Statistical inference for conditional quantiles in nonlinear time series models

So, Mike K. P.; Chung, Ray S. W.

doi:10.1016/j.jeconom.2015.03.037

“…To address these important but challenging empirical questions, we introduce a new heterogeneous panel quantile model with factor structures, in which a few unobservable factors may explain the co-movement of the asset return distributions in a large number of asset returns. Quantile regression methods have been previously used to model financial data (Engle and Manganelli (2004), Baur (2012), Baur et al (2013), Chuang et al (2009), Cappiello et al (2014), Chen (2015), So and Chung (2015), Gerlach et al (2016), Chen, Li and Nguyen (2017), Han et al (2016)). In this paper, we consider large-scale panel data that consist of a large number of asset return time series.…”

Section: Introductionmentioning

confidence: 99%

Quantile Co-Movement in Financial Markets; a Panel Quantile Model with Unobserved Heterogeneity

Ando

¹

,

Bai

²

2017

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This paper introduces a new procedure for analyzing the quantile co-movement of a large number of financial time series based on a large-scale panel data model with factor structures. The proposed method attempts to capture the unobservable heterogeneity of each of the financial time series based on sensitivity to explanatory variables and to the unobservable factor structure. In our model, the dimension of the common factor structure varies across quantiles, and the factor structure is allowed to be correlated with the explanatory variables. The proposed method allows for both cross-sectional and serial dependence, and heteroskedasticity, which are common in financial markets. We propose new estimation procedures for both frequentist and Bayesian frameworks. Consistency and asymptotic normality of the proposed estimator are established. We also propose a new model selection criterion for determining the number of common factors together with theoretical support. We apply the method to analyze the returns for over 6,000 international stocks from over 60 countries during the subprime crisis, European sovereign debt crisis, and subsequent period. The empirical analysis indicates that the common factor structure varies across quantiles. We find that the common factors for the quantiles and the common factors for the mean are different.

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“…In univariate volatility modeling, likelihood inference without specifying the error distribution was considered in the literature, such as Bollerslev and Wooldridge (1992) and So and Chung (2015), where quasi‐likelihoods were formulated and maximized for parameter estimation. This article proposes the quasi‐maximum likelihood (QML) estimation for covariance modeling.…”

Section: Introductionmentioning

confidence: 99%

Quasi‐maximum likelihood estimation of conditional autoregressive Wishart models

So

¹

2020

Journal Time Series Analysis

2

0

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In this article, we consider a quasi‐maximum likelihood (QML) estimation of conditional autoregressive Wishart models, which generalize the conditional autoregressive Wishart models by not restricting the conditional distribution of covariances to follow the Wishart distribution. Strong consistency is established under the existence of the expectation of the log of the determinant. Sufficient conditions for asymptotic normality of the QML estimator are derived. Monte Carlo experiments show an inefficiency caused by using non‐Wishart distributions, which are negligible for the sample size T = 500. We use the daily covariance matrix of the returns of the Nikkei 225 index and its futures for the QML estimation of the conditional autoregressive Wishart model. The results indicate its appropriateness for the QML estimation.

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“…To address these important but challenging empirical questions, we introduce a new heterogeneous panel quantile model with factor structures, in which a few unobservable factors may explain the co-movement of the asset return distributions in a large number of asset returns. Quantile regression methods have been previously used to model financial data (Engle and Manganelli (2004), Baur (2012), Baur et al (2013), Chuang et al (2009), Cappiello et al (2014), Chen (2015), So and Chung (2015), Gerlach et al (2016), Chen, Li and Nguyen (2017), Han et al (2016)). In this paper, we consider large-scale panel data that consist of a large number of asset return time series.…”

Section: Introductionmentioning

confidence: 99%

Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity

Ando

¹

,

Bai

²

2019

Journal of the American Statistical Association

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This paper introduces a new procedure for analyzing the quantile co-movement of a large number of financial time series based on a large-scale panel data model with factor structures. The proposed method attempts to capture the unobservable heterogeneity of each of the financial time series based on sensitivity to explanatory variables and to the unobservable factor structure. In our model, the dimension of the common factor structure varies across quantiles, and the factor structure is allowed to be correlated with the explanatory variables. The proposed method allows for both cross-sectional and serial dependence, and heteroskedasticity, which are common in financial markets. We propose new estimation procedures for both frequentist and Bayesian frameworks. Consistency and asymptotic normality of the proposed estimator are established. We also propose a new model selection criterion for determining the number of common factors together with theoretical support. We apply the method to analyze the returns for over 6,000 international stocks from over 60 countries during the subprime crisis, European sovereign debt crisis, and subsequent period. The empirical analysis indicates that the common factor structure varies across quantiles. We find that the common factors for the quantiles and the common factors for the mean are different.

show abstract

Statistical inference for conditional quantiles in nonlinear time series models

Cited by 11 publications

References 28 publications

Quantile Co-Movement in Financial Markets; a Panel Quantile Model with Unobserved Heterogeneity

Quantile Co-Movement in Financial Markets; a Panel Quantile Model with Unobserved Heterogeneity

Quasi‐maximum likelihood estimation of conditional autoregressive Wishart models

Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity

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