- 3
- Baillie, R., 1996, Long memory processes and fractional integration in econometrics, Journal of Econometrics 73, 5-59.

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- Prefix
- Helms, Kaen, and Rosenman (1984), Cheung and Lai (1993), Fang, Lai, and Lai (1994), and Barkoulas, Labys, and Onochie (1997a,b) report that stochastic long memory may be a feature of some spot and futures foreign currency rates and commodity prices.1 1 See
- Exact
- Baillie (1996)
- Suffix
- for a survey of fractional integration methods and other applications in economics and finance. -2In this study we investigate the presence of fractional dynamics in several important price series of Japanese financial assets.

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- Cheung, Y. W., 1993, Long memory in foreign-exchange rates, Journal of Business and Economic Statistics 11, 93-101.

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- Prefix
- Absence of long memory in stock returns is also reported by Aydogan and Booth (1988), Cheung, Lai, and Lai (1993), Cheung and Lai (1995), Crato (1994), and Barkoulas and Baum (1996). Booth, Kaen, and Koveos (1982) and
- Exact
- Cheung (1993)
- Suffix
- report long-memory evidence in spot exchange rates. Helms, Kaen, and Rosenman (1984), Cheung and Lai (1993), Fang, Lai, and Lai (1994), and Barkoulas, Labys, and Onochie (1997a,b) report that stochastic long memory may be a feature of some spot and futures foreign currency rates and commodity prices.1 1 See Baillie (1996) for a survey of fractional

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- Crato, N., 1994, Some international evidence regarding the stochastic memory of stock returns, Applied Financial Economics 4, 33-39.

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- Prefix
- This result is overturned by Lo (1991) via the development and implementation of the more appropriate modified R/S method. Absence of long memory in stock returns is also reported by Aydogan and Booth (1988), Cheung, Lai, and Lai (1993), Cheung and Lai (1995),
- Exact
- Crato (1994), and
- Suffix
- Barkoulas and Baum (1996). Booth, Kaen, and Koveos (1982) and Cheung (1993) report long-memory evidence in spot exchange rates. Helms, Kaen, and Rosenman (1984), Cheung and Lai (1993), Fang, Lai, and Lai (1994), and Barkoulas, Labys, and Onochie (1997a,b) report that stochastic long memory may be a feature of some spot and futures foreign currency rates and commodity prices.1

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- Hosking, J. R. M., 1981, Fractional Differencing, Biometrika 68, 165-176.

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- Such series exhibit hyperbolically decaying autocorrelations and low-frequency spectral distributions. Fractionally integrated processes can give rise to long memory (Mandelbrot (1977), Granger and Joyeux (1980),
- Exact
- Hosking (1981)).
- Suffix
- On the other hand, the short-memory, or short-term dependence, property describes the low-order correlation structure of a series. Short-memory series are typified by quickly declining autocorrelations and high-frequency spectral distributions.

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- The stochastic process ty is both stationary and invertible if all roots of Φ(L) and Θ(L) lie outside the unit circle and d<0.5. The process is nonstationary for d≥0.5, as it possesses infinite variance, i.e. see Granger and Joyeux (1980). Assuming that d∈0,0.5() and d≠0,
- Exact
- Hosking (1981)
- Suffix
- showed that the correlation function, (⋅), of an ARFIMA process is proportional to 2d−1k as k→∞. Consequently, the autocorrelations of the ARFIMA process decay hyperbolically to zero as k→∞ which is contrary to the faster, geometric decay of a stationary ARMA process.

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- 23
- Lo, A. W., 1991, Long-term memory in stock market prices, Econometrica 59, 12791313.

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- Prefix
- Given the implications of long memory for the theory and practice of financial economics, a number of studies have investigated the issue of persistence in financial asset returns. Using the rescaled-range (R/S) method, Greene and Fielitz (1977) report long memory in daily stock returns series. This result is overturned by
- Exact
- Lo (1991)
- Suffix
- via the development and implementation of the more appropriate modified R/S method. Absence of long memory in stock returns is also reported by Aydogan and Booth (1988), Cheung, Lai, and Lai (1993), Cheung and Lai (1995), Crato (1994), and Barkoulas and Baum (1996).

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- 24
- Mandelbrot, B. B., 1971, When can a price be arbitraged efficiently? a limit to the validity of the random walk and martingale models, Review of Economics and Statistics 53, 225-236. -12-

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- First, as long memory represents a special form of nonlinear dynamics, it calls into question linear modeling and invites the development of nonlinear pricing models at the theoretical level to account for longmemory behavior.
- Exact
- Mandelbrot (1971)
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- observes that in the presence of long memory, the arrival of new market information cannot be fully arbitraged away and martingale models of asset prices cannot be obtained from arbitrage. Second, pricing -1derivative securities with martingale methods may not be appropriate if the underlying continuous stochastic processes exhibit long memory.

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- Mandelbrot, B. B., 1977, Fractals: Form, Chance, and Dimension (Free Press, New York).

Total in-text references: 1- In-text reference with the coordinate start=1876
- Prefix
- If a series exhibits long memory, there is persistent temporal dependence between observations widely separated in time. Such series exhibit hyperbolically decaying autocorrelations and low-frequency spectral distributions. Fractionally integrated processes can give rise to long memory
- Exact
- (Mandelbrot (1977),
- Suffix
- Granger and Joyeux (1980), Hosking (1981)). On the other hand, the short-memory, or short-term dependence, property describes the low-order correlation structure of a series. Short-memory series are typified by quickly declining autocorrelations and high-frequency spectral distributions.

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- Phillips, P.C.B., 1987, Time series regression with a unit root. Econometrica 55, 277301.

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- The currency forward premia and Euroyen term premium series are nonstationary 4 Even though the evidence may not be very strong in support of long memory for the Euroyen term premia series, application of the Phillips-Perron
- Exact
- (Phillips (1987),
- Suffix
- Phillips and Perron (1988)) and Kwiatkowski, Phillips, Schmidt and Shin (1992) tests suggest that neither an I(1) nor an I(0) process is an appropriate representation of the series dynamics, thus alluding to the presence of a fractional root in the series. -9processes.

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- Robinson, P., 1995a, Log-periodogram regression of time series with long range dependence, Annals of Statistics 13, 1048-1072.

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- The properties of the regression method depend on the asymptotic distribution of the normalized periodogram, the derivation of which is not straightforward. Geweke and Porter-Hudak (1983) prove consistency and asymptotic normality for d<0, while
- Exact
- Robinson (1995a)
- Suffix
- proves consistency and asymptotic normality for d∈0,0.5() in the case of Gaussian ARMA innovations in (1). -52B. The Gaussian Semiparametric Method Robinson (1995b) proposes a Gaussian semiparametric estimate, referred to as the GS estimate hereafter, of the self-similarity parameter H, which is not defined in closed form.

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- Robinson, P., 1995b, Gaussian semiparametric estimation of long range dependence, Annals of Statistics 13, 1630-1661.

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- Geweke and Porter-Hudak (1983) prove consistency and asymptotic normality for d<0, while Robinson (1995a) proves consistency and asymptotic normality for d∈0,0.5() in the case of Gaussian ARMA innovations in (1). -52B. The Gaussian Semiparametric Method
- Exact
- Robinson (1995b)
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- proposes a Gaussian semiparametric estimate, referred to as the GS estimate hereafter, of the self-similarity parameter H, which is not defined in closed form. It is assumed that the spectral density of the time series, denoted by f⋅(), behaves as f()~G 1−2H as →+0(5) for G∈0,∞() and H∈0,1().

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- Yajima, Y., 1985, On the estimation of long memory time series models, Australian Journal of Statistics 27, 303-320. -13-

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- Second, pricing -1derivative securities with martingale methods may not be appropriate if the underlying continuous stochastic processes exhibit long memory. Third, statistical inferences concerning asset pricing models based on standard testing procedures may not be appropriate in the presence of long-memory series
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- (Yajima (1985)).
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- Finally, as long memory creates nonlinear dependence in the first moment of the distribution and generates a potentially predictable component in the series dynamics, its presence casts doubt on the weak form of the market efficiency hypothesis.

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