Modeling time series with zero observations

We consider situations in which a significant proportion of observations in a time series are zero, but the remaining observations are positive and measured on a continuous scale. We propose a new dynamic model in which the conditional distribution of the observations is constructed by shifting a distribution for non-zero observations to the left and censoring negative values. The key to generalizing the censoring approach to the dynamic case is to have (the logarithm of) the location/scale parameter driven by a filter that depends on the score of the conditional distribution. An exponential link function ∗Corresponding author. Email: [email protected]. 1 means that seasonal effects can be incorporated into the model and this is done by means of a cubic spline (which can potentially be timevarying). The model is fitted to daily rainfall in northern Australia and compared with a dynamic zero-augmented model.