Beta seasonal autoregressive moving average models

Abstract

In this paper we introduce the class of beta seasonal autoregressive moving average (β SARMA) models for modeling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta autoregressive moving average models [Rocha and Cribari-Neto, Test, 2009] by incorporating seasonal dynamics to the model dynamic structure. Besides introducing the new class of models, we develop parameter estimation, hypothesis testing inference, and diagnostic analysis tools. We also discuss out-of-sample forecasting. In particular, we provide closed-form expressions for the conditional score vector and for the conditional Fisher information matrix.We also evaluate the finite sample performances of conditional maximum likelihood estimators and white noise tests using Monte Carlo simulations. An empirical application is presented and discussed.Univariate time series modeling is commonly used in many fields. Most conventional time series models are based on the Gaussianity assumption [1]. A well-known class of this linear models is the class of autoregressive integrated moving average models (ARIMA) [2]. However, it has been recognized that the Gaussian assumption is too restrictive for many applications [3]. As a consequence, there has been increased interest in non-Gaussian time series models [4]. Some models for discrete variate time series are considered in [5,6,7]. In [8] is proposed a quasi-likelihood approach to regression models for discrete and continuous time series. In [9] is focused on time series modeling under non-Gaussian innovations. Non-Gaussian time series models are considered as instantaneous transformations of Gaussian time series in [10,1]. Time series models based on generalized linear models (GLM) [11] are considered in [12,13,14,15]. Other important and recent works on non-Gaussian time series modeling are [16,17,3,18,19,20,4]. A comprehensive reference on general models for time series analysis is [21]. * F. M. Bayer is with the

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