Rlgt-package: Getting started with the Rlgt package
In Rlgt: Bayesian Exponential Smoothing Models with Trend Modifications
Rlgt-package R Documentation
Getting started with the Rlgt package
Description
An implementation of Bayesian ETS models named
LGT (for non-seasonal time series data) and SGT (for seasonal time series data).
These models have been tested on the M3 competition dataset in which they
outperform all of the models originally participating in the competition.
Getting started
The best way to get started with the package is to have a look at the vignettes and the various demos that ship with the package.
There is a vignette with examples of how to use the various methods included in the package, and a vignette that discusses some of the
theoretical background.
As to the demos, you can find their source code in the "demo" subfolder in the package sources (available on CRAN).
There are some basic demos and other more advanced ones that run on subsets of the M3 dataset and run potentially for hours.
The package contains models for seasonal and non-seasonal data, allows for external regressors, and different
error distributions. In the following, we briefly also present some of the theoretical background of the methods.
LGT (Local and Global Trend)
The LGT model is constructed based on Holt’s linear trend method.
The model is designed to allow for a more general term of error by allowing
for heteroscedasticity and an addition of constant "global" trend in the model.
Model Equations
In terms of mathematical notation, the model can be fully represented as follows:
y_{t+1} \sim Student (\nu,y_{t+1}, \sigma _{t+1}) \quad (eq.1.1)
\widehat{y}_{t+1}=l_{t}+ \gamma l_{t}^{ \rho }+ \lambda b_{t} \quad (eq. 1.2)
l_{t+1}= \alpha y_{t+1}+ \left( 1- \alpha \right) \left( l_{t} \right) \quad (eq. 1.3)
b_{t+1}= \beta \left( l_{t+1}-l_{t} \right) + \left( 1- \beta \right) b_{t} \quad (eq. 1.4)
\widehat{\sigma}_{t+1}= \sigma l_{t}^{ \tau}+ \xi \quad (eq. 1.5)
Notations
y_{t}value of the dependent variable of interest at time t
\widehat{y}_{t+1}forecasted value of y at time t+1 given information up to time t
\widehat{\sigma}_{t+1}forecasted deviation at time t+1 given information up to time t
l_{t}level at time t
b_{t}local trend at time t
Parameters
\nudegrees of freedom of the t-distribution
\gammacoefficient of the global trend
\rhopower coefficient of the global trend
\lambdadamping coefficient of the local trend
\alphasmoothing parameter for the level term
\betasmoothing parameter for the local trend term
\sigmacoefficient of the size of error function
\taupower coefficient of the size of error function
\xibase or minimum value of the size of error function
SGT (Seasonal, Global Trend)
The SGT model was designed as a seasonal counterpart to the LGT model.
Similar to LGT, this model is devised to allow for a global trend term and heteroscedastic error.
Model Equations
y_{t+1} \sim Student \left( \nu,\widehat{y}_{t+1}, \sigma _{t+1} \right) \quad (eq. 2.1)
\widehat{y}_{t+1}= \left( l_{t}+ \gamma l_{t}^{ \rho } \right) s_{t+1} \quad (eq. 2.2)
l_{t+1}= \alpha \frac{y_{t+1}}{s_{t+1}}+ \left( 1- \alpha \right) \left( l_{t} \right) \quad (eq. 2.3)
s_{t+m+1}= \zeta \frac{y_{t+1}}{l_{t+1}}+ \left( 1- \zeta \right) s_{t+1} \quad (eq. 2.4)
\widehat{\sigma}_{t+1}= \sigma \widehat{y}_{t+1}^{ \tau}+ \xi \quad (eq. 2.5)
Additional Notations
s_{t}seasonality factor at time t
m number of seasons in the data (e.g. 12 for monthly, 4 for quarterly)
Additional Parameters
\zetasmoothing parameter for the seasonality terms
S2GT (Double Seasonal, Global Trend)
S2GT is designed as an extension to SGT for time series data which exhibit two seasonality patterns.
Model Equations
y_{t+1} \sim Student \left( \nu,\widehat{y}_{t+1}, \sigma _{t+1} \right) \quad (eq. 3.1)
\widehat{y}_{t+1}=\left( l_{t}+ \gamma l_{t}^{ \rho } \right) s_{t+1}w_{t+1} \quad (eq. 3.2)
l_{t}= \alpha \frac{y_{t}}{s_{t}w_{t}}+ \left( 1- \alpha \right) \left( l_{t-1} \right) \quad (eq. 3.3)
s_{t+m}= \zeta \frac{y_{t}}{l_{t}w_{t}}+ \left( 1- \zeta \right) s_{t} \quad (eq. 3.4)
w_{t+d}= \delta \frac{y_{t}}{l_{t}s_{t}}+ \left( 1- \delta \right) w_{t} \quad (eq. 3.5)
\widehat{\sigma} _{t+1}= \sigma y_{t+1}^{ \tau}+ \xi \quad (eq. 3.6)
Additional Notations
w_{t}second seasonality factor prevailing at time t
dnumber of (second) seasons in a complete period (e.g. 12 for monthly, 4 for quarterly)
Additional Parameters
\deltasmoothing parameters for the second seasonality factors
NA
The best way to get started with the package is to have a look at the vignettes and the various demos that ship with the package.
There is a vignette with examples of how to use the various methods included in the package, and a vignette that discusses some of the
theoretical background.
As to the demos, you can find their source code in the "demo" subfolder in the package sources (available on CRAN).
There are some basic demos and other more advanced ones that run on subsets of the M3 dataset and run potentially for hours.
The package contains models for seasonal and non-seasonal data, allows for external regressors, and different
error distributions. In the following, we briefly also present some of the theoretical background of the methods.
Rlgt documentation built on Sept. 16, 2023, 1:08 a.m.
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| Rlgt-package | R Documentation |
Getting started with the Rlgt package
Description
An implementation of Bayesian ETS models named LGT (for non-seasonal time series data) and SGT (for seasonal time series data). These models have been tested on the M3 competition dataset in which they outperform all of the models originally participating in the competition.
Getting started
The best way to get started with the package is to have a look at the vignettes and the various demos that ship with the package. There is a vignette with examples of how to use the various methods included in the package, and a vignette that discusses some of the theoretical background.
As to the demos, you can find their source code in the "demo" subfolder in the package sources (available on CRAN). There are some basic demos and other more advanced ones that run on subsets of the M3 dataset and run potentially for hours.
The package contains models for seasonal and non-seasonal data, allows for external regressors, and different error distributions. In the following, we briefly also present some of the theoretical background of the methods.
LGT (Local and Global Trend)
The LGT model is constructed based on Holt’s linear trend method. The model is designed to allow for a more general term of error by allowing for heteroscedasticity and an addition of constant "global" trend in the model.
Model Equations
In terms of mathematical notation, the model can be fully represented as follows:
y_{t+1} \sim Student (\nu,y_{t+1}, \sigma _{t+1}) \quad (eq.1.1)
\widehat{y}_{t+1}=l_{t}+ \gamma l_{t}^{ \rho }+ \lambda b_{t} \quad (eq. 1.2)
l_{t+1}= \alpha y_{t+1}+ \left( 1- \alpha \right) \left( l_{t} \right) \quad (eq. 1.3)
b_{t+1}= \beta \left( l_{t+1}-l_{t} \right) + \left( 1- \beta \right) b_{t} \quad (eq. 1.4)
\widehat{\sigma}_{t+1}= \sigma l_{t}^{ \tau}+ \xi \quad (eq. 1.5)
Notations
y_{t}value of the dependent variable of interest at time t
\widehat{y}_{t+1}forecasted value of y at time t+1 given information up to time t
\widehat{\sigma}_{t+1}forecasted deviation at time t+1 given information up to time t
l_{t}level at time t
b_{t}local trend at time t
Parameters
\nudegrees of freedom of the t-distribution
\gammacoefficient of the global trend
\rhopower coefficient of the global trend
\lambdadamping coefficient of the local trend
\alphasmoothing parameter for the level term
\betasmoothing parameter for the local trend term
\sigmacoefficient of the size of error function
\taupower coefficient of the size of error function
\xibase or minimum value of the size of error function
SGT (Seasonal, Global Trend)
The SGT model was designed as a seasonal counterpart to the LGT model. Similar to LGT, this model is devised to allow for a global trend term and heteroscedastic error.
Model Equations
y_{t+1} \sim Student \left( \nu,\widehat{y}_{t+1}, \sigma _{t+1} \right) \quad (eq. 2.1)
\widehat{y}_{t+1}= \left( l_{t}+ \gamma l_{t}^{ \rho } \right) s_{t+1} \quad (eq. 2.2)
l_{t+1}= \alpha \frac{y_{t+1}}{s_{t+1}}+ \left( 1- \alpha \right) \left( l_{t} \right) \quad (eq. 2.3)
s_{t+m+1}= \zeta \frac{y_{t+1}}{l_{t+1}}+ \left( 1- \zeta \right) s_{t+1} \quad (eq. 2.4)
\widehat{\sigma}_{t+1}= \sigma \widehat{y}_{t+1}^{ \tau}+ \xi \quad (eq. 2.5)
Additional Notations
s_{t}seasonality factor at time t
mnumber of seasons in the data (e.g. 12 for monthly, 4 for quarterly)
Additional Parameters
\zetasmoothing parameter for the seasonality terms
S2GT (Double Seasonal, Global Trend)
S2GT is designed as an extension to SGT for time series data which exhibit two seasonality patterns.
Model Equations
y_{t+1} \sim Student \left( \nu,\widehat{y}_{t+1}, \sigma _{t+1} \right) \quad (eq. 3.1)
\widehat{y}_{t+1}=\left( l_{t}+ \gamma l_{t}^{ \rho } \right) s_{t+1}w_{t+1} \quad (eq. 3.2)
l_{t}= \alpha \frac{y_{t}}{s_{t}w_{t}}+ \left( 1- \alpha \right) \left( l_{t-1} \right) \quad (eq. 3.3)
s_{t+m}= \zeta \frac{y_{t}}{l_{t}w_{t}}+ \left( 1- \zeta \right) s_{t} \quad (eq. 3.4)
w_{t+d}= \delta \frac{y_{t}}{l_{t}s_{t}}+ \left( 1- \delta \right) w_{t} \quad (eq. 3.5)
\widehat{\sigma} _{t+1}= \sigma y_{t+1}^{ \tau}+ \xi \quad (eq. 3.6)
Additional Notations
w_{t}second seasonality factor prevailing at time t
dnumber of (second) seasons in a complete period (e.g. 12 for monthly, 4 for quarterly)
Additional Parameters
\deltasmoothing parameters for the second seasonality factors
NA
The best way to get started with the package is to have a look at the vignettes and the various demos that ship with the package. There is a vignette with examples of how to use the various methods included in the package, and a vignette that discusses some of the theoretical background.
As to the demos, you can find their source code in the "demo" subfolder in the package sources (available on CRAN). There are some basic demos and other more advanced ones that run on subsets of the M3 dataset and run potentially for hours.
The package contains models for seasonal and non-seasonal data, allows for external regressors, and different error distributions. In the following, we briefly also present some of the theoretical background of the methods.
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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