I can calculate the motion of heavenly bodies but not the madness of people. -Isaac Newton

## Autoregressive Conditional Poisson Model – I

Modeling the time series of count outcome is of interest in the operational risk while forecasting the frequency of losses. Below is an example showing how to estimate a simple ACP(1, 1) model, e.g. Autoregressive Conditional Poisson, without covariates with ACP package.

```library(acp)

### acp(1, 1) without covariates ###
mdl <- acp(y ~ -1, data = cnt)
summary(mdl)
# acp.formula(formula = y ~ -1, data = cnt)
#
#   Estimate   StdErr t.value   p.value
# a 0.632670 0.169027  3.7430 0.0002507 ***
# b 0.349642 0.067414  5.1865 6.213e-07 ***
# c 0.184509 0.134154  1.3753 0.1708881

### generate predictions ###
f <- predict(mdl)
pred <- data.frame(yhat = f, cnt)
tail(pred, 5)
#          yhat y
# 164 1.5396921 1
# 165 1.2663993 0
# 166 0.8663321 1
# 167 1.1421586 3
# 168 1.8923355 6

### calculate predictions manually ###
pv167 <- mdl\$coef[1] + mdl\$coef[2] * pred\$y[166] + mdl\$coef[3] * pred\$yhat[166]
# [1] 1.142159

pv168 <- mdl\$coef[1] + mdl\$coef[2] * pred\$y[167] + mdl\$coef[3] * pred\$yhat[167]
# [1] 1.892336

plot.ts(pred, main = "Predictions")
```