forecTheta-package: Forecasting Time Series by Theta Models

In forecTheta: Forecasting Time Series by Theta Models

Forecasting Time Series by Theta Models

Description

This package provides functions for forecasting univariate time series using several Theta models, originally proposed by Assimakopoulos and Nikolopoulos (2000) and later extended by Fiorucci et al. (2016). This version also includes implementations of bagging methods, based on the work of Bergmeir et al. (2016), applied to the DOTM, DSTM, OTM, and STM models.

Details

Package:	forecTheta
Type:	Package
Version:	3.0
Date:	2025-05-20
License:	GPL (>=2.0)

dotm(y, h)

bagged_dotm(y, h)

stheta(y, h)

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

PI_eval(obs, forec, lower_bounds, upper_bounds, name = c("MSIS", "ACD"), alpha = 0.05)

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

Author(s)

Jose Augusto Fiorucci, Francisco Louzada, Igor De Oliveira Barros Faluhelyi.

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

References

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>.

Bergmeir, C., Hyndman, R.J. and Benítez, J. M. (2016). Bagging exponential smoothing methods using STL decomposition and Box–Cox transformation. International journal of forecasting 32 (2), 303–312, <doi:10.1016/j.ijforecast.2015.07.002>.

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.

Gneiting, T. and Raftery, A.E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102 (477), 359–378, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/016214506000001437")}.

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

out3 <- stheta(y=as.ts(y[1:40]), h=10)
summary(out3)
plot(out3)

### 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")
errorMetric(obs=as.ts(y[41:50]), forec=out3$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")
errorMetric(obs=as.ts(y[41:50]), forec=out3$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
errorMetric(obs=as.ts(y[41:50]), forec=out3$mean, type = "AE", statistic = "M") / meanDiff1

forecTheta documentation built on June 8, 2025, 10:02 a.m.