fittestWavelet: Automatic prediction with wavelet transform

In TSPred: Functions for Benchmarking Time Series Prediction

Description

The function automatically applies a maximal overlap discrete wavelet transform to a provided univariate time series. The resulting components of the decomposed series are used as base for predicting and returning the next n consecutive values of the provided univariate time series using also automatically fitted models (ets or arima). It also evaluates fitness and prediction accuracy of the produced models.

Usage

fittestWavelet(
  timeseries,
  timeseries.test = NULL,
  h = 1,
  filters = c("haar", "d4", "la8", "bl14", "c6"),
  n.levels = NULL,
  maxlevel = NULL,
  boundary = "periodic",
  model = c("ets", "arima"),
  conf.level = 0.95,
  na.action = stats::na.omit,
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
    "logLik", "errors", "fitness"),
  ...
)

Arguments

timeseries	A vector or univariate time series.
timeseries.test	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.
h	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.
filters	A vector containing character strings indicating which wavelet filter to use in the decomposition. If length(filters)>1, the wavelet transform filter used for generating the return of the function is automatically selected. If NULL, all supported filters are considered for automatic selection. See 'Details'. For more details on all the supported filters and corresponding character strings see wt.filter.
n.levels	An integer specifying the level of the decomposition. If NULL, the level of the wavelet decomposition returned by the function is automatically selected within the interval 1:maxlevel. See 'Details'.
maxlevel	A numeric integer value corresponding to the maximal level of candidate wavelet decompositions to be produced and evaluated. If NULL, maxlevel is set as floor(log(((nobs-1)/(L-1))+1)/log(2)), where nobs=length(timeseries) and L is the length of the wavelet and scaling filters. See modwt and wt.filter. Ignored if n.levels is provided. See 'Details'.
boundary	Character string. Indicates which boundary method to use. See modwt.
model	Character string. Indicates which model is to be used for fitting and prediction of the components of the decomposed series.
conf.level	Confidence level for prediction intervals. See the forecast function of the forecast package. ~~Describe na.action here~~
na.action	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.
rank.by	Character string. Criteria used for ranking candidate decompositions/models/predictions generated during parameter selection. See 'Details'.
...	Additional arguments passed to the modeling functions. ~~Describe na.action here~~

Details

The function produces a maximal overlap discrete wavelet transform of timeseries. It performs a time series decomposition of level n.levels using the wavelet filter filters. See the modwt function. Each component series resulting from the decomposition (n.levels wavelet coefficients series and n.levels scaling coefficients series) is separately used as base for model fitting and prediction. If model="arima", arima models are used and automatically fitted using the auto.arima function. If model="ets", the function fits [forecast]ets models. The set of predictions for all component series are then reversed transformed in order to produce the next h consecutive values of the provided univariate time series in timeseries. See the imodwt function.

If length(filters)>1 or filters=NULL, it is automatically selected. For that, a set of candidate wavelet decompositions with different options of filters is generated and used for model fitting and prediction. Also, if n.levels is NULL, it is automatically set as a value within the interval 1:maxlevel (if maxlevel is not provided, it is calculated according to the wavelet filter based on code from modwt). For that, candidate decompositions are specified with different levels. The options of filter and/or level of decomposition which generate the best ranked model fitness/predictions 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 wavelet decompositions are used for time series prediction and the error measures are calculated by means of a cross-validation process. In the latter case, the component series of the candidate decompositions are modeled and model fitness criteria are calculated based on all observations in timeseries. In particular, the fitness criteria calculated for ranking the candidate decomposition correspond to the model produced for the n.levelsth scaling coefficients series as it can be considered the main component of a decomposition of level n.levels (Conejo,2005).

If rank.by is set as "errors" or "fitness", the candidate decompositions 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 decompositions. The rank.position.sum criterion is calculated as the sum of the rank positions of a decomposition (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

WT	An object of class modwt containing the wavelet transformed/decomposed time series.
level	The level of wavelet decomposition provided or automatically selected.
filter	A character string indicating the (provided or automatically selected) wavelet filter used in the decomposition.
AICc	Numeric value of the computed AICc criterion of the fitted model for the levelth scaling coefficients series.
AIC	Numeric value of the computed AIC criterion of the fitted model for the levelth scaling coefficients series.
BIC	Numeric value of the computed BIC criterion of the fitted model for the levelth scaling coefficients series.
logLik	Numeric value of the computed log-likelihood of the fitted model for the levelth scaling coefficients series.
pred	A list with the components mean, lower and upper, containing the predictions based on the best evaluated decomposition and the lower and upper limits for prediction intervals, respectively. All components are time series. See the forecast function in the forecast package.
MSE	Numeric value of the resulting MSE error of prediction. Require timeseries.test.
NMSE	Numeric value of the resulting NMSE error of prediction. Require timeseries.test.
MAPE	Numeric value of the resulting MAPE error of prediction. Require timeseries.test.
sMAPE	Numeric value of the resulting sMAPE error of prediction. Require timeseries.test.
MaxError	Numeric value of the maximal error of prediction. Require timeseries.test.
rank.val	Data.frame with the fitness or prediction accuracy criteria computed based on all candidate decompositions ranked by rank.by. It has the attribute "ranked.wt", which is a list of modwt objects containing all the candidate decompositions, also ranked by rank.by. Only provided if filters or n.levels were automatically selected.
rank.by	Ranking criteria used for ranking candidate decompositions and producing rank.val.

Author(s)

Rebecca Pontes Salles

References

A. J. Conejo, M. A. Plazas, R. Espinola, A. B. Molina, Day-ahead electricity price forecasting using the wavelet transform and ARIMA models, IEEE Transactions on Power Systems 20 (2005) 1035-1042.

T. Joo, S. Kim, Time series forecasting based on wavelet filtering, Expert Systems with Applications 42 (2015) 3868-3874.

C. Stolojescu, I. Railean, S. M. P. Lenca, A. Isar, A wavelet based prediction method for time series. In Proceedings of the 2010 International Conference Stochastic Modeling Techniques and Data Analysis, Chania, Greece (pp. 8-11) (2010).

See Also

fittestEMD, fittestMAS ~

Examples

data(CATS)

fW <- fittestWavelet(CATS[,1],h=20,model="arima")

#plot wavelet transform/decomposition
plot(fW$WT)

TSPred documentation built on Jan. 21, 2021, 5:10 p.m.