Abstract
We describe an R package cts for fitting a modified form of continuous time autoregressive model, which can be particularly useful with unequally sampled time series. The estimation is based on the application of the Kalman filter. The paper provides the methods and algorithms implemented in the package, including parameter estimation, spectral analysis, forecasting, model checking and Kalman smoothing. The package contains R functions which interface underlying Fortran routines. The package is applied to geophysical and medical data for illustration.
Highlights
The discrete time autoregressive model of order p, the AR(p), is a widely used tool for modeling spaced time series data
It can be fitted in a straightforward and reliable manner and has the capacity to approximate a second order stationary process to any required degree of precision by choice of a suitably high order. Various information criteria such as the AIC (Akaike 1974) or the BIC (Schwarz 1978) can, in practice be used to determine a suitable order when fitting to a finite data set. This model is clearly not appropriate for irregularly sampled data, for which various authors have advocated the use of the continuous time autoregressive model of order p, the CAR(p)
See Tunnicliffe Wilson and Morton (2004), this modified CAR(p) model has been named the CZAR(p) model and expressed in autoregressive form using the generalized continuous time shift operator with the alternative parameterization appearing in a natural manner
Summary
The discrete time autoregressive model of order p, the AR(p), is a widely used tool for modeling spaced time series data It can be fitted in a straightforward and reliable manner and has the capacity to approximate a second order stationary process to any required degree of precision by choice of a suitably high order. Various information criteria such as the AIC (Akaike 1974) or the BIC (Schwarz 1978) can, in practice be used to determine a suitable order when fitting to a finite data set.
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