mapafor {MAPA}

MAPA Forecast

Description

The following function produces in- and out-of-sample MAPA forecasts, for multiple steps ahead. This is the recommended function to use in forecasting with MAPA.

Usage

mapafor(y, mapafit, fh = -1, ifh = 1, 
        comb = c("w.mean","w.median","mean","median","wght"), 
        outplot = c(0,1), hybrid = c(TRUE, FALSE), 
        conf.lvl = NULL, xreg=NULL)

Arguments

y

In sample observations of a time series (vector).

mapafit

Fitted MAPA model (from mapaest).

fh

Forecast horizon. Default = ppy.

ifh

In-sample forecast horizon. Default = 0.

comb

Combination operator. This can be: "mean"; "median"; "wght" - where each aggregation level is weighted inversly to aggregation; "w.mean" - level and trend components are averaged, but seasonal and xreg follow the wght combination; "w.median" - as w.mean, but with median. It is suggested that for data with high sampling frequency to use one of the "w.mean" and "w.median".

outplot

Provide output plot. 0 = no; 1 = yes. Default is 1.

hybrid

Provide hybrid forecasts, as in Kourentzes et al. paper. If minimumAL > 1 then the minimumAL ETS forecasts are used. Default is TRUE.

conf.lvl

Vector of confidence level for prediction intervals. Values must be (0,1). If conf.lvl == NULL then no intervals are calculated. For example to get the intervals for 80% and 95% use conf.lvl=c(0.8,0.95).

xreg

Vector or matrix of exogenous variables to be included in the MAPA. If matrix then rows are observations and columns are variables. Must be at least as long as in-sample plus fh. Additional observations are unused.

Value

infor

In-sample forecasts.

outfor

Out-of-sample forecasts.

PI

Prediction intervals for given confidence levels.

MSE

In-sample MSE error.

MAE

In-sample MAE error.

Note

The calculation of the prediction intervals is based on the empirical multiple step ahead MSE. To speed up calculations set conf.lvl=NULL. If very long forecast horizons are requested then once no more t+h MSE can be calculated the following approximation is used: \sqrt{MSE_{t+1}}*\sqrt{h} for the error.

Author(s)

Nikolaos Kourentzes, [e-mail]; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapa, mapaest, mapacalc.

Examples

mapafit <- mapaest(admissions,outplot=0)
out <- mapafor(admissions,mapafit)