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Generalized Binary Time Series Models

Carsten Jentsch () and Lena Reichmann ()
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Carsten Jentsch: Faculty of Statistics, TU Dortmund University, D-44221 Dortmund, Germany
Lena Reichmann: Faculty of Statistics, TU Dortmund University, D-44221 Dortmund, Germany

Econometrics, 2019, vol. 7, issue 4, 1-26

Abstract: The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule–Walker equations hold that facilitate parameter estimation of gbAR models. Yule–Walker type equations are also derived for gbARMA processes.

Keywords: binary time series; autoregressive-moving average; autocovariance structure; Yule–Walker equations; stationarity (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2019
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