Functions for forecast univariate time series using the Dynamic Optimised Theta Model, Dynamic Standard Theta Model,
Optimised Theta Model and Standard Theta Model (Fiorucci et al, 2016).
We also provide an implementation for the Standard Theta Method (STheta) of Assimakopoulos and Nikolopoulos (2000).
If TRUE, the multiplicative seasonal decomposition is used.
If NULL and frequency(y)>=4 the time series is tested for statistically seasonal behaviour, with 90% of significance.
If s='additive' or close zero values been find in the multiplicative decomposition, the additive decomposition is performed hatter than multiplicative.
Default is NULL.
par_ini
Vector of initialization for (ell, alpha, theta) parameters.
estimation
If TRUE, the optim() function is consider for compute the minimum square estimator of parameters.
If FALSE, the models/methods are computed for par_ini values.
lower
The lower limit of parametric space.
upper
The upper limit of parametric space.
opt.method
The numeric optimisation method for optim() function.
Choose one among 'Nelder-Mead', 'L-BFGS-B', 'SANN'.
Details
By default (s=NULL), the 90% significance seasonal Z-test, used by Assimakopoulos and Nikolopoulos (2000), is applied for quarterly and monthly time series.
For details of each model see Fiorucci et al, 2016.
If you are looking for the methods presented in the arXiv paper (Fiorucci et al, 2015), see otm.arxiv() function.
Value
An object of thetaModel class with one list containing the elements:
$method
The name of the model/method
$y
The original time series.
$s
A binary indication for seasonal decomposition.
type
Classical seasonal decomposition type.
opt.method
The optimisation method used in the optim() function.
$par
The estimated values for (ell, alpha, theta) parameters
$weights
The estimated weights values.
$fitted
A time series element with the fitted points.
$residuals
A time series element with the residual points.
$mean
The forecasting values.
$level
The levels for prediction intervals.
$lower
Lower limits for prediction intervals.
$upper
Upper limits for prediction intervals.
$tests
The p.value of Teraesvirta Neural Network test applied on unseasoned time series and the p.value of Shapiro-Wilk test applied on unseasoned residuals.
Author(s)
Jose Augusto Fiorucci, Francisco Louzada and Bao Yiqi
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.