Time series models

Abstract

A time series is a sequence of observations that have been recorded over time. Almost invariably, observations that are close together in time are more strongly correlated than observations that are widely separated. The independence assumption of previous chapters is, in general, no longer valid. Variation in a single spatial dimension may have characteristics akin to those of time series, and the same types of models may find application there also. Many techniques have been developed to deal with the special nature of the dependence that is commonly found in such series. The present treatment will be introductory and restricted in scope, focusing on autoregressive integrated moving average (ARIMA) models. In the section that follows, annual depth measurements at a specific site on Lake Huron will be modeled directly as an ARIMA process. Section 9.2 will model a regression where the error term has a time series structure. The chapter will close with a brief discussion of “non-linear” time series, such as have been widely used in modeling financial time series. The analyses will use functions in the stats package, which is a recommended package, included with binary distributions. Additionally, there will be use of the forecast package. In order to make this available, install the forecasting bundle of packages. The brief discussion of non-linear time series (ARCH and GARCH models) will require access to the tseries package, which must be installed.