumstances, a causal process is also stationary. Furthermore, for a causal process, the infinite-order moving-average model will converge to a finite value. 

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