Type:	Package
Title:	Multiresolution Forecasting
Version:	0.1.9
Date:	2026-04-11
Maintainer:	Quirin Stier <research@quirin-stier.de>
Description:	Forecasting of univariate time series using feature extraction with variable prediction methods is provided. Feature extraction is done with a redundant Haar wavelet transform with filter h = (0.5, 0.5). The advantage of the approach compared to typical Fourier based methods is an dynamic adaptation to varying seasonalities. Currently implemented prediction methods based on the selected wavelets levels and scales are a regression and a multi-layer perceptron. Forecasts can be computed for horizon 1 or higher. Model selection is performed with an evolutionary optimization. Selection criteria are currently the AIC criterion, the Mean Absolute Error or the Mean Root Error. The data is split into three parts for model selection: Training, test, and evaluation dataset. The training data is for computing the weights of a parameter set. The test data is for choosing the best parameter set. The evaluation data is for assessing the forecast performance of the best parameter set on new data unknown to the model. This work is published in Stier, Q.; Gehlert, T.; Thrun, M.C. Multiresolution Forecasting for Industrial Applications. Processes 2021, 9, 1697. <doi:10.3390/pr9101697>.
Imports:	DEoptim, stats, forecast, monmlp, nnfor, wavelets, methods
Depends:	R (≥ 3.5.0)
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
Suggests:	knitr, rmarkdown
VignetteBuilder:	knitr
URL:	https://www.deepbionics.org
BugReports:	https://github.com/Quirinms/MRFR/issues
NeedsCompilation:	no
Packaged:	2026-04-12 12:30:22 UTC; quiri
Author:	Quirin Stier [aut, cre, ctb], Michael Thrun [ths, cph, rev, fnd, ctb]
Repository:	CRAN
Date/Publication:	2026-04-16 18:50:02 UTC

Multiresolution Forecasting

Description

Forecasting of univariate time series using feature extraction with variable prediction methods is provided. Feature extraction is done with a redundant Haar wavelet transform with filter h = (0.5, 0.5). The advantage of the approach compared to typical Fourier based methods is an dynamic adaptation to varying seasonalities. Currently implemented prediction methods based on the selected wavelets levels and scales are a regression and a multi-layer perceptron. Forecasts can be computed for horizon 1 or higher. Model selection is performed with an evolutionary optimization. Selection criteria are currently the AIC criterion, the Mean Absolute Error or the Mean Root Error. The data is split into three parts for model selection: Training, test, and evaluation dataset. The training data is for computing the weights of a parameter set. The test data is for choosing the best parameter set. The evaluation data is for assessing the forecast performance of the best parameter set on new data unknown to the model. This work is published in Stier, Q.; Gehlert, T.; Thrun, M.C. Multiresolution Forecasting for Industrial Applications. Processes 2021, 9, 1697. <doi:10.3390/pr9101697>. The package consists of a multiresolution forecasting method using a redundant Haar wavelet transform based on the manuscript [Stier et al., 2021] which is currently in press. One-step and multi-step forecasts are computable with this method. Nested and non-nested cross validation is possible.

Details

Forecasting of univariate time series using feature extraction with variable prediction methods is provided. Feature extraction is done with a redundant Haar wavelet transform with filter h = (0.5, 0.5). The advantage of the approach compared to typical Fourier based methods is an dynamic adaptation to varying seasonalities. Currently implemented prediction methods based on the selected wavelets levels and scales are a regression and a multi-layer perceptron. Forecasts can be computed for horizon 1 or higher. Model selection is performed with an evolutionary optimization. Selection criterias are currently the AIC criterion, the Mean Absolute Error or the Mean Root Error. The data is split into three parts for model selection: Training, test, and evaluation dataset. The training data is for computing the weights of a parameter set. The test data is for choosing the best parameter set. The evaluation data is for assessing the forecast performance of the best parameter set on new data unknown to the model.

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.; Gehlert, T.; Thrun, M.C. Multiresolution Forecasting for Industrial Applications. Processes 2021, 9, 1697. https://doi.org/10.3390/pr9101697

Entsoe DataFrame containing Time Series

Description

Data from a European Network of Transmission System Operators for Electricity Accessed: 2020-08-20, 2019. Time series contains 3652 data points without missing values. Data describes electrict load for time range between 2006 and 2015

Usage

data(entsoe)

Format

A DataFrame with 3652 rows and 2 columns

Source

Archive

Examples

data(entsoe)
data = entsoe$value

Forecast with Extreme Learning Machines

Description

This function creates a one step forecast using a multi layer perceptron with one hidden Layer. The number of input is the sum of all coefficients chosen with the parameter CoefficientCombination. The CoefficientCombination parameter controls the number of coefficients chosen for each wavelet and smooth part level individually.

Usage

mrf_elm_forecast(UnivariateData, Horizon, Aggregation, Threshold="hard",
Lambda=0.05)

Arguments

Value

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(as.vector(array(AirPassengers)))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
Aggregation = c(2,4)
if(requireNamespace('nnfor', quietly = TRUE)){
forecast = mrf_elm_forecast(UnivariateData, Horizon=1, Aggregation)
true_value = array(AirPassengers)[len_data]
error = true_value - forecast
}

Multiresolution Forecast

Description

Creates a multiresolution forecast for a given multiresolution model based on [Stier et al., 2021] which is currently in press. (mrf_train).

Usage

mrf_forecast(Model, Horizon=1)

Arguments

Value

List of

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Examples

data(AirPassengers)
Data = as.vector(AirPassengers)
len_data = length(Data)
Train = Data[1:(len_data-2)]
Test = Data[(len_data-1):len_data]
# One-step forecast (Multiresolution Forecast)
model = mrf_train(Train)
one_step = mrf_forecast(model, Horizon=1)
Error = one_step$Forecast - Test[1]
# Multi-step forecast (Multiresolution Forecast)
# Horizon = 2 => Forecast with Horizon 1 and 2 as vector
model = mrf_train(Train, Horizon=2)
multi_step = mrf_forecast(model, Horizon=2)
Error = multi_step$Forecast - Test

Model selection for Multiresolution Forecasts

Description

Evaluates the best coefficient combination for a given aggregation scheme based on a rolling forecasting origin based on the manuscript [Stier et al., 2021] which is currently in press.

Usage

mrf_model_selection(UnivariateData, Aggregation, Horizon = 1, Window = 2,
Method = "r", crit = "AIC", itermax = 1, lower_limit = 1, upper_limit = 2,
NumClusters = 1, Threshold="hard", Lambda=0.05)

Arguments

Details

The evaluation function (optimization function) is built with a rolling forecasting origin (rolling_window function), which computes a h-step ahead forecast (for h = 1, ..., horizon) for 'Window' many steps. The input space is searched with an evolutionary optimization method. The search is restricted to one fixed aggregation scheme (parameter: 'Aggregation'). The deployed forecast method can be an autoregression or a neural network (multilayer perceptron with one hidden layer).

Value

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Examples

data(entsoe)
UnivariateData = entsoe$value
Aggregation = c(2,4)
res = mrf_model_selection(UnivariateData, Aggregation, Horizon = 1, Window = 2,
Method = "r", crit = "AIC", itermax = 1, lower_limit = 1, upper_limit = 2,
NumClusters = 1)
BestCoefficientCombination = res$CoefficientCombination

Multiresolution Forecast

Description

This function creates a multi step forecast for all horizons from 1 to steps based on the manuscript [Stier et al., 2021] which is currently in press. The deployed forecast method can be an autoregression or a neural network (multilayer perceptron with one hidden layer). Multi step forecasts are computed recursively.

Usage

mrf_multi_step_forecast(UnivariateData, Horizon, Aggregation,
CoefficientCombination=NULL, Method = "r", Threshold="hard", Lambda=0.05)

Arguments

Value

List of

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Examples

data(AirPassengers)
len_data = length(array(AirPassengers))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
# One-step forecast (Multiresolution Forecast)
one_step = mrf_multi_step_forecast(UnivariateData = UnivariateData,
                                    Horizon = 2,
                                    CoefficientCombination = c(1,1,1),
                                    Aggregation = c(2,4),
                                    Method="r")
# Multi-step forecast (Multiresolution Forecast)
# Horizon = 2 => Forecast with Horizon 1 and 2 as vector
multi_step = mrf_multi_step_forecast(UnivariateData = UnivariateData,
                                      Horizon = 2,
                                      CoefficientCombination = c(1,1,1),
                                      Aggregation = c(2,4),
                                      Method="r")

One Step Forecast with Neural Network

Description

This function creates a one step forecast using a multi layer perceptron with one hidden Layer. The number of input is the sum of all coefficients chosen with the parameter CoefficientCombination. The CoefficientCombination parameter controls the number of coefficients chosen for each wavelet and smooth part level individually.

Usage

mrf_neuralnet_one_step_forecast(UnivariateData, CoefficientCombination,
Aggregation, Threshold="hard", Lambda=0.05)

Arguments

Value

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(as.vector(array(AirPassengers)))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
CoefficientCombination = c(1,1,1)
Aggregation = c(2,4)
if(requireNamespace('monmlp', quietly = TRUE)){
forecast = mrf_neuralnet_one_step_forecast(UnivariateData,
                                           CoefficientCombination,
                                           Aggregation)
true_value = array(AirPassengers)[len_data]
error = true_value - forecast
}

Forecast with nnetar

Description

This function creates a one step forecast using a multi layer perceptron with one hidden Layer. The number of input is the sum of all coefficients chosen with the parameter CoefficientCombination. The CoefficientCombination parameter controls the number of coefficients chosen for each wavelet and smooth part level individually.

Usage

mrf_nnetar_forecast(UnivariateData, Horizon, Aggregation, Threshold="hard",
Lambda=0.05)

Arguments

Value

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(as.vector(array(AirPassengers)))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
Aggregation = c(2,4)
if(requireNamespace('nnfor', quietly = TRUE)){
forecast = mrf_nnetar_forecast(UnivariateData, Horizon=1, Aggregation)
true_value = array(AirPassengers)[len_data]
error = true_value - forecast
}

mrf_one_step_forecast Step Forecast

Description

This function creates a one step forecast using the multiresolution forecasting framework based on the manuscript [Stier et al., 2021] which is currently in press.

Usage

mrf_one_step_forecast(UnivariateData, Aggregation,
CoefficientCombination=NULL,
Method="r", Threshold="hard", Lambda=0.05)

Arguments

Value

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Examples

data(AirPassengers)
len_data = length(array(AirPassengers))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
forecast = mrf_one_step_forecast(UnivariateData=UnivariateData,
CoefficientCombination=c(1,1,1), Aggregation=c(2,4))
true_value = array(AirPassengers)[len_data]
error = true_value - forecast

Least Square Method for Regression

Description

This function computes the weights for the autoregression depending on the given wavelet decomposition. It uses ordinary least square method for optimizing a linear equation system.

Usage

mrf_regression_lsm_optimization(points_in_future, lsmatrix)

Arguments

Value

List of

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(array(AirPassengers))
CoefficientCombination = c(1,1,1)
Aggregation = c(2,4)
UnivariateData = as.vector(AirPassengers)
# Decomposition
dec_res <- wavelet_decomposition(UnivariateData, Aggregation)
# Training
trs_res <- wavelet_training_equations(UnivariateData,
                                      dec_res$WaveletCoefficients,
                                      dec_res$SmoothCoefficients,
                                      dec_res$Scales,
                                      CoefficientCombination, Aggregation)
arr_future_points = trs_res$points_in_future
matrix = trs_res$lsmatrix
# Optimization method
weights = mrf_regression_lsm_optimization(arr_future_points, matrix)
# Forecast
scheme = wavelet_prediction_equation(dec_res$WaveletCoefficients,
dec_res$SmoothCoefficients, CoefficientCombination, Aggregation)
forecast = weights 

One Step Forecast with Regression

Description

This function creates a one step forecast using an autoregression method. The ccps parameter controls the number of coefficients chosen for each wavelet and smooth part level individually.

Usage

mrf_regression_one_step_forecast(UnivariateData, CoefficientCombination,
Aggregation, Threshold="hard", Lambda=0.05)

Arguments

Value

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(as.vector(array(AirPassengers)))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
CoefficientCombination = c(1,1,1)
Aggregation = c(2,4)
forecast = mrf_regression_one_step_forecast(UnivariateData,
                                            CoefficientCombination,
                                            Aggregation)
true_value = array(AirPassengers)[len_data]
error = true_value - forecast

Multiresolution Forecast Requirements

Description

Computes requirements for given model using insights of various published papers and the manuscript [Stier et al., 2021] which is currently in press.

Usage

mrf_requirement(UnivariateData, CoefficientCombination, Aggregation)

Arguments

Value

List of

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(entsoe)
UnivariateData = entsoe$value
mrf_requirement(UnivariateData, c(2,3,4), c(2,4))

Rolling forecasting origin for Multiresolution Forecasts

Description

This function computes a rolling forecasting origin for one- or multi-step forecasts with a specific method based on the manuscript [Stier et al., 2021] which is currently in press. Multi-step forecasts are computed recursively with the one step forecast method.

Usage

mrf_rolling_forecasting_origin(UnivariateData, Aggregation,
CoefficientCombination=NULL, Horizon = 2, Window = 3, Method = "r",
NumClusters = 1,
Threshold="hard", Lambda=0.05)

Arguments

Details

Thus, h-step forecast for h = 1,..., horizon for window_size many steps can be computed. The forecasting method can be an autoregression or a neural network (multilayer perceptron). The CoefficientCombination parameter controls the number of coefficients chosen for each wavelet and smooth part level individually. The NumClusters parameter determines the number of cluster used for parallel computation. NumClusters = 1 performs a non parallel version. NumClusters is constrained by the maximum number of clusters available minus one to prevent the machine to be overchallenged.

Value

List of

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Examples

data(AirPassengers)
UnivariateData=as.vector(array(AirPassengers))
res = mrf_rolling_forecasting_origin(UnivariateData,
                                 CoefficientCombination = c(10,10,10),
                                 Aggregation = c(2,4),
                                 Horizon = 2, Window = 3, Method = "r",
                                 NumClusters = 1)
Error = res$Error
Forecast = res$Forecast

Multiresolution Forecast

Description

Creates a multiresolution forecast model which can be used for forecasting with method 'mrf_forecast' based on the manuscript [Stier et al., 2021] which is currently in press.

Usage

mrf_train(Data, Horizon=1, Aggregation="auto", Method = "r",
TimeSteps4ModelSelection=2, crit="AIC", InSample=FALSE, Threshold="hard",
Lambda=0.05, NumClusters=1, itermax=1)

Arguments

Value

List with

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Examples

data(AirPassengers)
Data = as.vector(AirPassengers)
len_data = length(Data)
Train = Data[1:(len_data-2)]
Test = Data[(len_data-1):len_data]
# One-step forecast (Multiresolution Forecast)
model = mrf_train(Train)
one_step = mrf_forecast(model, Horizon=1)
Error = one_step$Forecast - Test[1]
# Multi-step forecast (Multiresolution Forecast)
# Horizon = 2 => Forecast with Horizon 1 and 2 as vector
model = mrf_train(Train, Horizon=2)
multi_step = mrf_forecast(model, Horizon=2)
Error = multi_step$Forecast - Test

Redundant Haar Wavelet Decomposition

Description

This function decomposes a time series in its wavelet and smooth coefficients using the redundant Haar wavelet transform.

Usage

wavelet_decomposition(UnivariateData, Aggregation = c(2, 4, 8, 16, 32),
Threshold="hard", Lambda=0.05)

Arguments

Details

The resulting wavelet and smooth coefficients are stored in so called wavelet and smooth part levels. The smooth part level is created from the original times series by aggregation (average). This makes the times series in some sense smoother, hence the naming. Each individual smooth part level can be created from the original time series by aggregating over different number of values. The different smooth part levels are ordered, so that the number of values used for aggregation are ascending. A dyadic scheme is recommended (increasing sequences of the power of two). The dyadic scheme for 5 levels would require agg_per_lvl = c(2, 4, 8, 16, 32). So the first smooth part level would be the average of two points of the original time series, the second smooth part level would be the average of four points, and so on. This averaging is applied asymmetrical. That means, that the result of the average of a sequence of points is obtained for the last point in time of that sequence. So each smooth part level starts with a certain offset, since no average can be obtained for the first particular points in time. The wavelet levels are the differences between the original time series and the smooth levels. The first wavelet level is the difference of the original time series and the first smooth part level. The second wavelet level is the difference of the first and second smooth part level and so on.

Value

List of

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
plot(AirPassengers, type = "l", col = "black")
UnivariateData = as.vector(array(AirPassengers))
dec_res = wavelet_decomposition(UnivariateData, Aggregation = c(2,4))
plot(dec_res$SmoothCoefficients[2,4:length(dec_res$SmoothCoefficients[2,])],
type = "l", col = "blue")
lines(array(AirPassengers)[4:length(dec_res$SmoothCoefficients[2,])],
col = "black")

One Step Forecast with Regression

Description

This function delivers the required wavelet and smooth coefficients from the decomposition based on a prediction scheme.

Usage

wavelet_prediction_equation(WaveletCoefficients, SmoothCoefficients,
CoefficientCombination, Aggregation)

Arguments

Value

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(array(AirPassengers))
CoefficientCombination = c(1,1,1)
Aggregation = c(2,4)
UnivariateData = as.vector(AirPassengers)
# Decomposition
dec_res <- wavelet_decomposition(UnivariateData, Aggregation)
# Training
trs_res <- wavelet_training_equations(UnivariateData,
                                      dec_res$WaveletCoefficients,
                                      dec_res$SmoothCoefficients,
                                      dec_res$Scales,
                                      CoefficientCombination, Aggregation)
arr_future_points = trs_res$points_in_future
matrix = trs_res$lsmatrix
# Optimization method
weights = mrf_regression_lsm_optimization(arr_future_points, matrix)
# Forecast
scheme = wavelet_prediction_equation(dec_res$WaveletCoefficients,
dec_res$SmoothCoefficients, CoefficientCombination, Aggregation)
forecast = weights 

Generic Training Scheme for wavelet framework

Description

This function computes the input for the training phase required for one step forecasts. This computational step is required for all one step forecast procedures contained in this package.

Usage

wavelet_training_equations(UnivariateData, WaveletCoefficients,
SmoothCoefficients, Scales, CoefficientCombination, Aggregation)

Arguments

Value

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(array(AirPassengers))
CoefficientCombination = c(1,1,1)
Aggregation = c(2,4)
UnivariateData = as.vector(AirPassengers)
# Decomposition
dec_res <- wavelet_decomposition(UnivariateData, Aggregation)
# Training
trs_res <- wavelet_training_equations(UnivariateData,
                                      dec_res$WaveletCoefficients,
                                      dec_res$SmoothCoefficients,
                                      dec_res$Scales,
                                      CoefficientCombination, Aggregation)
arr_future_points = trs_res$points_in_future
matrix = trs_res$lsmatrix
# Optimization method
weights = mrf_regression_lsm_optimization(arr_future_points, matrix)
# Forecast
scheme = wavelet_prediction_equation(dec_res$WaveletCoefficients,
dec_res$SmoothCoefficients, CoefficientCombination, Aggregation)
forecast = weights