Time series models with asymmetric Laplace innovations

Trindade, A. Alexandre; Zhu, Yun; Andrews, Beth

doi:10.1080/00949650903071088

Cited by 24 publications

(9 citation statements)

References 26 publications

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“…However, in many applications, the assumption of normality might be unrealistic, especially for highly skewed or sharply peaked data. For a stationary autoregressive model, although maximizing a Gaussian likelihood results in consistent and asymptotically normal parameter estimates under the assumption that the innovations are independent and identically distributed but not necessarily normal, it is known that the estimates are not efficient in general unless the innovations are normal (Brockwell and Davis, 1991;Trindade et al, 2010). Accordingly, the normality assumption on AD or PAC models may also result in inefficient estimation and lead to incorrect inference when the data depart from normality.…”

Section: Antedependence Models Of Longitudinal Datamentioning

confidence: 99%

Antedependence Models for Skewed Continuous Longitudinal Data

Chang¹

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A special thanks to my family. Words can not express how grateful I am to my parents for all of the sacrifices that you've made on my behalf. Your prayer for me was what sustained me thus far. I would also like to thank to my beloved husband, Dr. Tai-Hsuan Wu. Thank you for supporting me for everything, and especially I can thank you enough for encouraging me throughout this experience. To my beloved daughter Elena Wu, I would like to express my thanks for being such a good girl always cheering me up.

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Section: Antedependence Models Of Longitudinal Datamentioning

confidence: 99%

Antedependence Models for Skewed Continuous Longitudinal Data

Chang¹

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“…We use monthly prices (in level) to estimate models for electricity traded (Bottazzi and Secchi, 2011;Trindade et al, 2010) in Nordpool countries: in particular, Finland and Denmark. The prices, which have been obtained directly from the corresponding power exchanges, are plotted in Figure 5.…”

Section: Nordpool Electricity Prices Datamentioning

confidence: 99%

Loss-based approach to two-piece location-scale distributions with applications to dependent data

2019

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Two-piece location-scale models are used for modeling data presenting departures from symmetry. In this paper, we propose an objective Bayesian methodology for the tail parameter of two particular distributions of the above family: the skewed exponential power distribution and the skewed generalised logistic distribution. We apply the proposed objective approach to time series models and linear regression models where the error terms follow the distributions object of study. The performance of the proposed approach is illustrated through simulation experiments and real data analysis. The methodology yields improvements in density forecasts, as shown by the analysis we carry out on the electricity prices in Nordpool markets.MSC: 62F15, 62M10.In the literature, the asymmetric Laplace distribution (ALD) or the asymmetric Studentt distribution (AST) have gained importance in a wide range of disciplines, such as economics (Zhao et al., 2007;Leisen et al., 2017), financial analysis (Zhu and Galbraith, 2010;Kozubowski and Podgorski, 2001;Harvey and Lange, 2016) and microbiology (Rubio and Steel, 2011). However, the application of the SEPD and SGLD to represent the errors of time series and regression models, has received limited attention in the context of objective Bayesian analysis. The aim of this paper is to contribute to the above research area by introducing an information theoretical approach to address inference on the tail parameter of the two skewed distributions.As currently there is a growing interest in electricity prices (see Weron (2014) and Nowotarski and Weron (2018) for a review), we will contribute to the analysis of monthly electricity prices in the Nordpool market, in particular for Denmark and Finland through an autoregressive model with errors distributed as a SEPD. Compared to the standard frequentist autoregressive approach, which is the benchmark in the literature (see Conejo et al. (2005), Misiorek et al. (2006 and Maciejowska and Weron (2015)), we can show that our methodology improves the density forecasting. In addition, we consider a linear regression model where the residuals are SGLD with a loss-based prior on the tail parameter. We illustrate the above model by studying the Small Cell Cancer data set in Ying et al. (1995) and in Rubio and Yu (2017).The structure of this document is as follows. In Section 2 we introduce the general two-piece location-scale distribution and discuss special distributions further developed in the paper, such as the SEPD and the SGLD. Section 3 focuses on the derivation of the objective priors for the parameters of the models here considered. In Section 4 we analyse the frequentist properties of the proposed prior using data simulated from regression models and time series models. Section 5 deals with real data, in particular we model electricity prices and a cancer dataset. Final discussion points and conclusions are presented in Section 6.

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“…Lognormal and gamma distributions received a great deal of attention in the ARMA modeling of hydrological datasets and realized volatility datasets of stocks (Braga and Calmon (2017); Zhang and Li (2019)). In comparison, the Laplace distribution is more applicable to the modeling of certain types of financial and engineering datasets (Trindade et al (2010)), Bayer et al (2018) proposed a beta seasonal ARMA model for modeling air relative humidity datasets.…”

Section: Introductionmentioning

confidence: 99%

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

Kasraie

Sayyareh

2020

JIRSS

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When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have less been used. The main reason is the difficulty in estimating the autoregressive-moving average model parameters. The purpose of this study is to address this intricacy by approximating maximum likelihood estimators, which is particularly important from model selection perspective. Accordingly, the coefficients and residual distribution parameters of the first-order stationary autoregressive-moving average model with residuals that follow exponential and Weibull families, were estimated. Then based on the simulation study, the obtained theoretical results were investigated and it was shown that the modified maximum likelihood estimators were suitable estimators to estimate the first-order autoregressive-moving average model parameters in nonnormal mode. In a numerical example positive skewness of obtained residuals from fitting the first-order autoregressive-moving average model was shown. Following that, the parameters of candidate residual distributions estimated by modified maximum likelihood estimators and one of the estimated models for modeling the data was selected.

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Time series models with asymmetric Laplace innovations

Cited by 24 publications

References 26 publications

Antedependence Models for Skewed Continuous Longitudinal Data

Antedependence Models for Skewed Continuous Longitudinal Data

Loss-based approach to two-piece location-scale distributions with applications to dependent data

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

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