Compositional and Count Time Series

Many series have natural constraints placed upon them which should be adhered to in both modeling and forecasting. Compositional time series are proportions or shares of a whole and must therefore be fractions that sum to one across the series for each observation. Thus, for example, any forecasts of future proportions must obey these constraints. An approach which transforms the series using log-ratios is recommended which naturally imposes these constraints. Some time series are recorded as, typically small, integers or counts and thus cannot be treated as continuous variables, as has been implicitly assumed throughout the book. To model and forecast such series "coherently", integer-autoregressive (IN-AR) models, typically with Poisson distributed innovations, can be used. Related time series are "intermittent"—those that contain long sequences of zeros—and nonnegative time series.