Long-Range Dependence, Fractal Processes, and Intra-Daily Data

Abstract

With the availability of intra-daily price data, researchers have focused more attention on market microstructure issues to understand and help formulate strategies for the timing of trades. The purpose of this article is to provide a brief survey of the research employing intra-daily price data. Specifically, we review stylized facts of intra-daily data, econometric issues of data analysis, application of intra-daily data in volatility and liquidity research, and the applications to market microstructure theory. Long-range dependence is observed in intra-daily data. Because fractal processes or fractional integrated models are usually used to model long-range dependence, we also provide a review of fractal processes and long-range dependence in order to consider them in future research using intra-daily data.

Mixed-stable approach to the management of the portfolio using high-frequency financial data

“…However, the real-world financial data often do not follow this assumption. Their behaviour is characterized by such features as skewness, kurtosis, heavy tails, self-similarity and multifractality [28,29,34,35].…”

Fractals or I.I.D.: Evidence of long-range dependence and heavy tailedness from modeling German equity market returns

“…Recent theoretical and empirical research on long-range dependence in economics and finance is provided by Rangarajan and Ding (2006) and Teyssiére and Kirman (2006). Sun et al (2007) provide a review of long-range dependence research based on intra-daily data. (2005) have demonstrated the advantages of stable distributions in financial modeling.…”

ADAGE: a framework for supporting user-driven ad-hoc data analysis processes

“…In addition, Dow Jones Factiva also includes regulatory announcements originating from financial exchanges. Both news and market data are generated at a high-frequency, also referred to as "real time tick data" or "tick-by-tick data" [28]-it is not uncommon to find multiple records generated within the same millisecond. Due to the vast amounts of historical data available, high-frequency datasets are typically of hundreds of megabytes to many gigabytes in size.…”