
 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 lowfrequency spectral
distributions. Fractionally integrated processes can give rise to long memory
 Exact

(Mandelbrot (1977), Granger and Joyeux (1980), 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.
 Exact

Mandelbrot (1971)
 Suffix

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
 Exact

(Yajima (1985)).
 Suffix

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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4091
 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,
 Exact

Greene and Fielitz (1977)
 Suffix

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 Booth (1988), Cheung, Lai, and Lai (1993), Cheung and Lai (1995), Crato
(1994), and Barkoulas and Baum (1996).
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 Start

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
 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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4347
 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
 Exact

Aydogan and 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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 Start

4401
 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),
 Exact

Cheung and Lai (1995), Crato (1994), and Barkoulas and Baum (1996).
 Suffix

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
 Exact

Cheung (1993)
 Suffix

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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 Start

4601
 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 Cheung (1993) report longmemory evidence in spot exchange rates. Helms, Kaen, and
Rosenman (1984),
 Exact

Cheung and Lai (1993),
 Suffix

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 integration methods and other applications in economics
and finance.
2In this study we investigate the pres
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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
 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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 Start

6851
 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
 Exact

Granger and Joyeux (1980).
 Suffix

Assuming that d∈0,0.5() and d≠0,
Hosking (1981) 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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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,
 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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7872
 Prefix

For d∈0.5,1[) the process is mean reverting, even though it is not
covariance stationary, as there is no longrun impact of an innovation on future
values of the process.
We estimate the longmemory parameter using the spectral regression and
Gaussian semiparametric methods, which we present next.
42A. The Spectral Regression Method
 Exact

Geweke and PorterHudak (1983)
 Suffix

suggest a semiparametric procedure to obtain
an estimate of the fractional differencing parameter d based on the slope of the
spectral density function around the angular frequency =0. More specifically, let
I() be the periodogram of y at frequency defined by
I() =
1
2T
eit
t=1
T
∑(yt−y )
2
.(3)
Then the spectral regression is defined by
+ , =1,...,(4)
lnI
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 Start

8812
 Prefix

Assuming that
T→∞
limgT()=∞,
T→∞
lim
gT()
T
=0, and
T→∞
lim
lnT()2
gT()
=0, the
negative of the OLS estimate of the slope coefficient in (4) provides an estimate of d.
The properties of the regression method depend on the asymptotic distribution of the
normalized periodogram, the derivation of which is not straightforward.
 Exact

Geweke and PorterHudak (1983)
 Suffix

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
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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 Start

8900
 Prefix

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
 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 selfsimilarity parameter H, which is not defined in
closed form.
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9064
 Prefix

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
 Exact

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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13574
 Prefix

A shock to the forward premia series exhibits significant
persistence but it eventually dissipates at a slow hyperbolic rate of decay. The strong
autocorrelation in the forward premia series is attributed to the strong
autocorrelation in the interestrate differential (see
 Exact

Brenner and Kroner (1995)
 Suffix

for
theoretical arguments and Akella and Patel (1991) for empirical evidence).3 Similar
evidence of long memory is also found in Baillie and Bollerslev (1994) for the U.S.dollar forward premia series for the Canadian dollar, Deutsche mark, and British
pound.
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 Start

13629
 Prefix

A shock to the forward premia series exhibits significant
persistence but it eventually dissipates at a slow hyperbolic rate of decay. The strong
autocorrelation in the forward premia series is attributed to the strong
autocorrelation in the interestrate differential (see Brenner and Kroner (1995) for
theoretical arguments and
 Exact

Akella and Patel (1991)
 Suffix

for empirical evidence).3 Similar
evidence of long memory is also found in Baillie and Bollerslev (1994) for the U.S.dollar forward premia series for the Canadian dollar, Deutsche mark, and British
pound.
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13727
 Prefix

The strong
autocorrelation in the forward premia series is attributed to the strong
autocorrelation in the interestrate differential (see Brenner and Kroner (1995) for
theoretical arguments and Akella and Patel (1991) for empirical evidence).3 Similar
evidence of long memory is also found in
 Exact

Baillie and Bollerslev (1994)
 Suffix

for the U.S.dollar forward premia series for the Canadian dollar, Deutsche mark, and British
pound.
Finally, we test for stochastic long memory in 3month and 6month Euroyen
rates and the corresponding term premium series (the 6month rate minus the 3month rate).
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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
 Exact

(Phillips (1987), Phillips and Perron (1988)) and Kwiatkowski, Phillips, Schmidt and Shin (1992)
 Suffix

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. The martingale model appears to be appropriate for the spot and forward
rates and stock price series.
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