The function predicts and returns the next n consecutive values of a univariate time series using the best evaluated polynomial regression model automatically fitted with Kalman filter. It also evaluates the fitness of the produced model, using AICc, AIC, BIC and logLik criteria, and its prediction accuracy, using the MSE, NMSE, MAPE, sMAPE and maximal error accuracy measures.
fittestPolyRKF(
timeseries,
timeseries.test = NULL,
h = NULL,
na.action = stats::na.omit,
level = 0.9,
order = NULL,
minorder = 0,
maxorder = 5,
initQ = NULL,
filtered = TRUE,
rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
"logLik", "errors", "fitness")
)A vector or univariate time series which contains the
values used for fitting a polynomial regression model with Kalman filter.
~~Describe timeseries here~~
A vector or univariate time series containing a
continuation for timeseries with actual values. It is used as a
testing set and base for calculation of prediction error measures. Ignored
if NULL.
Number of consecutive values of the time series to be predicted. If
h is NULL, the number of consecutive values to be predicted is
assumed to be equal to the length of timeseries.test. Required when
timeseries.test is NULL.
A function for treating missing values in timeseries
and timeseries.test. The default function is na.omit,
which omits any missing values found in timeseries or
timeseries.test.
Confidence level for prediction intervals. See the
predict.SSModel function in the KFAS package.
~~Describe na.action here~~
A numeric integer value corresponding to the order of
polynomial regression to be fitted. If NULL, the order of the
polynomial regression returned by the function is automatically selected
within the interval minorder:maxorder. See 'Details'.
A numeric integer value corresponding to the minimum order
of candidate polynomial regression to be fitted and evaluated. Ignored if
order is provided. See 'Details'.
A numeric integer value corresponding to the maximal order
of candidate polynomial regression to be fitted and evaluated. Ignored if
order is provided. See 'Details'.
Numeric argument regarding the initial values for the
covariance of disturbances parameter to be optimized over. The initial
values to be optimized are set to rep(initQ,(order+1)). See the
Q argument of the SSModel function in the KFAS
package and the examples in KFAS. If NULL, initQ
is automatically set. See 'Details'.
If filtered is TRUE, Kalman filtered time
series observations are used for prediction, otherwise, Kalman smoothed
observations are used for prediction.
Character string. Criteria used for ranking candidate models
generated using different options of values for order and/or
initQ. Ignored if both order and initQ are provided.
See 'Details'.
A list with components:
An object of class "SSModel" containing the best evaluated polynomial regression model fitted with Kalman Filter.
The order argument provided (or automatically selected) for the best evaluated polynomial regression model fitted with Kalman Filter.
The initQ argument provided (or automatically selected) for optimization of the best evaluated polynomial regression model fitted with Kalman Filter.
Numeric value of the computed AICc criterion of the best evaluated model.
Numeric value of the computed AIC criterion of the best evaluated model.
Numeric value of the computed BIC criterion of the best evaluated model.
Numeric value of the computed log-likelihood of the best evaluated model.
A list with the components mean,
lower and upper, containing the predictions of the best
evaluated model and the lower and upper limits for prediction intervals,
respectively. All components are time series. See
predict.SSModel.
Numeric value of the resulting
MSE error of prediction. Require timeseries.test.
Numeric value of the resulting NMSE error of prediction. Require
timeseries.test.
Numeric value of the resulting MAPE
error of prediction. Require timeseries.test.
Numeric
value of the resulting sMAPE error of prediction. Require
timeseries.test.
Numeric value of the maximal error
of prediction. Require timeseries.test.
Data.frame
with the fitness or prediction accuracy criteria computed for all candidate
polynomial regression with Kalman filter models ranked by rank.by. It
has the attribute "ranked.models", which is a list of objects of
class "SSModel" containing all the candidate polynomial regression models
fitted with Kalman Filter, also ranked by rank.by. Only provided if
order or initQ were automatically selected.
Ranking criteria used for ranking candidate models and
producing rank.val.
The polynomial regression model produced and returned by the function is
generated and represented as state space model (SSModel) based
on code from the dlmodeler package. See dlmodeler.polynomial.
The model is optimized using the Kalman filter and functions of the
KFAS package (see fitSSM).
If order is NULL, it is automatically selected. For that, a
set of candidate polynomial regression state space models of orders from
minorder to maxorder is generated and evaluated. Also, if
initQ is NULL, it is automatically set as either
log(stats::var(timeseries)) or 0. For that, candidate models receive
different initial parameterization of initQ during the model
optimization process. The value options of order and/or initQ
which generate the best ranked candidate polynomial regression model
acoording to the criteria in rank.by are selected.
The ranking criteria in rank.by may be set as a prediction error
measure (such as MSE, NMSE, MAPE,
sMAPE or MAXError), or as a fitness criteria
(such as AIC, AICc, BIC or
logLik). In the former case, the candidate models are used for
time series prediction and the error measures are calculated by means of a
cross-validation process. In the latter case, the candidate models are
fitted and fitness criteria are calculated based on all observations in
timeseries.
If rank.by is set as "errors" or "fitness", the
candidate models are ranked by all the mentioned prediction error measures
or fitness criteria, respectively. The wheight of the ranking criteria is
equally distributed. In this case, a rank.position.sum criterion is
produced for ranking the candidate models. The rank.position.sum
criterion is calculated as the sum of the rank positions of a model (1 = 1st
position = better ranked model, 2 = 2nd position, etc.) on each calculated
ranking criteria.
R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.
R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.
# NOT RUN {
# }
# NOT RUN {
data(CATS,CATS.cont)
fPolyRKF <- fittestPolyRKF(CATS[,1],CATS.cont[,1])
#predicted values
pred <- fPolyRKF$pred
#extracting Kalman filtered and smoothed time series from the best fitted model
fs <- KFAS::KFS(fPolyRKF$model,filtering=c("state","mean"),smoothing=c("state","mean"))
f <- fitted(fs, filtered = TRUE) #Kalman filtered time series
s <- fitted(fs) #Kalman smoothed time series
#plotting the time series data
plot(c(CATS[,1],CATS.cont[,1]),type='o',lwd=2,xlim=c(960,1000),ylim=c(0,200),
xlab="Time",ylab="PRKF")
#plotting the Kalman filtered time series
lines(f,col='red',lty=2,lwd=2)
#plotting the Kalman smoothed time series
lines(s,col='green',lty=2,lwd=2)
#plotting predicted values
lines(ts(pred$mean,start=981),lwd=2,col='blue')
#plotting prediction intervals
lines(ts(pred$lower,start=981),lwd=2,col='light blue')
lines(ts(pred$upper,start=981),lwd=2,col='light blue')
# }
# NOT RUN {
# }
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