Foreign Exchange

Long Memory in the Foreign Exchange Market

Cheung (1993) finds evidence of long memory in exchange-rate data.

"Significant evidence of positive long-range dependence is found in the Euroyen returns series. The estimated fractional models result in dramatic out-of-sample forecasting improvements over longer horizons compared to benchmark linear models, thus providing strong evidence against the martingale model."
Barkoulas and Baum (1997)

"While the exponent values were not significantly large enough to conclude in favour of statistical long-term dependence in the currency returns series..."
Batten and Ellis (1999)

"Contrary to the findings of some previous studies alluding to the presence of long memory in major currency rates, our evidence provides wide support to the martingale model (and therefore for foreign exchange market efficiency) for our broader sample of foreign currency rates. Any inference of long-range dependence is fragile, especially for the major currency rates. However, long-memory dynamics are found in a small number of secondary (nonmajor) currency rates."
Barkoulas et al.

Baum, Barkoulas and Caglayan (1999) suggest "rejection of the doctrine of absolute long-run purchasing power parity during the post-Bretton Woods era".

"The Hurst (1951) approach suggests the presence of time-varying long-term dependence in some of the subperiods and for the whole sample period. However this result was not supported when the Lo (1991) procedure was applied to the various subperiods. This suggests that the significant Hurst (1951) result identified in some of the subperiods was due to low-order or short-term dependence in that particular series. Thus in line with Fama’s (1998) suggestion that long-term anomalies may be due to “methodological illusions” we procedure used and the period being tested. We conclude that other researchers may have inadvertently introduced a sample or method bias in their studies of the time series properties of the spot USD/Yen."
Batten, Ellis and Fethererston (2000)

"Findings have generally been in favour of the presence of non-linear dependence consistent with long-memory (Peters 1994; Van De Gucht, Dekimpe and Kwok 1996; Opong, Mulholland, Fox and Farahmand, 1999; Barkoulas, Labys and Onochie, 1999). Using the classical rescaled range method proposed by Hurst (1951), Peters finds evidence of significant positive dependence in USD/DMK, USD/JPY and USD/CHF daily exchange rates. Using a variety of univariate and multivariate persistence measures, Van De Gucht et al. similarly find that a number of exchange rate series exhibit long- run behaviour that deviate from a strict random walk. The results are consistent with those of Cheung (1993) who finds evidence of long-term memory in spot currency markets using spectral regression techniques. However the results of a recent study on the Japanese yen by Batten, Ellis and Fetherston (2000) casts doubt on the earlier Peter’s result and supports Fama’s (1998) conclusion: there was no evidence of long-term dependency with the results from earlier researchers being “methodological illusions”.
Analysing mean absolute logarithmic price changes for five foreign exchange rate pairs, Muller et al. (1990) find that intraday price changes scale at approximately H = 0.59.
the lagged correlation structure does not suggest the presence of long-term memory." [...]
no significant evidence of dependence between series increments for the four currencies is found.
the exponent values of the currency return series are not significantly large enough to conclude in favour of statistical long-term dependence..."
Batten and Ellis (2001)

Cheung and Lai (2001) show that "the puzzling behavior of real yen rates may stem from long-memory dynamics, which undermine unit-root tests in their ability to detect mean reversion. The longmemory findings are consistent with the long swings in yen exchange rates during the current float. Further analysis also reveals evidence of non-monotonic reversion toward parity."

"This paper examines dollar interventions by the G3 governments since 1989, and the reasons that trader reactions to these interventions might differ over time and across central banks. Market microstructure theory provides a framework for understanding the process by which sterilized central bank interventions are observed and interpreted by traders, and how this process, in turn, might influence exchange rates. Using intra-daily and daily exchange rate and intervention data, the paper analyzes the influence of interventions on exchange rate volatility, finding evidence of both within day and daily impact effects, but little evidence that interventions increase longer-term volatility."
Dominguez (2003)

"USD/DEM tick data are slightly trending, not mean-reverting, on time scales of 60 ticks (about 15 minutes) or less." Dunis and Zhou [book]

"However,when non-U.S. dollar real exchange rates are used, we find only two cases out of fifteen where the null hypothes is of an unit-root with short-term dependence can be rejected in favor of the alternative hypothesis of long-term dependence using the modified rescaled range test, and only one case when using the rescaled variance test. Our results therefore provide a contrast to the recent favorable panel unit-root test results."
Ahking (2004)