`R/model.R`

`fasster-model.Rd`

Implements FASSTER

FASSTER(formula, include = NULL, ...)

formula | An object of class "formula" (refer to 'Formula' for usage) |
---|---|

include | How many terms should be included to fit the model |

... | Not used |

Returns a mable containing the fitted FASSTER model.

The fasster model extends commonly used state space models by introducing a switching component to the measurement equation. This is implemented using a time-varying DLM with the switching behaviour encoded in the measurement matrix.

`fasster`

inherits the standard formula specification from `lm`

for specifying exogenous regressors, including interactions and `I()`

functionality as described in `formula`

.

Special DLM components can be specified using special functions defined below:

seas(s): Creates seasonal factors with seasonal period s

fourier(s, K): Creates seasonal fourier terms with seasonal period s and K harmonics

poly(n): Creates a polynomial of order n (poly(1) creates a level, poly(2) creates a trend)

ARMA(ar, ma): Creates ARMA terms with coefficient vectors ar and ma

custom(dlm): Creates a custom dlm structure, using

`dlm`

The switching operator, `%S%`

requires the switching factor variable on the LHS, and the model to switch over on the RHS (as built using the above components)

The model parameters are estimated using the following heuristic:

Filter the data using the specified model with non-zero state variances

Obtain smoothed states \((\theta^{(s)}t=\theta_t|D_T)\) to approximate correct behaviour

The initial state parameters taken from the first smoothed state: \(m_0=E(\theta^{(s)}_0)\), \(C_0=Var(\theta^{(s)}_0)\)

Obtain state noise variances from the smoothed variance of \(w_t\): \(W=Var(w^{(s)}_t)=Var(\theta^{(s)}_t-G\theta^{(s)}_{t-1})\) Obtain measurement noise variance from smoothed variance of \(v_t\): \(V=Var(v^{(s)}_t)=Var(y_t-F_t\theta^{(s)}_t)\)

Repair restricted state variances for seasonal factors and ARMA terms

#> # A mable: 2 x 2 #> # Key: key [2] #> key `FASSTER(mdeaths ~ fdeaths + poly(1) + trig(12))` #> <chr> <model> #> 1 fdeaths <FASSTER> #> 2 mdeaths <FASSTER>