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94 records from EconBiz based on author Name
1. Inference on the maximal rank of time-varying covariance matrices using high-frequency data
abstractWe study the rank of the instantaneous or spot covariance matrix Σ(t) of a multidimensional continuous semi-martingale X(t). Given highfrequency observations X(i=n), i = 0; : : : ;n, we test the null hypothesis rank (Σ(t)) ≤ r for all t against local alternatives where the average (r + 1)st eigenvalue is larger than some signal detection rate vn. A major problem is that the inherent averaging in local covariance statistics produces a bias that distorts the rank statistics. We show that the bias depends on the regularity and a spectral gap of Σ(t).We establish explicit matrix perturbation and concentration results that provide non-asymptotic uniform critical values and optimal signal detection rates vn. This leads to a rank estimation method via sequential testing. For a class of stochastic volatility models, we determine data-driven critical values via normed p-variations of estimated local covariance matrices. The methods are illustrated by simulations and an application to high-frequency data of U.S. government bonds.
Reiß, Markus; Winkelmann, Lars;2021
Type: Graue Literatur; Non-commercial literature; Arbeitspapier; Working Paper;
Availability:
Link Link Link Link Link 2. Inference on the maximal rank of time-varying covariance matrices using high-frequency data
Reiß, Markus; Winkelmann, Lars;2021
Type: Working Paper;
Availability:
Link 3. Estimating the spot covariation of asset prices : statistical theory and empirical evidence
Bibinger, Markus; Hautsch, Nikolaus; Malec, Peter; Reiß, Markus;2019
Type: Aufsatz in Zeitschrift; Article in journal;
Availability: Link Link Link
Citations: 29 (based on OpenCitations)
4. Nonparametric test for a constant beta over a fixed time interval
abstractWe derive a nonparametric test for constant (continuous) beta over a fixed interval of time. Continuous beta is defined as the ratio of the continuous covariation between an asset and observable risk factor (e.g., the market return) and the continuous variation of the latter. Our test is based on discrete observations of a bivariate It^o semimartingale with mesh of the observation grid shrinking to zero. We first form a consistent and asymptotically mixed normal estimate of beta using all the observations within the time interval under the null hypothesis that beta is constant. Using it we form an estimate of the residual component of the asset returns that is orthogonal (in martingale sense) to the risk factor. Our test is then based on the distinctive asymptotic behavior, under the null and alternative hypothesis, of the sample covariation between the risk factor and the estimated residual component of the asset returns over blocks with asymptotically shrinking time span. Optimality of the test is considered as well. We document satisfactory finite sample properties of the test on simulated data. In an empirical application based on 10-minute data we analyze the time variation in market betas of four assets over the period 2006-2012. The results suggest that (for likely structural reasons) for one of the assets there is statistically nontrivial variation in market beta even for a period as short as a week. On the other hand, for the rest of the assets in our analysis we find evidence that a window of constant beta of one week to one month is statistically plausible.
Reiß, Markus; Todorov, Viktor; Tauchen, George Eugene;2014
Type: Arbeitspapier; Working Paper; Graue Literatur; Non-commercial literature;
Availability:
Link 5. Estimating the spot covariation of asset prices : statistical theory and empirical evidence
abstractWe propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We extend the LMM estimator to allow for autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. We prove the consistency and asymptotic normality of the proposed spot covariance estimator. Based on extensive simulations we provide empirical guidance on the optimal implementation of the estimator and apply it to high-frequency data of a cross-section of NASDAQ blue chip stocks. Employing the estimator to estimate spot covariances, correlations and betas in normal but also extreme-event periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, (iii) are strongly serially correlated, and (iv) can increase strongly and nearly instantaneously if new information arrives.
Bibinger, Markus; Hautsch, Nikolaus; Malec, Peter; Reiß, Markus;2014
Type: Arbeitspapier; Working Paper; Graue Literatur; Non-commercial literature;
Availability: Link Link Link
Citations: 4 (based on OpenCitations)
6. Improved volatility estimation based on limit order books
abstractFor a semi-martingale Xt, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation (X;X)t is constructed based on observations in the vicinity of Xt. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. A major application is the estimation of the integrated squared volatility of an effcient price process Xt from intra-day order book quotes. We derive n -1/3 as optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with n observations (in mean). This considerably improves upon the classical n -1/4-rate obtained from transaction prices under microstructure noise.
Bibinger, Markus; Jirak, Moritz; Reiß, Markus;2014
Type: Arbeitspapier; Working Paper; Graue Literatur; Non-commercial literature;
Availability:
Link 7. Estimating the spot covariation of asset prices : statistical theory and empirical evidence
abstractWe propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We extend the LMM estimator to allow for autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. We prove the consistency and asymptotic normality of the proposed spot covariance estimator. Based on extensive simulations we provide empirical guidance on the optimal implementation of the estimator and apply it to high-frequency data of a cross-section of NASDAQ blue chip stocks. Employing the estimator to estimate spot covariances, correlations and betas in normal but also extreme-event periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, (iii) are strongly serially correlated, and (iv) can increase strongly and nearly instantaneously if new information arrives.
Bibinger, Markus; Hautsch, Nikolaus; Malec, Peter; Reiß, Markus;2014
Type: Arbeitspapier; Working Paper; Graue Literatur; Non-commercial literature;
Availability:
Link 8. Estimating the quadratic covariation matrix from noisy observations : local method of moments and efficiency
abstractAn efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semiparametric efficiency is established in the Cramér-Rao sense. Main findings are that non-synchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour. -- adaptive estimation ; asymptotic equivalence ; asynchronous observations ; integrated covolatility matrix ; quadratic covariation ; semiparametric efficiency ; microstructure noise ; spectral estimation
Bibinger, Markus; Hautsch, Nikolaus; Malec, Peter; Reiß, Markus;2013
Type: Arbeitspapier; Working Paper; Graue Literatur; Non-commercial literature;
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Link 9. A Donsker theorem for Lévy measures
abstractGiven n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator. The class of Lévy processes covered includes several relevant examples such as compound Poisson, Gamma and self-decomposable processes. Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes. -- uniform central limit theorem ; nonlinear inverse problem ; smoothed empirical processes ; pseudo-differential operators ; jump measure
Nickl, Richard; Reiß, Markus;2012
Type: Arbeitspapier; Working Paper; Graue Literatur; Non-commercial literature;
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Link 10. Pointwise adaptive estimation for quantile regression
abstractA nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is the basis for denoising CT scans in cancer research. -- M-estimation ; median regression ; robust estimation ; local model selection ; unsupervised learning ; local bandwidth selection ; median filter ; Lepski procedure ; minimax rate ; image denoising
Reiß, Markus; Rozenholc, Yves; Cuenod, Charles A.;2011
Type: Arbeitspapier; Working Paper; Graue Literatur; Non-commercial literature;
Availability:
Link