Estimating parameters in autoregressive models with asymmetric innovations

Wong, Wing-Keung; Bian, Guorui

doi:10.1016/j.spl.2004.10.022

Cited by 58 publications

(43 citation statements)

References 31 publications

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“…In this paper, the underlying distribution is assumed to be symmetric and student t, and the method of modified maximum likelihood (MML) estimation (Tiku, 1968;Tiku et al, 1999Tiku et al, , 2000Tiku et al, , 2001) is used. This paper extends the results given in Bian and Tiku (1997), Tiku et al (1999Tiku et al ( , 2000Tiku et al ( , 2001), Wong and Bian (2005), and Tiku (2005, 2010). Tiku et al (1999) develop MML estimators for the simple linear regression model with symmetric innovations, Tiku et al (2000) derive MML estimators for the first-order autoregressive model with symmetric innovations, Tiku et al (2001) refine the MML estimator for the simple linear regression model with t distribution innovations, and Bian and Tiku (1997) adopt the Bayesian approach to examine a standard multiple regression model with independently and identically distributed (iid) errors.…”

Section: Introductionsupporting

confidence: 88%

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Robust Estimation and Forecasting of the Capital Asset Pricing Model

2010

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In this paper, we develop a modified maximum likelihood (MML) estimator for the multiple linear regression model with underlying student t distribution. We obtain the closed form of the estimators, derive the asymptotic properties, and demonstrate that the MML estimator is more appropriate for estimating the parameters of the Capital Asset Pricing Model by comparing its performance with least squares estimators (LSE) on the monthly returns of US portfolios. The empirical results reveal that the MML estimators are more efficient than LSE in terms of the relative efficiency of one-step-ahead forecast mean square error in small samples.JEL classifications: C1, C2, G1.

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Section: Introductionsupporting

confidence: 88%

“…These estimators are explicit functions of sample observations, and hence are straightforward to compute. Moreover, they are as efficient as ML estimators (Tiku et al, 1999(Tiku et al, , 2000(Tiku et al, , 2001Wong and Bian, 2005). We also derive the asymptotic properties of the MML estimators.…”

Section: Introductionmentioning

confidence: 96%

Robust Estimation and Forecasting of the Capital Asset Pricing Model

2010

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“…Wong and Bian (2005) extend the results to the case where the underlying distribution is a generalized logistic distribution. The generalized logistic distribution family represents very wide range of skewed distributions, from highly right skewed to highly left skewed.…”

Section: Other Econometric Models/testsmentioning

confidence: 58%

Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections

2018

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This paper provides a review of some connecting literature in Decision Sciences, Economics, Finance, Business, Computing, and Big Data. We then discuss some research that is related to the six cognate disciplines. Academics could develop theoretical models and subsequent econometric and statistical models to estimate the parameters in the associated models. Moreover, they could then conduct simulations to examine whether the estimators or statistics in the new theories on estimation and hypothesis have small size and high power. Thereafter, academics and practitioners could then apply their theories to analyze interesting problems and issues in the six disciplines and other cognate areas. KeywordsDecision sciences, economics, finance, business, computing, and big data, theoretical models, econometric and statistical models, applications. JEL Classification AbstractThis paper provides a review of some connecting literature in Decision Sciences, Economics, Finance, Business, Computing, and Big Data. We then discuss some research that is related to the six cognate disciplines. Academics could develop theoretical models and subsequent econometric and statistical models to estimate the parameters in the associated models. Moreover, they could then conduct simulations to examine whether the estimators or statistics in the new theories on estimation and hypothesis have small size and high power. Thereafter, academics and practitioners could then apply their theories to analyze interesting problems and issues in the six disciplines and other cognate areas.

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“…To prove otherwise, Levy and Wiener (1998) recommend employing the subjective weighting functions. We would suggest applying the Bayesian approach (Matsumura, et al 1990) and then use the advanced statistical techniques (see for example, Wong and Miller 1990;Tiku et al 2000;Wong and Bian 2005) to estimate the subjectively distort probabilities. Prospect theory will satisfy the Bayesian expected utility maximization.…”

Section: Discussionmentioning

confidence: 99%

Prospect and Markowitz stochastic dominance

2007

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Levy and Levy ( , 2004 develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy's Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD.Prospect theory has been regarded as a challenge to the expected utility paradigm. Levy and prove that the second order PSD and MSD satisfy the expected utility paradigm. In our paper we take Levy and Levy's results one step further by showing that both PSD and MSD of any order are consistent with the expected utility paradigm.Furthermore, we formulate some other properties for the PSD and MSD including the hierarchy that exists in both PSD and MSD relationships; arbitrage opportunities that exist in the first orders of both PSD and MSD; and that for any two prospects under certain conditions, their third order MSD preference will be 'the opposite' of or 'the same' as their counterpart third order PSD preference. By extending Levy and Levy's work, we provide investors with more tools for empirical analysis, with which they can identify the first order PSD and MSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors to identify the third order PSD and MSD prospects and make better choices.

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Estimating parameters in autoregressive models with asymmetric innovations

Cited by 58 publications

References 31 publications

Robust Estimation and Forecasting of the Capital Asset Pricing Model

Robust Estimation and Forecasting of the Capital Asset Pricing Model

Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections

Prospect and Markowitz stochastic dominance

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