Description Usage Arguments Details Value Author(s) References See Also Examples
Fit a continuous AR model to an irregularly sampled univariate time series with the Kalman filter
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  car(x, y=NULL, scale = 1.5, order = 3, ctrl=car_control())
## S3 method for class 'car'
print(x, digits = 3, ...)
## S3 method for class 'car'
summary(object, ...)
## S3 method for class 'car'
plot(x, type=c("spec", "pred", "diag"),...)
## S3 method for class 'car'
predict(object, se.fit = TRUE, digits = 3, plot.it=TRUE,...)
## S3 method for class 'car'
spectrum(object, frmult=1, n.freq, plot.it = TRUE, na.action = na.fail, ...)
## S3 method for class 'car'
AIC(object, ..., k=NULL)
## S3 method for class 'car'
tsdiag(object, gof.lag = 10, ...)
## S3 method for class 'car'
kalsmo(object)

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 
y 
not used if 
scale 
The kappa value referred to in the paper by Belcher et a. (1994). We now recommend selection of kappa along with the model order by using AIC. Also, it is suggested to choose kappa close to 2pi times 1/mean.delta (reciprocal of the mean time between observations), though it is a good idea to explore somewhat lower and higher values to see whether the spectrum estimates were sensitive to this choice. Choosing kappa lower increases the risk of trying to estimate the spectrum beyond the effective Nyquist frequency of the data  though this does depend on the distribution of intersample times. 
order 
order of autoregression. 
ctrl 
control parameters used in predict and numerical optimization. 
object 
object of class 
type 
in 
se.fit 
Logical: should standard errors of prediction be returned? 
digits 
return value digits 
plot.it 
Logical: plot the forecast values? 
gof.lag 
the maximum number of lags for a Portmanteau goodnessoffit test 
frmult 
numerical value, can be used to multiply the frequency range 
n.freq 
number of frequency 
k 
penalty, not used 
na.action 

... 
further arguments to be passed to particular methods 
spectrum
returns (and by default plots) the spectral density of the fitted model.
tsdiag
is a generic diagnostic function for continuous AR model. It will generally plot the residuals,
often standadized, the autocorrelation function of the residuals, and
the pvalues of a Portmanteau test for all lags up to gof.lag
.
The method for car
object plots residuals scaled by the estimate of their (individual) variance, and use the Ljung–Box version of the portmanteau test.
AIC
For continuous CAR model selection, tstatistic and AIC are calculated
based on reparameterized coefficients phi
and covariance matrix
ecov
. From the tstatistic, the final model is chosen such that
if the true model order
is less than the large value used for
model estimation then for i > order
the deviations of the
estimated parameters phi
from their true value of 0 will be
small. From the AIC, the final model is chosen based on the smallest AIC
value. A table with tstatistic and AIC for the corresponding model order.
factab
calculate characteristic roots and system frequency from the estimated
reparameterized coefficients of CAR fits.
smooth
computes components corresponding to the diagonal transition matrix with the Kalman smoother. This may not be stable for some data due to numerical inversion of matrix.
A list of class "car"
with the following elements:
n.used 
The number of observations 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 of Belcher et al. 
vri 
If vri=1, estimate the observation noise ratio. 
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 
delb 
The estimated standard error of 
essp 
The estimated correlation matrix of 
ecov 
The estimated covariance matrix of 
rootr 
The real part of roots of 
rooti 
The imaginary part of roots of 
tim 
The numeric vector of sampled time. 
ser 
The numeric vector of observations at sampled time

filser 
The filtered time series with the Kalman filter. 
filvar 
The estimated variance of Kalman filtered time series

sser 
The smoothed time series with the Kalman smoother. 
svar 
The estimated variance of smoothed time series

stdred 
The standardized residuals from the fitted model. 
pretime 
Time of predictions. 
pred 
Predictions for the 
prv 
Prediction variance of 
pre2 
Fitted values including 
prv2 
Variance of fitted values including 
fty 
Forecast type 
tnit 
Numeric vector: iteration 
ss 
Numeric vector: sum of squares for each 
bit 
Matrix with rows for 
aic 
AIC value for the fitted model 
bic 
BIC value for the fitted model 
G. Tunnicliffe Wilson and Zhu Wang
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
Wang, Zhu and Woodward, W. A. and Gray, H. L. (2009). The Application of the Kalman Filter to Nonstationary Time Series through Time Deformation. Journal of Time Series Analysis, 30(5), 559574.
Wang, Zhu (2013). cts: An R Package for Continuous Time Autoregressive Models via Kalman Filter. Journal of Statistical Software, Vol. 53(5), 1–19. http://www.jstatsoft.org/v53/i05
car_control
for predict and numerical optimization parameters, and AIC
for model selection
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  data(V22174)
fit < car(V22174,scale=0.2,order=7, ctrl=car_control(trace=TRUE))
summary(fit)
spectrum(fit)
tsdiag(fit)
AIC(fit)
factab(fit)
###fitted values vs observed values
ntim < dim(V22174)[1]
plot(V22174[,1], V22174[,2], type="l")
points(V22174[,1], fit$pre2[1:ntim], col="red")
### alternatively
fit2 < car(V22174,scale=0.2,order=7, ctrl=car_control(fty=3))
plot(V22174[,1], V22174[,2], type="l")
points(V22174[,1], fit2$pre2, col="red")
data(asth)
fit < car(asth,scale=0.25,order=4, ctrl=car_control(n.ahead=10))
kalsmo(fit)

Attaching package: 'cts'
The following objects are masked from 'package:stats':
spectrum, tsdiag
READING OF MODEL PARAMETER PARAMETER SUCCESSFUL
READING OF CONTROL PARAMETER SUCCESSFUL
ROOT EQUALITY SWITCH:
[1] 1
MAIN LOOP IN RESG1 BEGINS
ITERATION 0:
LAMBDA =
[1] 0.01
INITIAL SUM OF SQUARES =
[1] 12.92737
INITIAL PARAMETER VALUES
[1] 0 0 0 0 0 0 0
INITIAL VALUE OF CONSTANT TERM =
[1] 0.1053049
MAIN LOOP IN RESG1 BEGINS
MAIN LOOP IN RESG1 BEGINS
MAIN LOOP IN RESG1 BEGINS
MAIN LOOP IN RESG1 BEGINS
MAIN LOOP IN RESG1 BEGINS
MAIN LOOP IN RESG1 BEGINS
ROOT EQUALITY SWITCH:
[1] 0
ITERATION :
[1] 1
LAMBDA:
[1] 0.001
SUM OF SQUARES =
[1] 9.107596
PARAMETER VALUES
[1] 0.30940142 0.12339492 0.08810410 0.04348192 0.41661288 0.10084202
[7] 0.20167791 0.17401878
ROOT EQUALITY SWITCH:
[1] 0
ROOT EQUALITY SWITCH:
[1] 0
ROOT EQUALITY SWITCH:
[1] 0
ITERATION :
[1] 2
LAMBDA:
[1] 0.01
SUM OF SQUARES =
[1] 8.853833
PARAMETER VALUES
[1] 0.394234150 0.214279964 0.099421439 0.007241027 0.531324736
[6] 0.242421399 0.334272521 0.172746273
ROOT EQUALITY SWITCH:
[1] 0
ITERATION :
[1] 3
LAMBDA:
[1] 0.001
SUM OF SQUARES =
[1] 8.754946
PARAMETER VALUES
[1] 0.49817173 0.33311175 0.09249703 0.02483595 0.60470553 0.37474650
[7] 0.46502435 0.17300766
ROOT EQUALITY SWITCH:
[1] 0
ITERATION :
[1] 4
LAMBDA:
[1] 1e04
SUM OF SQUARES =
[1] 8.745203
PARAMETER VALUES
[1] 0.49787052 0.35157496 0.08335691 0.01990383 0.60243629 0.36674995
[7] 0.47582980 0.17321285
ROOT EQUALITY SWITCH:
[1] 0
ITERATION :
[1] 5
LAMBDA:
[1] 1e05
SUM OF SQUARES =
[1] 8.744615
PARAMETER VALUES
[1] 0.50211925 0.35494164 0.08588158 0.02213610 0.60544366 0.37311695
[7] 0.48349319 0.17331639
ROOT EQUALITY SWITCH:
[1] 0
PROCESSING COMPLETED
ITERATIONS COMPLETED:
[1] 6
CONVERGENCE ACHIEVED
SEARCH PROGRESSED
FINAL SUM OF SQUARES:
[1] 8.74455
MEAN SUM OF SQUARES :
[1] 0.05605481
INNOVATION PROCESS VARIANCE ESTIMATE:
[1] 1.369916e09
GEOMETRIC MEAN VARIANCE MULTIPLIER:
[1] 40918427
FINAL PARAMETER VALUES:
[1] 0.50100015 0.35535886 0.08542050 0.02177307 0.60469577 0.37050651
[7] 0.48268799 0.17330672
MAIN LOOP IN RESG1 BEGINS
Call:
car(x = V22174, scale = 0.2, order = 7, ctrl = car_control(trace = TRUE))
Order of model = 7, sigma^2 = 1.37e09
Estimated coefficients (standard errors):
phi_1 phi_2 phi_3 phi_4 phi_5 phi_6 phi_7
coef 0.501 0.355 0.085 0.022 0.605 0.371 0.483
S.E. 0.108 0.111 0.060 0.071 0.084 0.124 0.112
Estimated mean (standard error):
[1] 0.173
[1] 0.022
Call:
car(x = V22174, scale = 0.2, order = 7, ctrl = car_control(trace = TRUE))
Model selection statistics
order t.statistic AIC
1 4.77 20.78
2 4.45 38.57
3 3.25 47.15
4 2.37 50.76
5 6.11 86.05
6 0.76 84.63
7 4.32 101.27
Call:
factab(object = fit)
Characteristic root of original parameterization in alpha
1 2 3 4 5
0.006+0.058i 0.0060.058i 0.029+0.300i 0.0290.300i 0.030+0.135i
6 7
0.0300.135i 11.921+0.000i
Frequency
1 2 3 4 5 6 7
0.009 0.009 0.048 0.048 0.022 0.022 0.000
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.