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Article

Generalized Binary Time Series Models

1
Faculty of Statistics, TU Dortmund University, D-44221 Dortmund, Germany
2
Mathematical Institute, University of Mannheim, D-68131 Mannheim, Germany
*
Author to whom correspondence should be addressed.
Econometrics 2019, 7(4), 47; https://doi.org/10.3390/econometrics7040047
Received: 21 June 2019 / Revised: 1 December 2019 / Accepted: 9 December 2019 / Published: 14 December 2019
(This article belongs to the Special Issue Discrete-Valued Time Series: Modelling, Estimation and Forecasting)
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. View Full-Text
Keywords: binary time series; autoregressive-moving average; autocovariance structure; Yule–Walker equations; stationarity binary time series; autoregressive-moving average; autocovariance structure; Yule–Walker equations; stationarity
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MDPI and ACS Style

Jentsch, C.; Reichmann, L. Generalized Binary Time Series Models. Econometrics 2019, 7, 47. https://doi.org/10.3390/econometrics7040047

AMA Style

Jentsch C, Reichmann L. Generalized Binary Time Series Models. Econometrics. 2019; 7(4):47. https://doi.org/10.3390/econometrics7040047

Chicago/Turabian Style

Jentsch, Carsten, and Lena Reichmann. 2019. "Generalized Binary Time Series Models" Econometrics 7, no. 4: 47. https://doi.org/10.3390/econometrics7040047

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