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LONG RANGE DEPENDENCE
"... Abstract. The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested. A number of related topics is also discussed, including connections with non-stationary processes, with ergodic theory, self-similar processes and fractionally differenced pr ..."
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Cited by 14 (1 self)
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Abstract. The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested. A number of related topics is also discussed, including connections with non-stationary processes, with ergodic theory, self-similar processes and fractionally differenced processes, heavy tails and light tails, limit theorems and large deviations. 1.
Donsker type theorem for the Rosenblatt process and a binary market
, 2008
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4 ASYMPTOTIC PROPORTION OF ARBITRAGE POINTS IN FRACTIONAL BINARY MARKETS
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Article Measures of Causality in Complex Datasets with Application to Financial Data
, 2014
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When VaR is Higher than Expected
"... Multi-period value-at-risk (VaR) forecasts are essential in many financial risk management applications. This paper addresses financial risk prediction for equity markets under long range dependence. We present the major prop-erties of long memory, its implications for risk management and a novel ap ..."
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Multi-period value-at-risk (VaR) forecasts are essential in many financial risk management applications. This paper addresses financial risk prediction for equity markets under long range dependence. We present the major prop-erties of long memory, its implications for risk management and a novel ap-proach to multi-period market risk prediction under long memory. Our em-pirical study of established equity markets covers daily index observations during the period January 1975 to December 2007. We document substan-tial long range dependence in absolute as well as squared returns, indicating a significant influence of long memory effects on volatility. We account for long memory in multi-period value-at-risk forecasts via a scaling based mod-ification of the GARCH(1,1) forecast. Our results show that (i) traditional value-at-risk forecasting techniques underestimate market risk while (ii) our new approach outperforms traditional techniques with as short as 10 or more trading days.
DETC2011/47880 EFFECTS OF MEDIAN FILTERING ON FRACTIONAL PROCESSES
"... Median filtering, an effective non-linear signal enhance-ment technique, has been successfully used for the suppres-sion of impulsive noise and extracting features from noisy sig-nals. Although median filtering can effectively preserve the sharp changes in signals, some signal distortion may be intr ..."
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Median filtering, an effective non-linear signal enhance-ment technique, has been successfully used for the suppres-sion of impulsive noise and extracting features from noisy sig-nals. Although median filtering can effectively preserve the sharp changes in signals, some signal distortion may be introduced and some features of signals may be lost. In this research, we in-vestigate the effects of median filtering on fractional processes which are characterized by the heavy-tailed distribution or the long-range dependence (LRD). The effects of median filtering on heavy-tailed distribution characteristic of α-stable processes, and on LRD property of long-range dependent processes are in-vestigated, respectively. Besides, the effects of median filtering on both the heavy tailed distribution and the LRD properties of fractional autoregressive integrated moving average (FARIMA) with stable innovations time series are studied. The analysis re-sults show that the heavy-tailed distribution and the LRD prop-erties of fractional processes are evidently affected by median filtering. 1
Mathematical Institute,
"... Limit order books are used to match buyers and sellers in more than half of the world’s financial markets, and have been studied extensively in several disciplines during the past decade. This survey highlights the many insights from the wealth of empricial and theoretical studies that have been con ..."
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Limit order books are used to match buyers and sellers in more than half of the world’s financial markets, and have been studied extensively in several disciplines during the past decade. This survey highlights the many insights from the wealth of empricial and theoretical studies that have been conducted, and the numerous unsolved problems that remain. We illustrate the differences between observations from empirical studies of limit order books and the models that attempt to replicate them. In particular, many modelling assumptions are poorly supported by data and several well-established empirical facts have yet to be reproduced satisfactorily by models. By examining existing models of limit order books, we identify some key unresolved questions and difficultes currently facing researchers of limit order trading.
