Time Series 1

Objectifs

Know the main linear models used and their characteristics.
Estimate model parameters and test their validity.
Recognize the main characteristics of a time series using the usual graphical tools.
Conduct a complete statistical process: find suitable models, check their validity for the data and forecast future values.

Plan

Trend, seasonality and linear filtering.
Stationary processes, autocovariance, autocorrelation.
ARMA processes, causality, invertibility, innovation, estimation.
Box-Jenkins method, non-stationary (S)ARIMA processes, unit root test.
Forecasting: best linear predictor, exponential smoothing.
Exogenous contributions, ARMAX processes and cross-correlation. Heteroskedasticity and (G)ARCH processes.

Prérequis

Probability and inferential statistics