apc.forecast.apc {apc}

Forecast models with APC structure.

Description

Computes forecasts for a model with APC structure. Forecasts of the linear predictor are given for all models. This is done for the triangle which shares age and cohort indices with the data.

Usage

apc.forecast.apc(apc.fit,extrapolation.type="I0",
suppress.warning=TRUE)

Arguments

apc.fit

List. Output from apc.fit.model. Note: apc.fit.model should be run with APC structure so that apc.fit$model.design=="APC". Point forecasts of the response are only provided for a Poisson response model where apc.fit$model.family=="poisson.response" and for an over-disperse Poisson response model where apc.fit$model.family=="od.poisson.response". For other models only point forecasts of the linear predictor are provided, that is the first two values linear.predictors.forecast and index.trap.J.

extrapolation.type

Character. Choices for extrapolating the differenced period parameter ("Delta.beta_per"). Default is "I0".

"I2"

Extrapolates future DDbeta by 0.

"I1"

Extrapolates future DDbeta as follows. Compute Dbeta=cumsum(DDbeta) for j=3,...,J. This determines Dbeta upto arbitrary level. Compute average mean(Dbeta). Forecast DDbeta[J+1]=mean(Dbeta)-Dbeta[J]. Forecast DDbeta[J+h]=0 for h>1. This forecast is invariant to arbitrary level.

"I0"

Extrapolates future DDbeta as follows. Compute beta=cumsum(cumsum(DDbeta)) for j=3,...,J. This determines beta upto arbitrary linear trend. Regress on 1 and demeaned trend=j-(n+1)/2 giving estimates mu1 and mu2. Forecast beta[J+1]=mu1 + mu2*(n+1-(n+1)/2). Forecast beta[J+2]=mu1 + mu2*(n+2-(n+1)/2). Forecast DDbeta[J+h]=beta[J+h]-2*beta[J+h-1]+beta[J+h-2] for h=1,2. Forecast DDbeta[J+h]=0 for h>2. This forecast is invariant to arbitrary linear trend.

All methods are invariant to ad hoc identification of the implied period time effect, by following the ideas put forward in Kuang, Nielsen and Nielsen (2008b).

suppress.warning

Logical. If true, suppresses warnings from apc.data.list.subset, which is called internally. Default is "TRUE".

Details

The example below is based on the smaller data reserving sets data.loss.TA.

Value

linear.predictors.forecast

Vector. Linear predictors for forecast area.

index.trap.J

Matrix. age-coh coordinates for vector. Similar structure to index.trap in apc.index, see apc.get.index.

trap.response.forecast

Matrix. Includes data and point forecasts. Forecasts in lower right triangle. Trapezoid format.

response.forecast.cell

Matrix. 4 columns. 1: Point forecasts. 2: corresponding forecast standard errors 3: process standard errors 4: estimation standard errors Note that the square of column 2 equals the sums of squares of columns 3 and 4 Note that index.trap.J gives the age-coh coordinates for each entry.

response.forecast.age

Same as response.forecast.cell, but point forecasts by age cumulated over period/cohort.

response.forecast.per

Same as response.forecast.cell, but point forecasts by per cumulated over age/cohort.

response.forecast.coh

Same as response.forecast.cell, but point forecasts by coh cumulated over age/period.

response.forecast.all

Same as response.forecast.cell, but point forecasts cumulated by age and coh.

xi.per.dd.extrapolated

The extrapolated double differences.

xi.extrapolated

The extrapolated parameters.

Author(s)

Bent Nielsen <[e-mail]> 10 Sep 2016

References

Kuang, D., Nielsen, B. and Nielsen, J.P. (2008b) Forecasting with the age-period-cohort model and the extended chain-ladder model. Biometrika 95, 987-991. Download: Article; Earlier version Nuffield DP.

See Also

The example below uses Taylor and Ashe reserving see data.loss.TA

Examples

#####################
#  EXAMPLE with reserving data: data.loss.TA()

data	<- data.loss.TA()
fit.apc	<- apc.fit.model(data,"poisson.response","APC")
forecast	<- apc.forecast.apc(fit.apc)

#	forecasts by "policy-year"
forecast$response.forecast.coh
#	         forecast
#	coh_2    91718.82
#	coh_3   464661.38
#	coh_4   704591.94
#	coh_5  1025337.23
#	coh_6  1503253.81
#	coh_7  2330768.44
#	coh_8  4115906.56
#	coh_9  4257958.30
#	coh_10 4567231.84
#	forecasts of "cash-flow"
forecast$response.forecast.per
#	        forecast
#	per_11 5274762.58
#	per_12 4213526.23
#	per_13 3188451.80
#	per_14 2210649.45
#	per_15 1644203.06
#	per_16 1236495.32
#	per_17  764552.75
#	per_18  444205.71
#	per_19   84581.44
#	forecast  of "total reserve"
forecast$response.forecast.all
#	    forecast
#	all 19061428