Estimating the transition between two intersecting straight lines

“…In response to this criticism, Bacon and Watts (1971) first proposed a more gradual regime transition via a smooth continuous transition function. A smooth transition model is more general than a threshold model in the sense that it covers the sharp threshold transition function as a special case.…”

Section: Introductionmentioning

confidence: 99%

Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity

Chen

Lin

2011

Comput Econ

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Capital asset pricing model (CAPM) has become a fundamental tool in finance for assessing the cost of capital, risk management, portfolio diversification and other financial assets. It is generally believed that the market risks of the assets, often denoted by a beta coefficient, should change over time. In this paper, we model timevarying market betas in CAPM by a smooth transition regime switching CAPM with heteroscedasticity, which provides flexible nonlinear representation of market betas as well as flexible asymmetry and clustering in volatility. We also employ the quantile regression to investigate the nonlinear behavior in the market betas and volatility under various market conditions represented by different quantile levels. Parameter estimation is done by a Bayesian approach. Finally, we analyze some Dow Jones Industrial stocks to demonstrate our proposed models. The model selection method shows that the proposed smooth transition quantile CAPM-GARCH model is strongly preferred over a sharp threshold transition and a symmetric CAPM-GARCH model.

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“…MacNeill andMao 1995 andPastor andGuallar 1998). There are many terminologies to describe a change point regression, such as: "segmented" (Lerman 1980), "broken-line" (Ulm 1991), "structural change", "structural break" or "smoothing transition" (Bacon and Watts 1971), in which the relationship between the response and explanatory variable is piecewise linear. In epidemiologic studies, segmented regression models often occur as threshold models, where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold.…”

Section: Introductionmentioning

confidence: 99%

“…Bayesian approaches to the change-point problem can allow for flexible relationships between parameters in various regimes and are, these days, computationally fairly straightforward and timely. Bayesian analysis of change-point linear models includes the work of Bacon and Watts (1971), Ferreira (1975), Smith and Cook (1980) and others. A Gibbs sampler approach for Bayesian inference in the change-point problem was first discussed by Carlin et al (1992), who implemented a hierarchical Bayesian regression model with a single changepoint.…”

Section: Introductionmentioning

confidence: 99%

A comparison of estimators for regression models with change points

et al. 2010

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We consider two problems concerning locating change points in a linear regression model. One involves jump discontinuities (change-point) in a regression model and the other involves regression lines connected at unknown points. We compare four methods for estimating single or multiple change points in a regression model, when both the error variance and regression coefficients change simultaneously at the unknown point(s): Bayesian, Julious, grid search, and the segmented methods. The proposed methods are evaluated via a simulation study and compared via some standard measures of estimation bias and precision. Finally, the methods are illustrated and compared using three real data sets. The simulation and empirical results overall favor both the segmented and Bayesian methods of estimation, which simultaneously estimate the change point and the other model parameters, though only the Bayesian method is able to handle both continuous and dis-continuous change point problems successfully. If it is known that regression lines are continuous then the segmented method ranked first among methods.

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Estimating the transition between two intersecting straight lines

Cited by 392 publications

References 6 publications

Changes in mandibular cortical width measurements with age in men and women

Changes in mandibular cortical width measurements with age in men and women

Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity

A comparison of estimators for regression models with change points

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