altf {fDMA}

Computes a Few Alternative Forecasts.

Description

It is necessary to compare a given forecast method with some alternative ones. This function computes selected forecast quality measures for a few selected forecast methods (which might be treated as alternative ones to Dynamic Model Averaging, Dynamic Model Selection, etc.).

Naive forecast (naive) is computed in a way that all forecasts are set to be the value of the last observation.

For rolling OLS forecast (roll. OLS) for the first periods (until the size of a window is obtained) are estimated through recursive OLS (rec. OLS).

Autoregressive models (AR(1) and AR(2)) are computed by ordinary least squares method.

Time-varying parameters models (TVP, TVP-AR(1) and TVP-AR(2)) are computed as tvp with V=1 and lambda=0.99.

Auto ARIMA (auto ARIMA) is computed as auto.arima.

ME (Mean Error), RMSE (Root Mean Squared Error), MAE (Mean Absolute Error), MPE (Mean Percentage Errror) and MAPE (Mean Absolute Percentage Error) are computed as accuracy. HR (Hit Ratio) is computed as hit.ratio.

Usage

altf(y,x,window=NULL,initial.period=NULL,d=NULL,f=NULL,fmod=NULL,c=NULL)

Arguments

y

numeric or a column matrix of a dependent variable

x

matrix of independent variables, different columns correspond to different independent variables

window

optional, numeric, a size of a rolling regression window (a number of observations), if not specified 10% of all observations are taken

initial.period

optional, numeric, a number of observation since which forecast quality measures are computed, if not specified the whole sample is used, i.e., initial.period=1, this argument also divides the sample into in-sample and out-of-sample for non-recursive methods (OLS, AR(1), AR(2), auto ARIMA)

d

optional, logical, a parameter used for HR (Hit Ratio) calculation, should be d=FALSE for level time-series and d=TRUE if time-series represent changes, if not specified d=FALSE

f

optional, logical vector, indicating which of alternative forecasts – naive, OLS, rec. OLS, roll. OLS, TVP, AR(1), AR(2), auto ARIMA, TVP-AR(1) and TVP-AR(2) – should be computed, if not specified f=c(rep(TRUE,10)), i.e., all alternative forecasts are computed

fmod

optional, class dma object, a model to be compared with alternative forecast

c

optional, logical, a parameter indicating whether constant is included in models, if not specified c=TRUE is used, i.e., constant is included

Value

class altf object, list of

$summary

matrix of forecast quality measures ordered by columns, forecast methods are ordered by rows

$y.hat

list of predicted values from all forecasting methods which were applied

$y

y, forecasted time-series

$coeff.

list of coefficients from all forecasting methods which were applied (for naive forecast they are not computed)

$p.val.

list of p-values for t-test of statistical significance for coefficients from all forecasting methods which were applied (for naive and TVP models they are not computed, and for auto ARIMA z-test is used)

See Also

plot.altf, print.altf, summary.altf, rec.reg, roll.reg, altf2, altf3, altf4.

Examples

wti <- crudeoil[-1,1]
drivers <- (lag(crudeoil[,-1],k=1))[-1,]
ld.wti <- (diff(log(wti)))[-1,]
ld.drivers <- (diff(log(drivers)))[-1,]

a1 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,initial.period=60)

# models where constant term is not included in modelled equations (if applicable)
a2 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,c=FALSE,initial.period=60)

# compute just selected models
fcomp <- c(TRUE,TRUE,TRUE,FALSE,FALSE,FALSE,TRUE,TRUE,TRUE,FALSE)
a3 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,initial.period=60)

m1 <- fDMA(y=ld.wti,x=ld.drivers,alpha=0.99,lambda=0.90,initvar=10)
a4 <- altf(y=ld.wti,x=ld.drivers,d=TRUE,f=fcomp,fmod=m1,initial.period=60)