Volume 9, Numbers 3-4, 283-304, DOI: 10.1023/A:1024105822304

Long-Term Memory and Applying the Multi-Factor ARFIMA Models in Financial Markets

Chikashi Tsuji

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Abstract

Exploiting the classical R/S and modified R/S analysis, we first reveal theevidence of long-term memory in liquidity, volume, and volatility. Thereafter,we estimate the fractionally integrated autoregressive movingaverage ARFIMA models by both the exact-maximum likelihood (EML) and themodified-profile likelihood (MPL) methods. Furthermore, based on the theoryof financial economics, we extend the simple ARFIMA models to the Multi-FactorARFIMA models by incorporating the mutual relationships among financial marketvariables and present the effectiveness of the Multi-Factor ARFIMA models infinancial markets.

ARFIMA - fractional differencing - long-range dependence - R/S analysis

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