Download or read book Estimating Long Memory in Volatility written by Clifford M. Hurvich and published by . This book was released on 2009 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider semiparametric estimation of the memory parameter in a modelwhich includes as special cases both the long-memory stochasticvolatility (LMSV) and fractionally integrated exponential GARCH(FIEGARCH) models. Under our general model the logarithms of the squaredreturns can be decomposed into the sum of a long-memory signal and awhite noise. We consider periodogram-based estimators which explicitlyaccount for the noise term in a local Whittle criterion function. Weallow the optional inclusion of an additional term to allow for acorrelation between the signal and noise processes, as would occur inthe FIEGARCH model. We also allow for potential nonstationarity involatility, by allowing the signal process to have a memory parameter d1=2. We show that the local Whittle estimator is consistent for d 2 (0;1). We also show that a modi ed version of the local Whittle estimatoris asymptotically normal for d 2 (0; 3=4), and essentially recovers theoptimal semiparametric rate of convergence for this problem. Inparticular if the spectral density of the short memory component of thesignal is suficiently smooth, a convergence rate of n2=5-amp;delta; for d 2(0; 3=4) can be attained, where n is the sample size and amp;delta; amp;gt; 0is arbitrarily small. This represents a strong improvement over theperformance of existing semiparametric estimators of persistence involatility. We also prove that the standard Gaussian semiparametricestimator is asymptotically normal if d = 0. This yields a test forlong memory in volatility.
Download or read book Estimation of Long Memory in Volatility written by Rohit Deo and published by . This book was released on 2008 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss some of the issues pertaining to modelling and estimating long memory in volatility. Themain focus is on semi parametric estimation of the memory parameter in the long memory stochasticvolatility model. We present the asymptotic properties of the log periodogram regression estimator ofthe memory parameter in this model. A modest simulation study of the estimator is also presented tostudy its behaviour when the volatility possesses only short memory. We conclude with a discussionof the appropriate choice of transformation of returns to measure persistence in volatility.
Download or read book Log periodogram Estimation of Long Memory Volatility Dependencies with Conditionally Heavy Tailed Returns written by Jonathan H. Wright and published by . This book was released on 2000 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many recent papers have used semiparametric methods, especially the log-periodogram regression, to detect and estimate long memory in the volatility of asset returns. In these papers, the volatility is proxied by measures such as squared, log-squared and absolute returns. While the evidence for the existence of long memory is strong using any of these measures, the actual long memory parameter estimates can be sensitive to which measure is used. In Monte-Carlo simulations, I find that the choice of volatility measure makes little difference to the log-periodogram regression estimator if the data is Gaussian conditional on the volatility process. But, if the data is conditionally leptokurtic, the log periodogram regression estimator using squared returns has a large downward bias, which is avoided by using other volatility measures. In U.S. stock return data, I find that squared returns give much lower estimates of the long memory parameter than the alternative volatility measures, which is consistent with the simulation results. I conclude that researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies.
Download or read book Long Memory in Economics written by Gilles Teyssière and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assembles three different strands of long memory analysis: statistical literature on the properties of, and tests for, LRD processes; mathematical literature on the stochastic processes involved; and models from economic theory providing plausible micro foundations for the occurrence of long memory in economics.
Download or read book Large Sample Inference For Long Memory Processes written by Donatas Surgailis and published by World Scientific Publishing Company. This book was released on 2012-04-27 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Box and Jenkins (1970) made the idea of obtaining a stationary time series by differencing the given, possibly nonstationary, time series popular. Numerous time series in economics are found to have this property. Subsequently, Granger and Joyeux (1980) and Hosking (1981) found examples of time series whose fractional difference becomes a short memory process, in particular, a white noise, while the initial series has unbounded spectral density at the origin, i.e. exhibits long memory.Further examples of data following long memory were found in hydrology and in network traffic data while in finance the phenomenon of strong dependence was established by dramatic empirical success of long memory processes in modeling the volatility of the asset prices and power transforms of stock market returns.At present there is a need for a text from where an interested reader can methodically learn about some basic asymptotic theory and techniques found useful in the analysis of statistical inference procedures for long memory processes. This text makes an attempt in this direction. The authors provide in a concise style a text at the graduate level summarizing theoretical developments both for short and long memory processes and their applications to statistics. The book also contains some real data applications and mentions some unsolved inference problems for interested researchers in the field./a
Download or read book Time Series Analysis with Long Memory in View written by Uwe Hassler and published by John Wiley & Sons. This book was released on 2018-09-07 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a simple exposition of the basic time series material, and insights into underlying technical aspects and methods of proof Long memory time series are characterized by a strong dependence between distant events. This book introduces readers to the theory and foundations of univariate time series analysis with a focus on long memory and fractional integration, which are embedded into the general framework. It presents the general theory of time series, including some issues that are not treated in other books on time series, such as ergodicity, persistence versus memory, asymptotic properties of the periodogram, and Whittle estimation. Further chapters address the general functional central limit theory, parametric and semiparametric estimation of the long memory parameter, and locally optimal tests. Intuitive and easy to read, Time Series Analysis with Long Memory in View offers chapters that cover: Stationary Processes; Moving Averages and Linear Processes; Frequency Domain Analysis; Differencing and Integration; Fractionally Integrated Processes; Sample Means; Parametric Estimators; Semiparametric Estimators; and Testing. It also discusses further topics. This book: Offers beginning-of-chapter examples as well as end-of-chapter technical arguments and proofs Contains many new results on long memory processes which have not appeared in previous and existing textbooks Takes a basic mathematics (Calculus) approach to the topic of time series analysis with long memory Contains 25 illustrative figures as well as lists of notations and acronyms Time Series Analysis with Long Memory in View is an ideal text for first year PhD students, researchers, and practitioners in statistics, econometrics, and any application area that uses time series over a long period. It would also benefit researchers, undergraduates, and practitioners in those areas who require a rigorous introduction to time series analysis.
Download or read book Long Memory Processes written by Jan Beran and published by Springer Science & Business Media. This book was released on 2013-05-14 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.
Download or read book Handbook of Modeling High Frequency Data in Finance written by Frederi G. Viens and published by John Wiley & Sons. This book was released on 2011-12-20 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: CUTTING-EDGE DEVELOPMENTS IN HIGH-FREQUENCY FINANCIAL ECONOMETRICS In recent years, the availability of high-frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High-Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data. A one-stop compilation of empirical and analytical research, this handbook explores data sampled with high-frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real-world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high-frequency finance, such as: Designing new methodology to discover elasticity and plasticity of price evolution Constructing microstructure simulation models Calculation of option prices in the presence of jumps and transaction costs Using boosting for financial analysis and trading The handbook motivates practitioners to apply high-frequency finance to real-world situations by including exclusive topics such as risk measurement and management, UHF data, microstructure, dynamic multi-period optimization, mortgage data models, hybrid Monte Carlo, retirement, trading systems and forecasting, pricing, and boosting. The diverse topics and viewpoints presented in each chapter ensure that readers are supplied with a wide treatment of practical methods. Handbook of Modeling High-Frequency Data in Finance is an essential reference for academics and practitioners in finance, business, and econometrics who work with high-frequency data in their everyday work. It also serves as a supplement for risk management and high-frequency finance courses at the upper-undergraduate and graduate levels.
Download or read book Bias Reduced Estimation of Long Memory Stochastic Volatility written by Per Skaarup Frederiksen and published by . This book was released on 2008 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long memory stochastic volatility models with potential nonstationarity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining bias reduction as well as a rate of convergence arbitrarily close to the parametric rate, n1=2. A Monte Carlo study is conducted to support the theoretical results, and an analysis of daily exchange rates demonstrates the empirical usefulness of the estimators.
Download or read book An Introduction to High Frequency Finance written by Ramazan Gençay and published by Elsevier. This book was released on 2001-05-29 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Liquid markets generate hundreds or thousands of ticks (the minimum change in price a security can have, either up or down) every business day. Data vendors such as Reuters transmit more than 275,000 prices per day for foreign exchange spot rates alone. Thus, high-frequency data can be a fundamental object of study, as traders make decisions by observing high-frequency or tick-by-tick data. Yet most studies published in financial literature deal with low frequency, regularly spaced data. For a variety of reasons, high-frequency data are becoming a way for understanding market microstructure. This book discusses the best mathematical models and tools for dealing with such vast amounts of data. This book provides a framework for the analysis, modeling, and inference of high frequency financial time series. With particular emphasis on foreign exchange markets, as well as currency, interest rate, and bond futures markets, this unified view of high frequency time series methods investigates the price formation process and concludes by reviewing techniques for constructing systematic trading models for financial assets.
Download or read book On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models written by Rohit Deo and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider semiparametric estimation of the memory parameter in a long memorystochastic volatility model. We study the estimator based on a log periodogramregression as originally proposed by Geweke and Porter-Hudak (1983,Journal of Time Series Analysis 4, 221 238). Expressions for the asymptotic biasand variance of the estimator are obtained, and the asymptotic distribution is shownto be the same as that obtained in recent literature for a Gaussian long memoryseries. The theoretical result does not require omission of a block of frequenciesnear the origin. We show that this ability to use the lowest frequencies is particularlydesirable in the context of the long memory stochastic volatility model.
Download or read book Long Memory in Stock Returns written by Avishek Bhandari and published by . This book was released on 2018 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The estimation and the analysis of long memory parameters have mainly focused on the analysis of long-range dependence in stock return volatility using traditional time and spectral domain estimators of long memory. The definitive ubiquity and existence of long memory in the volatility of stock returns is an established stylized fact. The presence of long memory requires major revisions in the standard estimation procedures without which the estimated results can be seriously biased. Therefore, a wavelet based semi-parametric estimator of long range dependence is applied to test for the presence of long memory in the Indian stock returns and returns volatility. We find the presence of long memory in the volatility of the stock returns as well as the returns themselves, when the analysis is performed using rolling windows. The presence of long-memory implies that distant observations in each of the volatility series are related to each other. This implication leads to the rejection of efficient markets as long range dependence in returns volatility seems to be incompatible with market efficiency.
Download or read book Long Memory in the Volatility of Indian Financial Market An Empirical Analysis Based on Indian Data written by Dilip Kumar and published by Anchor Academic Publishing (aap_verlag). This book was released on 2014-04-10 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the long memory characteristics in the volatility of the Indian stock market, the Indian exchange rates and the Indian banking sector. This book also reviews the chain of approaches to estimate the long memory parameter. The long memory characteristics of the financial time series are widely studied and have implications for various economics and finance theories. The most important financial implication is related to the violation of the weak-form of market efficiency which encourages the traders, investors and portfolio managers to develop models for making predictions and to construct and implement speculative trading and investment strategies. In an efficient market, the price of an asset should follow a random walk process in which the price change is unaffected by ist lagged price changes and has no memory.
Download or read book Time Series with Long Memory written by Peter M. Robinson and published by Advanced Texts in Econometrics. This book was released on 2003 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long memory time series are characterized by a strong dependence between distant events.
Download or read book Log Periodogram Estimation of Long Memory Volatility Dependencies with Conditionally Heavy Tailed Returns written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The U.S. Federal Reserve Board presents the full text of an article entitled "Log-Periodogram Estimation of Long Memory Volatility Dependencies with Conditionally Heavy Tailed Returns," by Jonathan H. Wright. The article discusses why researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies.
Download or read book Long Memory Volatility Persistence in High Frequency Precious Metals Returns written by Kashif Saleem and published by . This book was released on 2014 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using high frequency data, this paper examines the long memory property in the conditional volatility of the precious metals return series at different time frequencies using FIGARCH models. Very significant long memory characteristics have been detected in absolute returns by using Semiparametric local Whittle estimation of the long memory parameter. Estimation of the long memory parameter across many different data sampling frequencies gives consistent estimates of the long memory parameter, indicating that the series are exactly to show some degree of self-similarity. Results indicate that the long memory property remains quite consistent across different time frequencies for both unconditional and conditional volatility measures. This study is useful for investors and traders (with different trading horizons) and it can be used in predicting expected future volatility and in designing and implementing trading strategies at different time frequencies.
Download or read book Estimation of Long Memory in Volatility Using Wavelets written by Lucie Kraicova and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work studies wavelet-based Whittle estimator of the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroscedasticity (FIEGARCH) model, often used for modeling long memory in volatility of financial assets. The newly proposed estimator approximates the spectral density using wavelet transform, which makes it more robust to certain types of irregularities in data. Based on an extensive Monte Carlo study, both behaviour of the proposed estimator and its relative performance with respect to traditional estimators are assessed. In addition, we study properties of the estimators in presence of jumps, which brings interesting discussion. We find that wavelet-based estimator may become an attractive robust and fast alternative to the traditional methods of estimation.
