The function predicts and returns the next n consecutive values of a univariate time series using the best evaluated automatically fitted polynomial regression model. 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.
fittestPolyR(
timeseries,
timeseries.test = NULL,
h = NULL,
order = NULL,
minorder = 0,
maxorder = 5,
raw = FALSE,
na.action = stats::na.omit,
level = 0.95,
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.
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 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'.
If TRUE, use raw and not orthogonal polynomials.
Orthogonal polynomials help avoid correlation between variables. Default is
FALSE. See poly of the stats package.
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.lm function in the stats package.
Character string. Criteria used for ranking candidate models generated. See 'Details'.
A list with components:
An object of class "stats::lm" containing the best evaluated polynomial regression model.
The order argument provided (or automatically selected) for the best evaluated polynomial regression model.
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.lm.
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 coefficients
and the fitness or prediction accuracy criteria computed for all candidate
polynomial regression models ranked by rank.by. It has the attribute
"model.calls", which is a list of objects of class "expression"
containing the calls of all the candidate polynomial regression models, also
ranked by rank.by.
Ranking criteria used for ranking
candidate models and producing rank.val.
A set with candidate polynomial regression models of order order is
generated with help from the dredge function from the
MuMIn package. The candidate models are ranked acoording to the
criteria in rank.by and the best ranked model is returned by the
function.
If order is NULL, it is automatically selected. For that, the
candidate polynomial regression models generated receive orders from
minorder to maxorder. The value option of order which
generate the best ranked candidate polynomial regression model acoording to
the criteria in rank.by is 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 {
data(CATS,CATS.cont)
fPolyR <- fittestPolyR(CATS[,3],CATS.cont[,3])
#predicted values
pred <- fPolyR$pred
#plotting the time series data
plot(c(CATS[,3],CATS.cont[,3]),type='o',lwd=2,xlim=c(960,1000),ylim=c(-100,300),
xlab="Time",ylab="PR")
#plotting predicted values
lines(ts(pred$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')
# }
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