- 2
- 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=6192
- Prefix
- of the plausible sources of nonlinearity in foreign exchange rates. 3 Long-memory methods have been applied extensively to financial asset price series: for stock prices (Lo (1991)), futures prices (Barkoulas, Labys, and Onochie (1999)), commodity prices (Barkoulas, Labys, and Onochie (1997)), Eurocurrency deposit rates (Barkoulas and Baum (1997)), for example. See
- Exact
- Baillie (1996)
- Suffix
- for a survey of fractional integration methods and applications in economics and finance. distant observations, its presence entails that past returns can help predict future returns, and the possibility of consistent speculative profits arises.4 Applying rescaled-range (R/S) analysis to daily exchange rates for the British pound, French franc, and Deutsche mark, Booth, Kaen, and Koveos

- In-text reference with the coordinate start=6192
- 3
- Baillie, R. and T. Bollerslev (1989), Common stochastic trends in a system of exchange rates, Journal of Finance, 44, 167-181.

Total in-text references: 1- In-text reference with the coordinate start=3039
- Prefix
- The standard tool in analyzing the stochastic behavior of exchange rates has been the autoregressive integrated moving average (ARIMA) model. Along these lines, a large body of past research (see, for example,
- Exact
- Baillie and Bollerslev (1989))
- Suffix
- documents that foreign currency rates are best characterized as pure unit-root (random-walk or martingale) processes, thus making predictability of exchange rate movements impossible.

- In-text reference with the coordinate start=3039
- 4
- Barkoulas, J. and C. F. Baum (1997), Fractional differencing modeling and forecasting of Eurocurrency deposit rates, Journal of Financial Research, 20(3), 355-372.

Total in-text references: 1- In-text reference with the coordinate start=6139
- Prefix
- of the structural exchange rate model are some of the plausible sources of nonlinearity in foreign exchange rates. 3 Long-memory methods have been applied extensively to financial asset price series: for stock prices (Lo (1991)), futures prices (Barkoulas, Labys, and Onochie (1999)), commodity prices (Barkoulas, Labys, and Onochie (1997)), Eurocurrency deposit rates
- Exact
- (Barkoulas and Baum (1997)),
- Suffix
- for example. See Baillie (1996) for a survey of fractional integration methods and applications in economics and finance. distant observations, its presence entails that past returns can help predict future returns, and the possibility of consistent speculative profits arises.4 Applying rescaled-range (R/S) analysis to daily exchange rates for the British pound, French franc, and Deu

- In-text reference with the coordinate start=6139
- 7
- Booth, G. G., F. R. Kaen and P. E. Koveos (1982), R/S analysis of foreign exchange markets under two international monetary regimes, Journal of Monetary Economics, 10, 407-415.

Total in-text references: 2- In-text reference with the coordinate start=16549
- Prefix
- For the Italian lira, rejection of the unit-root null hypothesis is obtained but it is restricted to a particular estimation window size, thus lacking robustness. This evidence for the major currency rates does not confirm the long-memory evidence reported in
- Exact
- Booth et al. (1982) and Cheung (1993).
- Suffix
- For the remaining currencies, consistent evidence of long memory is apparent for the Danish krone, Luxembourg franc, Portugese escudo, and Spanish peseta. For the Belgian franc, Swedish krona, Finnish markka, and Greek drachma, weak evidence of fractional dynamic behavior is found, but only for a specific estimation window size.

- In-text reference with the coordinate start=24118
- Prefix
- A sensitivity analysis suggests that, when evidence of long memory is obtained, it is sporadic and generally temporally unstable. The evidence of long memory in major currency rates reported in
- Exact
- Booth et al. (1982) and Cheung (1993)
- Suffix
- would appear to be an artifact of the sample period and currencies considered in those studies. For all but three of the broader set of currencies analyzed here, we find that the unit-root hypothesis is robust to long-memory alternatives, providing strong support for martingale behavior of currency rates and, therefore, for foreign exchange market efficiency.

- In-text reference with the coordinate start=16549
- 8
- Cheung, Y. W. (1993), Long memory in foreign-exchange rates, Journal of Business and

Total in-text references: 3- In-text reference with the coordinate start=16549
- Prefix
- For the Italian lira, rejection of the unit-root null hypothesis is obtained but it is restricted to a particular estimation window size, thus lacking robustness. This evidence for the major currency rates does not confirm the long-memory evidence reported in
- Exact
- Booth et al. (1982) and Cheung (1993).
- Suffix
- For the remaining currencies, consistent evidence of long memory is apparent for the Danish krone, Luxembourg franc, Portugese escudo, and Spanish peseta. For the Belgian franc, Swedish krona, Finnish markka, and Greek drachma, weak evidence of fractional dynamic behavior is found, but only for a specific estimation window size.

- In-text reference with the coordinate start=24118
- Prefix
- A sensitivity analysis suggests that, when evidence of long memory is obtained, it is sporadic and generally temporally unstable. The evidence of long memory in major currency rates reported in
- Exact
- Booth et al. (1982) and Cheung (1993)
- Suffix
- would appear to be an artifact of the sample period and currencies considered in those studies. For all but three of the broader set of currencies analyzed here, we find that the unit-root hypothesis is robust to long-memory alternatives, providing strong support for martingale behavior of currency rates and, therefore, for foreign exchange market efficiency.

- In-text reference with the coordinate start=25250
- Prefix
- These weekly rates represent Friday noon-time bid prices from the New York foreign exchange market and were obtained from the Federal Reserve Board of Governors. When Friday prices are not available Thursday prices are used. (The construction of the data set of weekly observations follows
- Exact
- Cheung (1993)).
- Suffix
- For the U.S. dollar nominal rates for the Austrian schilling, Danish krone, Luxembourg franc, Norwegian krone, Finnish markka, Portugese escudo, and Spanish peseta, the frequency of observation is monthly and the sample covers the period 08/1973 to 12/1995 for a total of 268 returns observations.

- In-text reference with the coordinate start=16549
- 11
- Diebold, F. and J. Nason (1990), Nonparametric exchange rate prediction?, Journal of

Total in-text references: 1- In-text reference with the coordinate start=3838
- Prefix
- For example, size and limited maturity of forward contracts may make it difficult for firms to hedge their foreign exchange risk. improve upon the predictive accuracy of random-walk forecasts motivated many researchers to turn to nonlinear models.2 Engel and Hamilton (1990) use a Markov switching model for exchange rate changes while
- Exact
- Diebold and Nason (1990) and Meese and Rose (1990)
- Suffix
- use variants of local regression, a nearest-neighbor nonparametric technique. Kuan and Liu (1995) use feedforward and recurrent artificial neural networks to produce conditional mean forecasts of foreign exchange rates.

- In-text reference with the coordinate start=3838
- 13
- Engel, C. and J. D. Hamilton (1990), Long swings in the dollar: Are they in the data and do markets know it?, American Economic Review, 80, 689-713.

Total in-text references: 1- In-text reference with the coordinate start=3746
- Prefix
- For example, size and limited maturity of forward contracts may make it difficult for firms to hedge their foreign exchange risk. improve upon the predictive accuracy of random-walk forecasts motivated many researchers to turn to nonlinear models.2
- Exact
- Engel and Hamilton (1990)
- Suffix
- use a Markov switching model for exchange rate changes while Diebold and Nason (1990) and Meese and Rose (1990) use variants of local regression, a nearest-neighbor nonparametric technique.

- In-text reference with the coordinate start=3746
- 16
- Henry M. and Robinson P. M. (1999), Bandwidth choice in Gaussian semiparametric estimation of long range dependence, working paper, Department of Economics, London School of

Total in-text references: 1- In-text reference with the coordinate start=18077
- Prefix
- The GPH results are not reported here but they are available upon request from the authors. 7 Monte Carlo simulations have shown that such bandwidth choices provide a good balance in the tradeoff between bias (which tends to increase with bandwidth) and sampling variability (which tends to decrease with bandwidth).
- Exact
- Henry and Robinson (1999)
- Suffix
- provide heuristic approximations of the minimum mean squared error optimal bandwidth. Inferences drawn below remain unaltered for other plausible bandwidth choices. 8 Alternative estimation methods of long-memory models include Sowell's (1992) exact maximum likelihood method, Fox and Taqqu's (1986) frequency domain approximate maximum likelihood method, and the condition

- In-text reference with the coordinate start=18077
- 17
- Hosking, J. R. M. (1981), Fractional Differencing, Biometrika, 68, 165-176.

Total in-text references: 1- In-text reference with the coordinate start=11017
- Prefix
- The arbitrary restriction of d to integer values gives rise to the standard autoregressive integrated moving average (ARIMA) model. 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. Assuming that d∈0, 0.5() and d≠0,
- Exact
- Hosking (1981)
- Suffix
- shows that the correlation function, ρ(⋅), 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=11017
- 18
- Kuan, C-M. and T. Liu (1995), Forecasting exchange rates using feedforward and recurrent neural networks, Journal of Applied Econometrics, 10, 347-364.

Total in-text references: 1- In-text reference with the coordinate start=3975
- Prefix
- their foreign exchange risk. improve upon the predictive accuracy of random-walk forecasts motivated many researchers to turn to nonlinear models.2 Engel and Hamilton (1990) use a Markov switching model for exchange rate changes while Diebold and Nason (1990) and Meese and Rose (1990) use variants of local regression, a nearest-neighbor nonparametric technique.
- Exact
- Kuan and Liu (1995)
- Suffix
- use feedforward and recurrent artificial neural networks to produce conditional mean forecasts of foreign exchange rates. Meese and Rose (1991) estimate structural models of exchange rate determination using a variety of nonparametric techniques.

- In-text reference with the coordinate start=3975
- 19
- Lo, A. W. (1991), Long-term memory in stock market prices, Econometrica, 59, 1279-1313.

Total in-text references: 2- In-text reference with the coordinate start=5972
- Prefix
- 2 Absence of risk-neutral behavior, the nature of the policy regime, time deformation, and misspecification of the functional form of the structural exchange rate model are some of the plausible sources of nonlinearity in foreign exchange rates. 3 Long-memory methods have been applied extensively to financial asset price series: for stock prices
- Exact
- (Lo (1991)),
- Suffix
- futures prices (Barkoulas, Labys, and Onochie (1999)), commodity prices (Barkoulas, Labys, and Onochie (1997)), Eurocurrency deposit rates (Barkoulas and Baum (1997)), for example.

- In-text reference with the coordinate start=9120
- Prefix
- Statistical inferences concerning asset pricing models based on standard testing procedures may not be appropriate in the presence of long-memory series. 5 The classical rescaled-range (R/S) method has a number of drawbacks (see
- Exact
- Lo (1991)).
- Suffix
- differencing) parameter for the foreign currency rates. We use the Gaussian semiparametric method to estimate the long-memory parameter. Contrary to previous findings of strong persistence, our evidence strongly favors the martingale model against long-memory alternatives in the foreign currency markets, thus supporting the market efficiency hypothesis in its weak form.

- In-text reference with the coordinate start=5972
- 20
- Mandelbrot, 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.

Total in-text references: 1- In-text reference with the coordinate start=8463
- Prefix
- 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.

- In-text reference with the coordinate start=8463
- 21
- Meese, R. A. and A. K. Rose (1990), Nonlinear, nonparametric, nonessential exchange rate estimation, American Economic Review Papers and Proceedings, 80, 192-196.

Total in-text references: 1- In-text reference with the coordinate start=3838
- Prefix
- For example, size and limited maturity of forward contracts may make it difficult for firms to hedge their foreign exchange risk. improve upon the predictive accuracy of random-walk forecasts motivated many researchers to turn to nonlinear models.2 Engel and Hamilton (1990) use a Markov switching model for exchange rate changes while
- Exact
- Diebold and Nason (1990) and Meese and Rose (1990)
- Suffix
- use variants of local regression, a nearest-neighbor nonparametric technique. Kuan and Liu (1995) use feedforward and recurrent artificial neural networks to produce conditional mean forecasts of foreign exchange rates.

- In-text reference with the coordinate start=3838
- 22
- Meese, R. A. and A. K. Rose (1991), An empirical assessment of nonlinearities in models of exchange rate determination, Review of Economic Studies, 80, 192-196.

Total in-text references: 1- In-text reference with the coordinate start=4116
- Prefix
- to nonlinear models.2 Engel and Hamilton (1990) use a Markov switching model for exchange rate changes while Diebold and Nason (1990) and Meese and Rose (1990) use variants of local regression, a nearest-neighbor nonparametric technique. Kuan and Liu (1995) use feedforward and recurrent artificial neural networks to produce conditional mean forecasts of foreign exchange rates.
- Exact
- Meese and Rose (1991)
- Suffix
- estimate structural models of exchange rate determination using a variety of nonparametric techniques. The success of these studies to explain exchange rate movements has been very limited, thus leaving the martingale model as the leading characterization of the data generating process of exchange rates.

- In-text reference with the coordinate start=4116
- 23
- Robinson, P. (1995), 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=11999
- Prefix
- For d∈0. 5,1[) the process is nonstationary (having an infinite variance) but it is mean reverting, as there is no long-run impact of an innovation on future values of the process. We estimate the long-memory parameter using Robinson's Gaussian semiparametric method.
- Exact
- Robinson (1995)
- Suffix
- proposes a Gaussian semiparametric estimate, GS 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 fξ()~G1−2Hξ as ξ→+0(3) for G∈0,∞() and H∈0,1().

- In-text reference with the coordinate start=11999
- 24
- Robinson, P. and M. Henry (1999), Long memory conditionally heteroscedastic errors in semiparametric estimation of long memory, working paper, Department of

Total in-text references: 1- In-text reference with the coordinate start=13188
- Prefix
- The GS estimator appears to be the most efficient semiparametric estimator developed so far. It is also consistent and has the same limiting distribution under conditional heteroscedasticity
- Exact
- (Robinson and Henry (1999)).
- Suffix
- 3. Data and Long-memory Results 3A. Data The data set consists of U.S. dollar nominal rates of weekly frequency for the Canadian dollar, Deutsche mark, British pound, French franc, Italian lira, Japanese yen, Swiss franc, Netherlands guilder, Swedish krona, and Belgian franc and of monthly frequency for the Austrian schilling, Danish krone, Luxembourg franc, Norw

- In-text reference with the coordinate start=13188