Abstract
The FitAR R (R Development Core Team 2008) package that is available on the Comprehensive R Archive Network is described. This package provides a comprehensive approach to fitting autoregressive and subset autoregressive time series. For long time series with complicated autocorrelation behavior, such as the monthly sunspot numbers, subset autoregression may prove more feasible and/or parsimonious than using AR or ARMA models. The two principal functions in this package are SelectModel and FitAR for automatic model selection and model fitting respectively. In addition to the regular autoregressive model and the usual subset autoregressive models (Tong 1977), these functions implement a new family of models. This new family of subset autoregressive models is obtained by using the partial autocorrelations as parameters and then selecting a subset of these parameters. Further properties and results for these models are discussed in McLeod and Zhang (2006). The advantages of this approach are that not only is an efficient algorithm for exact maximum likelihood implemented but that efficient methods are derived for selecting high-order subset models that may occur in massive datasets containing long time series. A new improved extended {BIC} criterion, {UBIC}, developed by Chen and Chen (2008) is implemented for subset model selection. A complete suite of model building functions for each of the three types of autoregressive models described above are included in the package. The package includes functions for time series plots, diagnostic testing and plotting, bootstrapping, simulation, forecasting, Box-Cox analysis, spectral density estimation and other useful time series procedures. As well as methods for standard generic functions including print, plot, predict and others, some new generic functions and methods are supplied that make it easier to work with the output from FitAR for bootstrapping, simulation, spectral density estimation and Box-Cox analysis.
Highlights
The family of AR(p) models for a time series zt, t = 1, 2, . . . , may be written in operator notation, φ(B)(zt − μ) = at, where φ(B) = 1 − φ1B − . . . − φpBp, μ is the mean of the series and at ∼ NID (0, σa2)
When plotting long time series the resolution may be improved by using a multipanel display which can be created using xyplot
The BoxCox method for ‘Arima’ objects implements a Box-Cox analysis for time series fit with the R arima function
Summary
The usual family of subset AR(p) models is obtained by taking a subset of the parameters φ1, . − φimBim. The usual family of subset AR(p) models is obtained by taking a subset of the parameters φ1, . The new family of subset models, denoted by ARz(i1, . Ζim as parameters and constraining other partial autocorrelations as zero1 This model forms a subset of the AR(p) model that may be written as φ(B)(zt − μ) = at, where the parameters φ1, . The most important advantage of the new parameterization is the efficiency with which subset AR models with large p may be identified This advantage is important with long and complex time series which are becoming available in massive datasets being collected in a variety of scientific fields. Description Non-subset AR model Usual subset AR model New family of subset AR models
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