MDM.test {multDM}

Computes Multivariate Diebold-Mariano Test for the Equal Predictive Accuracy of Two or More Non-nested Forecasting Models.

Description

This function computes multivariate Diebold-Mariano test for the equal predictive accuracy of two or more non-nested forecasting models. The null hypothesis of this test is that the evaluated forecasts have the same accuracy. The alternative hypothesis is that Equal predictive accuracy (EPA) does not hold.

Usage

MDM.test(realized,evaluated,q,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

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 htest object, list of

statistic

test statistic

parameter

q, a lag length

alternative

alternative hypothesis of the test

p.value

p-value

method

name of the test

data.name

names of the tested objects

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.test(realized=ts,evaluated=forecasts,q=10,statistic="S",loss.type="AE")