- 1
- Akella, S. R. and A. Patel, 1991, Are international real rates of interest cointegrated? Evidence from the recent floating exchange rate period, unpublished manuscript, University of Missouri.

Total in-text references: 1- In-text reference with the coordinate 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 interest-rate 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.

- In-text reference with the coordinate start=13629
- 2
- Aydogan, K. and G. G. Booth, 1988, Are there long cycles in common stock returns?, Southern Economic

Total in-text references: 1- In-text reference with the coordinate start=4347
- Prefix
- Using the rescaled-range (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 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 futur

- In-text reference with the coordinate start=4347
- 3
- Baillie, R., 1996, Long memory processes and fractional integration in econometrics, Journal of Econometrics 73, 5-59.

Total in-text references: 1- In-text reference with the coordinate start=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.

- In-text reference with the coordinate start=4870
- 4
- Baillie, R. and T. Bollerslev, 1994, The long memory of the forward premium, Journal of International Money and Finance 13, 565-571.

Total in-text references: 1- In-text reference with the coordinate start=13727
- Prefix
- The strong autocorrelation in the forward premia series is attributed to the strong autocorrelation in the interest-rate 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 3-month and 6-month Euroyen rates and the corresponding term premium series (the 6-month rate minus the 3month rate).

- In-text reference with the coordinate start=13727
- 5
- Barkoulas, J. T. and C. F. Baum, 1996, Long term dependence in stock returns, Economics Letters,

Total in-text references: 1- In-text reference with the coordinate 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 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

- In-text reference with the coordinate start=4401
- 9
- Brenner, R. and K. Kroner, 1995, Arbitrage, cointegration, and testing the unbiasedness hypothesis in financial markets, Journal of Financial and

Total in-text references: 1- In-text reference with the coordinate start=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 interest-rate 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.

- In-text reference with the coordinate start=13574
- 11
- Cheung, Y. W., 1993, Long memory in foreign-exchange rates, Journal of Business and Economic Statistics 11, 93-101.

Total in-text references: 1- In-text reference with the coordinate start=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 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

- In-text reference with the coordinate start=4503
- 12
- Cheung, Y. and K. Lai, 1993, Do gold market returns have long memory? Financial Review 28, 181-202. -11-

Total in-text references: 1- In-text reference with the coordinate 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 long-memory 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

- In-text reference with the coordinate start=4601
- 13
- Cheung, Y. and K. Lai, 1995, A search for long memory in international stock market returns, Journal of International Money and Finance 14, 597-615.

Total in-text references: 1- In-text reference with the coordinate 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 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

- In-text reference with the coordinate start=4401
- 15
- Crato, N., 1994, Some international evidence regarding the stochastic memory of stock returns, Applied Financial Economics 4, 33-39.

Total in-text references: 1- In-text reference with the coordinate 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 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

- In-text reference with the coordinate start=4401
- 17
- Geweke J. and S. Porter-Hudak, 1983, The estimation and application of long memory time series models, Journal of Time Series Analysis 4, 221-238.

Total in-text references: 2- In-text reference with the coordinate start=7872
- Prefix
- For d∈0.5,1[) the process is mean reverting, even though it is not covariance stationary, as there is no long-run impact of an innovation on future values of the process. We estimate the long-memory parameter using the spectral regression and Gaussian semiparametric methods, which we present next. -42A. The Spectral Regression Method
- Exact
- Geweke and Porter-Hudak (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

- In-text reference with the coordinate 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 Porter-Hudak (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 self-similarity parameter H, which is not defined in closed form.

- In-text reference with the coordinate start=7872
- 18
- Granger, C. W. J. and R. Joyeux, 1980, An introduction to long-memory time series models and fractional differencing, Journal of Time Series Analysis 1, 15-39.

Total in-text references: 2- 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), Granger and Joyeux (1980), 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.

- In-text reference with the coordinate 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.

- In-text reference with the coordinate start=1876
- 19
- Greene, M. T. and B. D. Fielitz, 1977, Long-term dependence in common stock returns, Journal of Financial Economics 5, 339-349.

Total in-text references: 1- In-text reference with the coordinate start=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 rescaled-range (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).

- In-text reference with the coordinate start=4091
- 21
- Hosking, J. R. M., 1981, Fractional Differencing, Biometrika 68, 165-176.

Total in-text references: 2- 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), Granger and Joyeux (1980), 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.

- In-text reference with the coordinate start=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.

- In-text reference with the coordinate start=1876
- 22
- Kwiatkowski, D., P.C.B. Phillips, P. Schmidt and Y. Shin, 1992, Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? Journal of Econometrics 54, 159-178.

Total in-text references: 1- In-text reference with the coordinate start=16084
- Prefix
- 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), 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.

- In-text reference with the coordinate start=16084
- 23
- Lo, A. W., 1991, Long-term memory in stock market prices, Econometrica 59, 12791313.

Total in-text references: 1- In-text reference with the coordinate 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 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).

- In-text reference with the coordinate start=4195
- 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-

Total in-text references: 1- In-text reference with the coordinate start=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.

- In-text reference with the coordinate start=2695
- 25
- 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), Granger and Joyeux (1980), 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.

- In-text reference with the coordinate start=1876
- 26
- Phillips, P.C.B., 1987, Time series regression with a unit root. Econometrica 55, 277301.

Total in-text references: 1- In-text reference with the coordinate start=16084
- Prefix
- 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), 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.

- In-text reference with the coordinate start=16084
- 27
- Phillips, P.C.B. and P. Perron, 1988, Testing for a unit root in time series regression. Biometrika 75, 335-346.

Total in-text references: 1- In-text reference with the coordinate start=16084
- Prefix
- 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), 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.

- In-text reference with the coordinate start=16084
- 28
- Robinson, P., 1995a, Log-periodogram regression of time series with long range dependence, Annals of Statistics 13, 1048-1072.

Total in-text references: 1- In-text reference with the coordinate 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 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.

- In-text reference with the coordinate start=8900
- 29
- Robinson, P., 1995b, Gaussian semiparametric estimation of long range dependence, Annals of Statistics 13, 1630-1661.

Total in-text references: 1- In-text reference with the coordinate start=9064
- Prefix
- 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)
- Suffix
- 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().

- In-text reference with the coordinate start=9064
- 30
- Yajima, Y., 1985, On the estimation of long memory time series models, Australian Journal of Statistics 27, 303-320. -13-

Total in-text references: 1- In-text reference with the coordinate start=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 long-memory 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.

- In-text reference with the coordinate start=3215