forecast.fitiMoMo: Forecast mortality rates using an improvement rate model

In amvillegas/iMoMo: Mortality Improvement Rate Modelling

Description

Forecast mortaility improvment rates and mortality rates using the fit from a mortality improvement rate model. The period indexes are κ_t^{(i)}, i = 1,..N, are forecasted using integrated vector autoregressive model. The cohort index γ_{t-x} is forecasted using an ARIMA(p, d, q). By default an ARIMA(1, 1, 0) with a constant is used.

Usage

## S3 method for class 'fitiMoMo'
forecast(
  object,
  h = 50,
  kt.order = c(1, 0),
  kt.include.constant = TRUE,
  kt.include.trend = FALSE,
  gc.order = c(1, 0, 0),
  gc.include.constant = TRUE,
  jumpRates = NULL,
  kt.lookback = NULL,
  gc.lookback = NULL,
  ...
)

Arguments

object	an object of class "fitiMoMo" with the fitted parameters of an improvement rate mortality model.
h	number of years ahead to forecast.
kt.order	an optional vector indicating the order of autorregression and of differetiation of the VARI model. The two components (p, d) are the AR order and the degree of differencing.
kt.include.constant	a logical value indicating if the VARI model should include a constant value. The default is TRUE.
kt.include.trend	a logical value indicating if the VARI model should have a linear trend. The default is FALSE.
gc.order	a specification of the ARIMA model for the cohort effect: the three components (p, d, q) are the AR order, the degree of differencing, and the MA. The default is an ARIMA(1, 0, 0).
gc.include.constant	a logical value indicating if the ARIMA model should include a constant value. The default is TRUE.
jumpRates	optional vector of moratlity rates for the last year used as starting rates. for the projection. If it is not provided the rates from the the actual rates from the final year are used.
kt.lookback	optional argument to specify the look-back window to use in the estimation of the time series model for the period indexes. By default all the estimated values are used. If kt.lookback is provided then the last kt.lookback years of κ_t^{(i)}, i = 1,..N, are used.
gc.lookback	optional argument to specify the look-back window to use in the estimation of the ARIMA model for the cohort effect. By default all the estimated values are used in estimating the ARIMA model. If gc.lookback is provided then the last gc.lookback years of γ_{t-x} are used.
...	other arguments.

Details

The modelling of the period indexes kappa_t is done using a integrated vector autoregressive model of differencing order d and autorregressive order p:

Δ^d k_t = C+Dt+∑_{i=1}^p A_i Δ^d k_{t-i} + ε_t

where C and D are N-dimensional vectors for parameters and A_1,...,A_p are N\times N matrices of autoregressive parampeters. If kt.include.constant is TRUE then C is included in the equation. Similarly, if kt.include.trend is TRUE then D is included in the equation.

Fitting and forecasting of the VAR model is done using the fucntion simpleVAR2.

Fitting and forecasting of the ARIMA model for the cohort index is done with function Arima from package forecast. See the latter function for further details on input arguments gc.order and gc.include.constant.

Value

A list of class "foriMoMo" with components:

improvements	a matrix with the point forecast of the improvement rates.
rates	a matrix with the point forecast of the rates.
ages	vector of ages corresponding to the rows of improvements.
years	vector of years for which a forecast has been produced. This corresponds to the columns of improvements.

#'

kt.f	forecasts of period indexes of the model. This is a list with the model fitted to κ_t; the mean(central) forecast; and the years for which a forecast was produced. If the model does not have any age-period terms (i.e. N=0) this is set to NULL.

#'

gc.f	forecasts of cohort index of the model. This is a list with the model fitted to γ_c; the mean(point) forecast; and the cohorts for which a forecast was produced. If the model does not have a cohort effect this is set to NULL.

#'

fittedImprovements

a matrix with the fitted in-sample improvements of the model for the years for which the improvement rate model was fitted.

#'

model

the model fit from which the forecast was produced.

amvillegas/iMoMo documentation built on Sept. 18, 2020, 11:25 p.m.