Estimation of Heteroscedasticity in Regression Analysis

Müller, Hans‐Georg; Stadtmüller, Ulrich

doi:10.1214/aos/1176350364

Cited by 253 publications

(130 citation statements)

References 18 publications

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“…This is the two-sided volatility estimate for the multivariate regression model (2). Herzel et al (2005) motivate the application of nonparametric regression by asymptotic results of Müller and Stadtmüller (1987). Moreover, they derive propositions on confidence intervals for (Σ i,j (t)) i,j .…”

Section: Estimating Volatilitiesmentioning

confidence: 99%

Challenging Traditional Risk Models by a Non-Stationary Approach with Nonparametric Heteroscedasticity

Gürtler

Rauh²

2012

SSRN Journal

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In this paper we analyze an econometric model for non-stationary asset returns. Volatility dynamics are modelled by nonparametric regression; consistency and asymptotic normality of a symmetric and of a one-sided kernel estimator are outlined with remarks on the bandwidth decision. Further attention is paid to asymmetry and heavy tails of the return distribution, involved by the framework for innovations. We survey the practicability and automatization of the implementation. For simulated price processes and a multitude of financial time series we observe a satisfying model approximation and good short-term forecasting abilities of the univariate approach. The non-stationary regression model outperforms parametric risk models and famous ARCH-type implementations.JEL classification: C14, C5

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Section: Estimating Volatilitiesmentioning

confidence: 99%

Challenging Traditional Risk Models by a Non-Stationary Approach with Nonparametric Heteroscedasticity

Gürtler

Rauh²

2012

SSRN Journal

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“…Discussion on the parametric variance function can be found in Carroll and Ruppert [11]. Muller and Stadtmuller [12], Chiou and Muller [13] and Ruppert et al [14] studied nonparametric variance estimation. Muller and Zhao [15] proposed a general semiparametric variance function model in a fixed design regression setting.…”

Section: Remarkmentioning

confidence: 99%

Efficient Estimation in Heteroscedastic Varying Coefficient Models

Wei

Wan

2015

Econometrics

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“…Regarding the included return information we have to distinguish later between the two-sided (symmetrical) and the one-sided (historical) estimation. Herzel et al (2005) motivate the application of nonparametric regression by theoretical results of Müller and Stadtmüller (1987) in an asymptotic context (compare section 3.2 in Herzel et al (2005)). That way, they additionally derive propositions on confidence intervals for (Σ i,j (t)) i,j .…”

Section: Estimating Volatilitiesmentioning

confidence: 99%

“…While a symmetric volatility estimatorσ(t) is employed to describe heteroscedasticity in the historical sample, a one-sided, historical versionσ (1) (t), that includes only past and present data, is employed for forecasting exercises. The statistical properties of nonparametric regression are executed for the symmetric case in Herzel et al (2005) and Mikosch and Starica (2004a) referring on the results of Müller and Stadtmüller (1987). Gürtler et al (2009) provide self-contained full proofs for both the two-sided and one-sided kernel estimators, we outline the consistency and asymptotic normality results here.…”

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confidence: 99%

Shortcomings of a Parametric VaR Approach and Nonparametric Improvements Based on a Non-Stationary Return Series Model

Gürtler

Rauh²

2009

SSRN Journal

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Abstract. In this paper we first investigate the validity of a general Value at Risk approach, which is widely used for risk management in banking and insurance companies. We discuss and widely reject the conventional assumptions, e.g. independent identically distributed normal returns, and as consequence develop an improved model for non-stationary returns. Therein volatility dynamics are modelled both exogenously and deterministic, captured by a nonparametric regression-type approach. Consistency and asymptotic normality of a symmetric and of a one-sided kernel estimator of volatility are outlined with remarks on the bandwidth decision. We pay further attention to asymmetry and heavy tails of the return distribution, implemented by the framework for innovations. On a multitude of financial time series for equity indices, exchange rates, interest rates and credit spreads it is shown that the univariate approach is practically manageable and outperforms the standard tools.

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Estimation of Heteroscedasticity in Regression Analysis

Cited by 253 publications

References 18 publications

Challenging Traditional Risk Models by a Non-Stationary Approach with Nonparametric Heteroscedasticity

Challenging Traditional Risk Models by a Non-Stationary Approach with Nonparametric Heteroscedasticity

Efficient Estimation in Heteroscedastic Varying Coefficient Models

Shortcomings of a Parametric VaR Approach and Nonparametric Improvements Based on a Non-Stationary Return Series Model

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