MDM.selection {multDM}

Selects Models with Outstanding Predictive Ability basing on Multivariate Diebold-Mariano Test.

Description

This function selects models with outstanding predictive ability basing on multivariate Diebold-Mariano test MDM.test.

Usage

MDM.selection(realized,evaluated,q,alpha,statistic="Sc",loss.type="SE")

Arguments

realized

vector of the real values of the modelled time-series

evaluated

matrix of the forecasts, columns correspond to time index, rows correspond to different models

q

numeric indicating a lag length beyond which we are willing to assume that the autocorrelation of loss differentials is essentially zero

alpha

numeric indicating a significance level for multivariate Diebold-Mariano tests

statistic

statistic="S" for the basic version of the test, and statistic="Sc" for the finite-sample correction, if not specified statistic="Sc" is used

loss.type

method to compute the loss function, loss.type="SE" will use squared errors, loss.type="AE" will use absolute errors, loss.type="SPE" will use squred proportional error (useful if errors are heteroskedastic), loss.type="ASE" will use absolute scaled error, if loss.type will be specified as some numeric, then the function of type exp(loss.type*errors)-1-loss.type*errors will be used (useful when it is more costly to underpredict realized than to overpredict), if not specified loss.type="SE" is used

Value

class MDM object, list of

outcomes

matrix with mean losses for the selected models, statistics corresponding to losses differentials and ranking of these statistics

p.value

numeric of p-value from the procedure, i.e., p-value of multivariate Diebold-Mariano test from the last step

alpha

alpha, i.e., the chosen significance level

eliminated

numeric indicating the number of eliminated models

References

Mariano R.S., Preve, D., 2012. Statistical tests for multiple forecast comparison. Journal of Econometrics 169, 123–130.

Examples

data(MDMforecasts)
ts <- MDMforecasts$ts
forecasts <- MDMforecasts$forecasts
MDM.selection(realized=ts,evaluated=forecasts,q=10,alpha=0.1,statistic="S",loss.type="AE")