# apc.forecast.apc: Forecast models with APC structure. In apc: Age-Period-Cohort Analysis

## 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

 ```1 2``` ```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 <bent.nielsen@nuffield.ox.ac.uk> 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.

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35``` ```##################### # 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 ```

### Example output

```         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
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
all 19061428
```

apc documentation built on Oct. 23, 2020, 6:17 p.m.