Coping with Nonstationarity in Categorical Time Series

Monnie Mcgee,Ian Harris

doi:10.1155/2012/417393

Abstract

Categorical time series are time-sequenced data in which the values at each time point are categories rather than measurements. A categorical time series is considered stationary if the marginal distribution of the data is constant over the time period for which it was gathered and the correlation between successive values is a function only of their distance from each other and not of their position in the series. However, there are many examples of categorical series which do not fit this rather strong definition of stationarity. Such data show various nonstationary behavior, such as a change in the probability of the occurrence of one or more categories. In this paper, we introduce an algorithm which corrects for nonstationarity in categorical time series. The algorithm produces series which are not stationary in the traditional sense often used for stationary categorical time series. The form of stationarity is weaker but still useful for parameter estimation. Simulation results show that this simple algorithm applied to a DAR(1) model can dramatically improve the parameter estimates.

Highlights

We introduce an algorithm which corrects for nonstationarity in categorical time series
Categorical time series are serially correlated data for which an observation at a time point is recorded in terms of a state or a category
Since the probability of an El Niño year changes quite abruptly, it is clear that these data do not fit the definition of stationarity used in categorical time series

Summary

Introduction

Categorical time series are serially correlated data for which an observation at a time point is recorded in terms of a state or a category. Since the probability of an El Niño year changes quite abruptly, it is clear that these data do not fit the definition of stationarity used in categorical time series. The data exhibit clear signs of nonstationarity: the National League dominated until roughly the 1980s or 1990s, and the American League has dominated in the last twenty years or so Another example not shown is data dealing with geomagnetic reversals of the polarity of the earth from North polarity to South polarity 2. League Baseball’s All-Star game from 1950 to 2011

The Flipping Algorithm

Nonstationary Series and the Effect of the Flipping Algorithm

Weakly Stationary Categorical Time Series

Detrending the All-Star Data

Discussion