Estimating the Covariance Matrix from Unsynchronized High Frequency Financial Data (Classic Reprint)
Estimating the Covariance Matrix from Unsynchronized High Frequency Financial Data (Classic Reprint)

Author: Bin Zhou

Publisher: Forgotten Books

Published: 2018-02-23

Total Pages: 28

ISBN-13: 9780332800066

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Excerpt from Estimating the Covariance Matrix From Unsynchronized High Frequency Financial Data The estimation of the covariance matrix of financial prices is necessary in port folio optimization and risk management. Besides sample covariance, many other estimators have been proposed (stein 1975, Dey and Srinivasan However, estimating the covariance matrix from daily data can have serious problems. Jobson and Korkie (1980) indicated that, in some cases, it is better to use the identical matrix instead of the sample covariance matrix in the port folio selection. The problem is that the number of observations is not enough to estimate all entries of a big covariance matrix. To get around the problem, one may want to collect more data over longer time interval. However, the changing condition of markets may prevent us to do so. Another approach is to impose constrains on the covariance matrix to reduce the number of free parameters (frost and Savaino, The constrain may be subjective and not reflect the reality of the market. This paper explores another possibility of using high frequency data. Because of fast-growing computer power, data is now available in ultra - high frequency, such as tick-by - tick. Exchange rates, for example, can easily have over one million observations in one year. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Estimating the Covariance Matrix from Unsynchronized High Frequency Financial Data...
Estimating the Covariance Matrix from Unsynchronized High Frequency Financial Data...

Author: Bin Zhou

Publisher: Hardpress Publishing

Published: 2013-12

Total Pages: 34

ISBN-13: 9781314878875

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Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Estimating the Variance Parameter from Noisy High Frequency Financial Data (Classic Reprint)
Estimating the Variance Parameter from Noisy High Frequency Financial Data (Classic Reprint)

Author: Bin Zhou

Publisher: Forgotten Books

Published: 2018-02-24

Total Pages: 30

ISBN-13: 9780332147468

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Excerpt from Estimating the Variance Parameter From Noisy High Frequency Financial Data I call the diffusion process the signal process and the fit observation noise. The observation noise is the deviation of data from the continuous process and is assumed to be independent from the diffusion process. Many things contribute to this observation noise. In the currency market, for example, non-binding quoting error is part of the noise. In other markets, bid and offer difference also contributes to the observation noise. Many other micro structural behaviors are all included in this so - called observation noise. For low frequency observations, the observation noise is overwhelmed by the sig nal change. When observation frequency increases, the signal change becomes smaller and smaller while the size of the noise remains the same. The noise totally dominates the price change in ultra-high frequency data. Viewing high frequency data as observation with noise certainly captures many basic characteristics of high frequency financial time series mentioned above. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Estimation of Covariance Matrix for High-dimensional Data and High-frequency Data
Estimation of Covariance Matrix for High-dimensional Data and High-frequency Data

Author: Changgee Chang

Publisher:

Published: 2012

Total Pages: 86

ISBN-13: 9781267601360

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The second part is multivariate volatility estimation in high frequency. I propose an estimator that extends the realized kernel method, which was introduced for univariate data. I look at the estimator from a different view and suggest a natural extension. Several asymptotic properties are discussed. I also investigate the optimal kernels and provide a regularization method that produces positive-definite covariance matrix. I conduct a simulation study to verify the asymptotic theory and the finite sample performance of the proposed method.

High-Frequency Covariance Matrix Estimation Using Price Durations
High-Frequency Covariance Matrix Estimation Using Price Durations

Author: Xiaolu Zhao

Publisher:

Published: 2018

Total Pages: 57

ISBN-13:

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We propose a price duration based covariance matrix estimator using high frequency transactions data. The effect of the last-tick time-synchronisation methodology, together with effects of important market microstructure components is analysed through a comprehensive Monte Carlo study. To decrease the number of negative eigenvalues produced by the non positive-semi-definite (psd) covariance matrix, we devise an average covariance estimator by taking an average of a wide range of duration based covariance matrix estimators. Empirically, candidate covariance estimators are implemented on 19 stocks from the DJIA. The duration based covariance estimator is shown to provide comparably accurate estimates with smaller variation compared with competing estimators. An out-of-sample GMV portfolio allocation problem is studied. A simple shrinkage technique is introduced to make the sample matrices psd and well-conditioned. Compared to competing high-frequency covariance matrix estimators, the duration based estimator is shown to give more stable portfolio weights and higher Sharpe ratios while maintaining comparably low portfolio variances.

Robust Estimation of a High-Dimensional Integrated Covariance Matrix
Robust Estimation of a High-Dimensional Integrated Covariance Matrix

Author: Takayuki Morimoto

Publisher:

Published: 2015

Total Pages: 16

ISBN-13:

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In this paper, we consider a robust method of estimating a realized covariance matrix calculated as the sum of cross products of intraday high-frequency returns. According to recent papers in financial econometrics, the realized covariance matrix is essentially contaminated with market microstructure noise. Although techniques for removing noise from the matrix have been studied since the early 2000s, they have primarily investigated a low-dimensional covariance matrix with statistically significant sample sizes. We focus on noise-robust covariance estimation under converse circumstances; that is, a high-dimensional covariance matrix possibly with a small sample size. For the estimation, we utilize a statistical hypothesis test based on the characteristic that the largest eigenvalue of the covariance matrix asymptotically follows a Tracy-Widom distribution. The null hypothesis assumes that log returns are not pure noises. If a sample eigenvalue is larger than the relevant critical value, then we fail to reject the null hypothesis. The simulation results show that the estimator studied here performs better than others as measured by mean squared error. The empirical analysis shows that our proposed estimator can be adopted to forecast future covariance matrices using real data.