A time-series model using asymmetric Laplace distribution

Jayakumar, K.; Kuttykrishnan, A.P.

doi:10.1016/j.spl.2005.10.028

Cited by 22 publications

(11 citation statements)

References 13 publications

(8 reference statements)

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“…The NLAR(1) and NLAR(2) models of Dewald and Lewis [8] and the NAREX(1) model of Novković [9], assume a marginal Laplace distribution and find the noise process to be a mixture of Laplace densities. Similar results are obtained by Jayakumar and Kuttykrishnan [10], who assume an asymmetric Laplace (AL) marginal distribution. On the other hand, Damsleth and El-Shaarawi [5] start with Laplace noise and find the marginal distribution of the process to be a linear combination of Laplace distributions.…”

Section: Introductionsupporting

confidence: 84%

Time series models with asymmetric Laplace innovations

Trindade

Zhu

Andrews

2009

Journal of Statistical Computation and Simulation

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We propose autoregressive moving average (ARMA) and generalized autoregressive conditional heteroscedastic (GARCH) models driven by asymmetric Laplace (AL) noise. The AL distribution plays, in the geometric-stable class, the analogous role played by the normal in the alpha-stable class, and has shown promise in the modelling of certain types of financial and engineering data. In the case of an ARMA model we derive the marginal distribution of the process, as well as its bivariate distribution when separated by a finite number of lags. The calculation of exact confidence bands for minimum mean-squared error linear predictors is shown to be straightforward. Conditional maximum likelihood-based inference is advocated, and corresponding asymptotic results are discussed. The models are particularly suited for processes that are skewed, peaked, and leptokurtic, but which appear to have some higher order moments. A case study of a fund of real estate returns reveals that AL noise models tend to deliver a superior fit with substantially less parameters than normal noise counterparts, and provide both a competitive fit and a greater degree of numerical stability with respect to other skewed distributions.

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Section: Introductionsupporting

confidence: 84%

Time series models with asymmetric Laplace innovations

Trindade

Zhu

Andrews

2009

Journal of Statistical Computation and Simulation

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“…1 Koenker and Machado (1999) and Yu and Moyeed (2001) illustrate the link between the solution to the standard quantile estimation problem and the likelihood for the asymmetric Laplace distribution (ALD). For more properties and applications of the ALD in the financial time series, readers are referred to Kotz et al (2001) and Jayakumar and Kuttykrishnan (2007).…”

Section: Bayesian Inferencementioning

confidence: 99%

“…For more properties and applications of the ALD in the financial time series, readers are referred to Kotz et al . () and Jayakumar and Kuttykrishnan ().…”

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confidence: 99%

Evidence of Stock Returns and Abnormal Trading Volume: A Threshold Quantile Regression Approach

Chen

Chiang

2015

Japanese Economic Review

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This paper presents a capital asset pricing model‐based threshold quantile regression model with a generalized autoregressive conditional heteroscedastic specification to examine relations between excess stock returns and “abnormal trading volume”. We employ an adaptive Bayesian Markov chain Monte Carlo method with asymmetric Laplace distribution to study six daily Dow Jones Industrial stocks. The proposed model captures asymmetric risk through market beta and volume coefficients, which change discretely between regimes. Moreover, they are driven by market information and various quantile levels. This study finds that abnormal volume has significantly negative effects on excess stock returns under low quantile levels; however, there are significantly positive effects under high quantile levels. The evidence indicates that each market beta varies with different quantile levels, capturing different states of market conditions.

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“…Pillai (1985), Anderson and Arnold (1993), Jayakumar et al (1995), Jayakumar (1997), Jayakumar and Ajitha (2003), Jose (2004a,b, 2006), Jose et al (2008), and Lishamol and Jose (2009) introduced various models utilizing generalizations of Laplace distributions such as -Laplace, Pakes generalized Linnik distribution, normal-Laplace, etc. Jayakumar and Kuttykrishnan (2007) developed time series models and discussed the applications of asymmetric Laplace distribution in modeling currency exchange rate, interest rate, stock price changes etc. Other contexts where this distribution finds application are returns from financial assets, agricultural crop prices and turbulent wind speeds.…”

Section: Introductionmentioning

confidence: 99%

Generalized Laplacian Distributions and Autoregressive Processes

Jose¹,

Thomas²

2011

Communications in Statistics - Theory and Methods

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Generalized Laplacian distribution is considered. A new distribution called geometric generalized Laplacian distribution is introduced and its properties are studied. First-and higher-order autoregressive processes with these stationary marginal distributions are developed and studied. Simulation studies are conducted and trajectories of the process are obtained for selected values of the parameters.Various areas of application of these models are discussed.

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A time-series model using asymmetric Laplace distribution

Cited by 22 publications

References 13 publications

Time series models with asymmetric Laplace innovations

Time series models with asymmetric Laplace innovations

Evidence of Stock Returns and Abnormal Trading Volume: A Threshold Quantile Regression Approach

Generalized Laplacian Distributions and Autoregressive Processes

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