forecTheta-Package {forecTheta}

Forecasting Time Series by Theta Models

Description

In this package we implement functions for forecast univariate time series using the several Theta Models (Fiorucci et al, 2015 and 2016) and the Standard Theta Method of Assimakopoulos and Nikolopoulos (2000).

Details

Package:	forecTheta
Type:	Package
Version:	2.6.2
Date:	2022-11-11
License:	GPL (>=2.0)

dotm(y, h)

stheta(y, h)

errorMetric(obs, forec, type = "sAPE", statistic = "M")

groe(y, forecFunction = ses, g = "sAPE", n1 = length(y)-10)

Author(s)

Jose Augusto Fiorucci, Francisco Louzada

Maintainer: Jose Augusto Fiorucci <[e-mail]>

References

Fiorucci J.A., Pellegrini T.R., Louzada F., Petropoulos F., Koehler, A. (2016). Models for optimising the theta method and their relationship to state space models, International Journal of Forecasting, 32 (4), 1151–1161, <doi:10.1016/j.ijforecast.2016.02.005>.

Fioruci J.A., Pellegrini T.R., Louzada F., Petropoulos F. (2015). The Optimised Theta Method. arXiv preprint, arXiv:1503.03529.

Assimakopoulos, V. and Nikolopoulos k. (2000). The theta model: a decomposition approach to forecasting. International Journal of Forecasting 16, 4, 521–530, <doi:10.1016/S0169-2070(00)00066-2>.

Tashman, L.J. (2000). Out-of-sample tests of forecasting accuracy: an analysis and review. International Journal of Forecasting, 16 (4), 437–450, <doi:10.1016/S0169-2070(00)00065-0>.

See Also

dotm, stheta, otm.arxiv, groe, rolOrig, fixOrig, errorMetric

Examples

##############################################################

y1 = 2+ 0.15*(1:20) + rnorm(20)
y2 = y1[20]+ 0.3*(1:30) + rnorm(30)
y =  as.ts(c(y1,y2))
out <- dotm(y, h=10)
summary(out)
plot(out)

out <- dotm(y=as.ts(y[1:40]), h=10)
summary(out)
plot(out)

out2 <- stheta(y=as.ts(y[1:40]), h=10)
summary(out2)
plot(out2)

### sMAPE metric
errorMetric(obs=as.ts(y[41:50]), forec=out$mean, type = "sAPE", statistic = "M")
errorMetric(obs=as.ts(y[41:50]), forec=out2$mean, type = "sAPE", statistic = "M")

### sMdAPE metric
errorMetric(obs=as.ts(y[41:50]), forec=out$mean, type = "sAPE", statistic = "Md")
errorMetric(obs=as.ts(y[41:50]), forec=out2$mean, type = "sAPE", statistic = "Md")

### MASE metric
meanDiff1 = mean(abs(diff(as.ts(y[1:40]), lag = 1)))
errorMetric(obs=as.ts(y[41:50]), forec=out$mean, type = "AE", statistic = "M") / meanDiff1
errorMetric(obs=as.ts(y[41:50]), forec=out2$mean, type = "AE", statistic = "M") / meanDiff1

#### cross validation (2 origins)
#groe( y=y, forecFunction = otm.arxiv, m=5, n1=40, p=2, theta=5)
#groe( y=y, forecFunction = stheta, m=5, n1=40, p=2)

#### cross validation (rolling origin evaluation)
#rolOrig( y=y, forecFunction = otm.arxiv, n1=40, theta=5)
#rolOrig( y=y, forecFunction = stheta, n1=40)