forecTheta-Package: 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 \& Nikolopoulos (2000). Moreover, it is including a function for compute the main errors metrics used in time series forecasting and a function for compute the Generalised Rolling Origin Evaluation, which contain as particular cases the Rolling Origin Evaluation and the Fixed Origin Evaluation of Tashman (2000).

Arguments

Author

Jose Augusto Fiorucci, Francisco Louzada and Bao Yiqi

Maintainer: Jose Augusto Fiorucci <jafiorucci@gmail.com>

Details

Package:	forecTheta
Type:	Package
Version:	2.2
Date:	2016-05-25
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)

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. Accepted Paper. https://www.researchgate.net/publication/294420765_Models_for_optimising_the_theta_method_and_their_relationship_to_state_space_models

Fiorucci J.A., Pellegrini T.R., Louzada F., Petropoulos F. (2015). The Optimised Theta Method. Free available at http://arxiv.org/abs/1503.03529 .

Assimakopoulos, V. and Nikolopoulos k. (2000). The theta model: a decomposition approach to forecasting. International Journal of Forecasting 16, 4, 521--530.

Tashman, L.J. (2000). Out-of-sample tests of forecasting accuracy: an analysis and review. International Journal of Forecasting 16 (4), 437--450.

Examples

Run this code


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

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)