gum() - Generalised Univariate Model
In smooth: Forecasting Using State Space Models

knitr::opts_chunk$set(fig.width=6, fig.height=4, fig.path='Figs/', fig.show='hold',
                      warning=FALSE, message=FALSE)

gum() constructs Generalised Exponential Smoothing - pure additive state-space model. It is a part of smooth package.

Let's load the necessary packages:

require(smooth)

Generalised Exponential Smoothing is a next step from CES. It is a state-space model in which all the matrices and vectors are estimated. It is very demanding in sample size, but is also insanely flexible.

A simple call by default constructs GUM$(1^1,1^m)$, where $m$ is frequency of the data. So for our example with AirPassengers data, we will have GUM$(1^1,1^{12})$:

gum(AirPassengers, h=18, holdout=TRUE)

But some different orders and lags can be specified. For example:

gum(AirPassengers, h=18, holdout=TRUE, orders=c(2,1), lags=c(1,12))

Function auto.gum() is now implemented in smooth, but it works slowly as it needs to check a large number of models:

auto.gum(AirPassengers, interval=TRUE, silent=FALSE)

In addition to standard values that other functions accept, GUM accepts predefined values for transition matrix, measurement and persistence vectors. For example, something more common can be passed to the function:

    transition <- matrix(c(1,0,0,1,1,0,0,0,1),3,3)
    measurement <- c(1,1,1)
    gum(AirPassengers, h=18, holdout=TRUE, orders=c(2,1), lags=c(1,12), transition=transition, measurement=measurement)

The resulting model will be equivalent to ETS(A,A,A). However due to different initialisation of optimisers and different method of number of parameters calculation, gum() above and es(y, "AAA", h=h, holdout=TRUE) will lead to different models.