arXiv subjects

Alexander Heinemann

Publications and source records attributed to Alexander Heinemann.

5 recordsLinked to original sources

arXiv2023

A Residual Bootstrap for Conditional Value-at-Risk

A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zakoïan (2015) associated with the conditional Value-at-Risk. The bootstrap's consistency is proven for a general class of volatility models and intervals are constructed for the conditional Value-at-Risk. A simulation study reveals that the equal-tailed percentile bootstrap interval tends to fall short of its nominal value. In contrast, the reversed-tails bootstrap interval yields accurate coverage. We also compare the theoretically analyzed fixed-design bootstrap with the recursive-design bootstrap. It turns out that the fixed-design bootstrap performs equally well in terms of average coverage, yet leads on average to shorter intervals in smaller samples. An empirical application illustrates the interval estimation.

econ.EM↗

arXiv2019

A Bootstrap Test for the Existence of Moments for GARCH Processes

This paper studies the joint inference on conditional volatility parameters and the innovation moments by means of bootstrap to test for the existence of moments for GARCH(p,q) processes. We propose a residual bootstrap to mimic the joint distribution of the quasi-maximum likelihood estimators and the empirical moments of the residuals and also prove its validity. A bootstrap-based test for the existence of moments is proposed, which provides asymptotically correctly-sized tests without losing its consistency property. It is simple to implement and extends to other GARCH-type settings. A simulation study demonstrates the test's size and power properties in finite samples and an empirical application illustrates the testing approach.

econ.EM↗

arXiv2019

A General Framework for Prediction in Time Series Models

In this paper we propose a general framework to analyze prediction in time series models and show how a wide class of popular time series models satisfies this framework. We postulate a set of high-level assumptions, and formally verify these assumptions for the aforementioned time series models. Our framework coincides with that of Beutner et al. (2019, arXiv:1710.00643) who establish the validity of conditional confidence intervals for predictions made in this framework. The current paper therefore complements the results in Beutner et al. (2019, arXiv:1710.00643) by providing practically relevant applications of their theory.

econ.EM↗

arXiv2019

A Justification of Conditional Confidence Intervals

To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the unrealistic assumption of observing two independent processes, where one is used for parameter estimation, and the other for conditioning upon. Such unrealistic foundation raises the question whether these intervals are theoretically justified in a realistic setting. This paper presents an asymptotic justification for this type of intervals that does not require such an unrealistic assumption, but relies on a sample-split approach instead. By showing that our sample-split intervals coincide asymptotically with the standard intervals, we provide a novel, and realistic, justification for confidence intervals of conditional objects. The analysis is carried out for a rich class of time series models.

econ.EM↗

arXiv2018

A Residual Bootstrap for Conditional Expected Shortfall

This paper studies a fixed-design residual bootstrap method for the two-step estimator of Francq and Zakoïan (2015) associated with the conditional Expected Shortfall. For a general class of volatility models the bootstrap is shown to be asymptotically valid under the conditions imposed by Beutner et al. (2018). A simulation study is conducted revealing that the average coverage rates are satisfactory for most settings considered. There is no clear evidence to have a preference for any of the three proposed bootstrap intervals. This contrasts results in Beutner et al. (2018) for the VaR, for which the reversed-tails interval has a superior performance.

econ.EM↗