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1876
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If a series exhibits long memory, there is persistent
temporal dependence between observations widely separated in time. Such series
exhibit hyperbolically decaying autocorrelations and lowfrequency spectral
distributions. Fractionally integrated processes can give rise to long memory
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(Mandelbrot (1977),
 Suffix

Granger and Joyeux (1980), Hosking (1981)). On the other hand,
the shortmemory, or shortterm dependence, property describes the loworder
correlation structure of a series. Shortmemory series are typified by quickly declining
autocorrelations and highfrequency spectral distributions.
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1922
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Such series
exhibit hyperbolically decaying autocorrelations and lowfrequency 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 shortmemory, or shortterm dependence, property describes the loworder
correlation structure of a series. Shortmemory series are typified by quickly declining
autocorrelations and highfrequency spectral distributions.
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2695
 Prefix

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.
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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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3215
 Prefix

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 longmemory 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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4195
 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 rescaledrange (R/S) method, Greene and Fielitz
(1977) report long memory in daily stock returns series. This result is overturned by
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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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 Start

4358
 Prefix

Using the rescaledrange (R/S) method, Greene and Fielitz
(1977) report long memory in daily stock returns series. 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
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Booth (1988),
 Suffix

Cheung, Lai, and Lai (1993), Cheung and Lai (1995), Crato
(1994), and Barkoulas and Baum (1996). Booth, Kaen, and Koveos (1982) and Cheung
(1993) report longmemory 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 futur
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4424
 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 longmemory 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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4503
 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
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Cheung (1993)
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report longmemory 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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4870
 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
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Baillie (1996)
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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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6910
 Prefix

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,
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Hosking (1981)
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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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8900
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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 PorterHudak (1983) prove consistency and asymptotic normality for d<0, while
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Robinson (1995a)
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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 selfsimilarity parameter H, which is not defined in
closed form.
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9064
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Geweke
and PorterHudak (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
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Robinson (1995b)
 Suffix

proposes a Gaussian semiparametric estimate, referred to as
the GS estimate hereafter, of the selfsimilarity 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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16084
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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 PhillipsPerron
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(Phillips (1987),
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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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