An Introduction to Discrete-Valued Time Series

Part IICategorical Time Series

The time series discussed in Part I had discrete and quantitative ranges, which allowed us to apply standard analytic tools used for real-valued time series analysis: the time series plot, the autocorrelation function, and many more. In the second part of this book, we consider another type of discrete-valued time series where we skip the second of the aforementioned assumptions. In other words, the time series now exhibit a qualitative range consisting of a finite number of categories (including the special case of a binary time series). In some applications, the categorical range exhibits at least a natural ordering; that is, it is ordinal. Otherwise, if not even such an inherent ordering exists, the range is said to be nominal. In particular, a nominal range implies a number of difficulties when trying to analyze the time series: completely different measures of dispersion or serial dependence have to be developed, and a visualization of the time series is quite demanding; see Chapter 6.

In addition, the modeling of categorical processes requires new approaches; see Chapter 7. The previously discussed INARMA and INGARCH models cannot be applied, but it is possible to adapt NDARMA models to the categorical case, thus offering some kind of counterpart to conventional ARMA models. The serial dependence structure of these discrete ARMA models, which cannot be expressed in terms of the autocorrelation function (since the range is qualitative), shows ...