tsgc (version 0.0)

SSModelDynGompertzReinit-class: Class for re-initialised dynamic Gompertz curve model

Description

This class allows the implementation of the reinitialisation procedure described in the vignette and summarised below. Let \(t=r\) denote the re-initialization date and \(r_0\) denote the date at which the cumulative series is set to 0. As the growth rate of cumulative cases is defined as \(g_t\equiv \frac{y_t}{Y_{t-1}}\), we have: $$\ln g_t = \ln y_t - \ln Y_{t-1} \;\;\;\; t=1, \ldots, r$$ $$\ln g_t^r = \ln y_t - \ln Y_{t-1}^r \;\;\;\; t=r+1, \ldots, T$$ $$Y_{t}^{r}=Y_{t-1}^{r}+y_{t} \;\;\;\; t=r,\ldots,T$$ where \(Y_{t}^{r}\) is the cumulative cases after re-initialization. We choose to set the cumulative cases to zero at \(r_0=r-1, Y_{r-1}^{r}=0\), such that the growth rate of cumulative cases is available from \(t=r+1\) onwards. We reinitialise the model by specifying the prior distribution for the initial states appropriately. See the vignette for details.

Methods

• new(Y, q = NULL, reinit.date=NULL, original.results=NULL, use.presample.info=TRUE) Create an instance of the SSModelDynGompertzReinit class.

  Parameters

  • Y The cumulated variable.

  • q The signal-to-noise ratio (ratio of slope to irregular variance). Defaults to 'NULL', in which case no signal-to-noise ratio will be imposed. Instead, it will be estimated.

  • reinit.date The reinitialisation date \(r\). Should be specified as an object of class "Date". Must be specified.

  • original.results Rather than re-estimating the model up to the reinit.date, a FilterResults class object can be specified here and the parameters for the reinitialisation will be taken from this object. Default is NULL. This parameter is optional.

  • use.presample.info Logical value denoting whether or not to use information from before the reinitialisation date in the reinitialisation procedure. Default is TRUE. If FALSE, the model is estimated from scratch from the reinitialisation date and no attempt to use information from before the reinitialisation date is made.

• get_model(y, q=NULL, sea.type = NULL, sea.period) Retrieves the model object, which is a dynamic Gompertz curve model reinitialised at self$reinit.date.

  Parameters

  • y The cumulated variable.

  • q The signal-to-noise ratio (ratio of slope to irregular variance). Defaults to 'NULL', in which case no signal-to-noise ratio will be imposed. Instead, it will be estimated.

  • sea.type Seasonal type. Options are 'trigonometric' and 'none'. 'trigonometric' will yield a model with a trigonometric seasonal component and 'none' will yield a model with no seasonal component.

  • sea.period The period of seasonality. For a day-of-the-week effect with daily data, this would be 7. Not required if sea.type = 'none'.

  Return Value

  KFS model object.

Examples

library(tsgc)
data(gauteng,package="tsgc")
idx.est <- zoo::index(gauteng) <= as.Date("2021-05-20")

# Specify a model
model.reinit <- SSModelDynGompertzReinit$new(Y = gauteng[idx.est], q = 0.005,
  reinit.date = as.Date("2021-04-29"))
# Estimate a specified model
res.reinit <- model.reinit$estimate()

## Alternatively, we could feed in a prior results object rather than a
## reinitialisation date. The results are identical to the above.

# Specify initial model
idx.orig <- zoo::index(gauteng) <= as.Date("2021-04-29")
model.orig <- SSModelDynamicGompertz$new(Y = gauteng[idx.orig], q = 0.005)
res.orig <- model.orig$estimate()
# Estimate a specified model
model.reinit2 <- SSModelDynGompertzReinit$new(Y = gauteng[idx.est],
q = 0.005, reinit.date = as.Date("2021-04-29"), original.results = res.orig)
res.reinit2 <- model.reinit2$estimate()