6 - Time Series Models

Summary

Common time series models allow for a correlation between observations that is likely to be largest for points that are close together in time. Adjustments can be made, also, for seasonal effects. Variation in a single spatial dimension may have characteristics akin to those of time series, and comparable models find application there. Autoregressive models, which make good intuitive sense and are simple to describe, are the starting point for discussion; then moving on to autoregressive moving average with possible differencing. The "forecast" package for R has mechanisms that allow automatic selection of model parameters. Exponential smoothing state space (exponential time series or ETS) models are an important alternative that have often proved effective in forecasting applications. ARCH and GARCH heteroskedasticity models are further classes that have been developed to handle the special characteristics of financial time series.