Introduction to the analysis of time series
General definitions, graphic representations
The unobservable components of a time series: the trend, the cycle, the seasonal component, the erratic component.
- Classic analysis of historical series
The additive model and the multiplicative model; the determination of the trend: the analytical method and the method of moving averages
Destagionalization of a time series
- Modern analysis of the time series: stochastic processes and ARIMA models
Stochastic processes; realization of stochastic processes and historical time series; stationary and invertible stochastic processes; Wold's theorem; ergodic processes.
The AR, MA and ARMA processes; the functions of global and partial autocorrelation; conditions of stationarity and invertibility; non-stationary processes; the ARIMA and SARIMA processes.
- The Box and Jenkins proceedings
- Forecasting and forecasting with the ARIMA models
The forecasts in general and those deriving from the analysis of phenomena in historical series. Evaluation of forecasts;