Ordinal Time Series: Modeling, Forecasting and Control

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An ordinal time series is a temporal sequence of discrete-valued observations, the range of which is qualitative and consists of a finite number of ordered categories. Ordinal time series arise in many different situations in economics and related fields. They can have various forms with respect to their dependence structure or their marginal distribution. These characteristics can be worked out by using analytical tools that have been recently developed for ordinal time series. Afterwards, an adequate modeling of the ordinal time series would be necessary, which could be used as a base for the forecasting of the time series or for the statistical control of its further course. This is the starting point of the planned research project, because neither for modeling nor for forecasting or controlling ordinal time series, there has been a sufficient repertoire of tailor-made methods to date. Instead, approaches for nominal time series are mostly used (which then, however, disregard the natural ordering of the categories), or those for quantitative time series (which then, however, implicitly assume a metric structure). The aim of the planned research project is to develop a comprehensive package of methods for the stochastic modeling, forecasting and control of ordinal time series. In this context, existing procedures are to be taken up, and the areas that are still open are to be closed by novel own contributions. The first step would be to develop a toolbox of as diverse models as possible, covering a wide range of stochastic properties. For all resulting model types, in addition to the actual model definition and the stochastic model properties, the question of model fitting (identification, estimation, validation) must always be considered. This would be followed by the sub-projects on forecasting and control, which should already incorporate the newly developed models. Concerning forecasting, adequate criteria for assessing the quality of prediction shall be derived (i.e., which account for the ordinal nature of the data) in order to then use them to empirically investigate the performance of the various forecast approaches (point, interval and PMF predictions) in detail. With regard to monitoring, control charts for serially dependent ordinal processes are to be developed and analyzed, where, in addition to sample-based charts, the focus is primarily on memory-type individuals charts, which have been completely lacking in the literature to date. For all proposed methods, the performance and applicability will investigated in detail, both through comprehensive comparative simulation studies and through the application to real-world data examples being relevant in economics.