Forecasting discrete valued low count time series

In the past, little emphasis has been placed on producing data coherent forecasts for discrete valued processes. In this paper the conditional median is suggested as a general method for producing coherent forecasts and is in contrast to the conventional conditional mean. When counts are low we suggest that the emphasis of the forecast method be changed from forecasting future values to forecasting the k-step-ahead conditional distribution. In practice, this usually depends on unknown parameters. We modify the distribution to account for estimation error in a coherent way. The ideas are exemplified by an analysis of Poisson Autoregressive model and of wage loss claims data.