car {cts}R Documentation

Fit Continuous Time AR Models to Irregularly Sampled Time Series

Description

Fit a continuous AR model to an irregularly sampled univariate time series with the Kalman filter

Usage

car(x, y=NULL, scale = 1.5, order = 3, ari= TRUE, phi = rep(0, order),
vri = FALSE, vr = 0, pfi = "MAPS", ccv = "CTES", lpv = TRUE,
scc = TRUE, n.ahead = 10, nit = 40, opm = 1, rgm = 1, req = 0.5,
con = 1e-05, rpe = 1, ivl = 0.01, fac = 10, stl = 1e-05,
sml = 100, gtl = 1e+05, kst = TRUE, fct = TRUE, fty=2)

Arguments

x two column data frame or matrix with the first column being the sampled time and the second column being the observations at the first column; otherwise x is a numeric vector of sampled time.
y not used if x has two columns; otherwise y is a numeric vector of observations at sampled time x.
scale The kappa value referred to in the paper.
order order of autoregression.
ari ari=TRUE: parameter starting values follow phi. ari=FALSE: they are taken as zero
phi parameter starting values used only if ari=TRUE.
vri vri=FALSE, observation noise not included in the model. vri=TRUE, observation noise included
vr 0.5, initial value of observation noise ratio: only if vri=TRUE
pfi always use the option pfi="MAPS".
ccv ccv="CTES" for constant term estimation. ccv="MNCT" if mean correction, ccv=NULL if omitted.
lpv lpv=TRUE always use this option.
scc scc=TRUE always use this option.
n.ahead number of steps ahead at which to predict.
nit number of iteations.
opm opm=1 always use this.
rgm rgm=1 always use this.
req root equality switch value.
con convergence criterion.
rpe relative size of parameter perturbations.
ivl initial value of step size constraint parameter.
fac step size constraint modification parameter. This value may be setup to fac=5 for better convergency.
stl typical smallest step size parameter.
sml typical small step size parametrr.
gtl typical greatest step size parameter.
kst kst=TRUE to save estimated states.
fct fct=TRUE to use all time series to fit the model.
fty fty=1 forecast past the end. fty=2 forecast last L-steps. fty=3 forecast last L-steps updated (filtering)types.

Details

See references.

Value

A list of class "car" with the following elements:

n.used The number of observations of ser used in fitting
order The order of the fitted model. This is chosen by the user.
np The number of parameters estimated. This may include the mean and the observation noise ratio.
scale The kappa value referred to in the paper.
vr The estimated observation noise ratio.
sigma2 The estimated innovation variance.
phi The estimated reparameterized autoregressive parameters.
x.mean The estimated mean of the series used in fitting and for use in prediction.
b All estimated parameters, which include phi, and possibly x.mean and vr.
delb The estimated standard error of b
essp The estimated correlation matrix of b
ecov The estimated covariance matrix of phi. See also aic
rootr The real part of roots of phi. See also aic
rooti The imaginary part of roots of phi. See also aic
tim The numeric vector of sampled time.
ser The numeric vector of observations at sampled time tim.
filser The filtered time series with the Kalman filter.
filvar The estimated variance of Kalman filtered time series filser
sser The smoothed time series with the Kalman smoother.
svar The estimated variance of smoothed time series sser
stdred The standardized residuals from the fitted model.
predict Predictions for the series which has been used to fit the model.
predict.var Prediction variance of predict

Author(s)

G. Tunnicliffe Wilson and Zhu Wang

References

Belcher, J. and Hampton, J. S. and Tunnicliffe Wilson, G. (1994). Parameterization of continuous time autoregressive models for irregularly sampled time series data. Journal of the Royal Statistical Society, Series B, Methodological,56,141–155

Jones, Richard H. (1981). Fitting a continuous time autoregression to discrete data. Applied Time Series Analysis II, 651–682

Wang, Zhu (2004). The Application of the Kalman Filter to Nonstationary Time Series through Time Deformation. PhD thesis, Southern Methodist University

See Also

aic for model selection

Examples

## Not run: 
data(V22174)
car(V22174,scale=0.2,order=7)

data(asth)
car(asth,scale=0.25,order=4)
## End(Not run)

[Package cts version 1.0 Index]