forecastLSW (version 1.0)

which.wavelet.best: Find out what wavelet is good for forecasting your series.

Description

A big question with many wavelet methods is which wavelet should one use for a particular task. This function tries some forecasting on your time series with all Daubechies compactly supported wavelets available to it and returns a list of the forecasting performance for each choice, and indicates which wavelet gave the best results. This wavelet can then be used in future forecasting.

Usage

which.wavelet.best(x, n.to.test = 10, go.back=5,
	forecast.type = "recursive", lapplyfn = lapply)

Value

A data frame containing information on the root mean squared forecasting error performance of the locally stationary forecasting method for different wavelets. The data frame has four columns and a row for each wavelet tried. The first and second column give the filter number and family for each wavelet. The third column gives the root mean squared error for each combination of wavelet. The fourth column contains an indicator that shows which wavelet was best (there might be more than one).

Arguments

x

Your times series (not necessarily of dyadic length!)

n.to.test

How many observations at the end to test as part of the assessment process. The default, 10, means that 10 observations at the end of the series will all be forecast. This number should be reasonably big to enable forecasts of more than a few data points, but not too large.

go.back

Controls the go.back argument to testforecast. Number of repeats of the procedure on successively one-unit of time earlier series.

forecast.type

The type of forecasting as detailed in forecastlpacf.

lapplyfn

Type of list processing function. By default it uses R's lapply function. However, if you use the parallel library you can replace this with mclapply which will make this function go faster using parallel computation. Don't forget to set the options(mc.cores=4) argument to what you wish (here it is set to 4 in this example, but you should set it to something that is appropriate for your machine environment).

Author

Guy Nason

Details

This function uses all choices of wavelet to forecast the last n.to.test observations of your time series. It works out the forecasting error in doing so for each choice of wavelet and returns a list telling you which wavelet did best.

References

Killick, R., Knight, M.I., Nason, G.P., Nunes M.A., Eckley I.A. (2023) Automatic Locally Stationary Time Series Forecasting with application to predicting U.K. Gross Value Added Time Series under sudden shocks caused by the COVID pandemic arXiv:2303.07772

See Also

testforecast

Examples

#
# Generate simulated example
#
x <- tvar2sim()
#
# Work out which wavelet is best for forecasting this series
#
# Note: to speed up I also do:
#	library("parallel")
#	options(mc.cores=4)	# You have a four core machine, eg 
#	tmp <- which.wavelet.best(x, lapplyfn=mclapply)
#
# Note2: The following command can take a few minutes to run, even on
#	a fairly recent (2013) machine. You can speed it up by using
#	parallel execution as noted above, or by reducing go.back or
#	by reducing n.to.test, and also shortening the time series x to
#	more recent values. However, you need to be careful if you shorten
#	x too much then you are not basing the best wavelet decision on the
#	right time series. Similarly, by reducing go.back you are not
#	insuring your answer across runs across many internal forecasts. 
#
if (FALSE) tmp <- which.wavelet.best(x)
#
# Print out what the result was:
#
if (FALSE) print(tmp)
#   filter.number      family       mse    min.mse
#1              1 DaubExPhase 0.2139173 <- Min MSE
#2              2 DaubExPhase 0.5040532           
#3              3 DaubExPhase 0.4064091           
#4              4 DaubExPhase 0.3077695           
#5              5 DaubExPhase 0.3706422           
#6              6 DaubExPhase 0.6617254           
#7              7 DaubExPhase 0.5477581           
#8              8 DaubExPhase 0.6881407           
#9              9 DaubExPhase 0.5514298           
#10            10 DaubExPhase 0.5551846           
#11             4 DaubLeAsymm 0.3134285           
#12             5 DaubLeAsymm 0.3910101           
#13             6 DaubLeAsymm 0.7480980           
#14             7 DaubLeAsymm 0.5700830           
#15             8 DaubLeAsymm 0.5661297           
#16             9 DaubLeAsymm 0.5689345           
#17            10 DaubLeAsymm 0.5580267