# Modeling Count Time Series with tscount Package

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The example below shows how to estimate a simple univariate Poisson time series model with the tscount package. While the model estimation is straightforward and yeilds very similar parameter estimates to the ones generated with the acp package (https://statcompute.wordpress.com/2015/03/29/autoregressive-conditional-poisson-model-i), the prediction mechanism is a bit tricky.

1) For the in-sample and the 1-step-ahead predictions:

**yhat_[t] = beta0 + beta1 * y_[t – 1] + beta2 * yhat_[t – 1]**

2) For the out-of-sample predictions with the observed Y unavailable:

**yhat_[t] = beta0 + beta1 * yhat_[t – 1] + beta2 * yhat_[t – 1]**

library(tscount) mdl <- tsglm(cnt$y, model = list(past_obs = 1, past_mean = 1), distr = "poisson") summary(mdl) # tsglm(ts = cnt$y, model = list(past_obs = 1, past_mean = 1), # distr = "poisson") # # Coefficients: # Estimate Std. Error # (Intercept) 0.632 0.1774 # beta_1 0.350 0.0687 # alpha_1 0.184 0.1455 # Standard errors obtained by normal approximation. # # Link function: identity # Distribution family: poisson # Number of coefficients: 3 # Log-likelihood: -279.2738 # AIC: 564.5476 # BIC: 573.9195 ### in-sample prediction ### cnt$yhat <- mdl$fitted.values tail(cnt, 3) # y yhat # 166 1 0.8637023 # 167 3 1.1404714 # 168 6 1.8918651 ### manually check ### beta <- mdl$coefficients pv167 <- beta[1] + beta[2] * cnt$y[166] + beta[3] * cnt$yhat[166] # 1.140471 pv168 <- beta[1] + beta[2] * cnt$y[167] + beta[3] * cnt$yhat[167] # 1.891865 ### out-of-sample prediction ### oot <- predict(mdl, n.ahead = 3) # [1] 3.080667 2.276211 1.846767 ### manually check ### ov2 <- beta[1] + beta[2] * oot[[1]][1] + beta[3] * oot[[1]][1] # 2.276211 ov3 <- beta[1] + beta[2] * oot[[1]][2] + beta[3] * oot[[1]][2] # 1.846767

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