IDEAS home Printed from https://ideas.repec.org/a/bla/manchs/v73y2005i2p165-213.html
   My bibliography  Save this article

Optimal And Adaptive Semi‐Parametric Narrowband And Broadband And Maximum Likelihood Estimation Of The Long‐Memory Parameter For Real Exchange Rates

Author

Listed:
  • SAEED HERAVI
  • KERRY PATTERSON

Abstract

The nature of the time series properties of real exchange rates remains a contentious issue primarily because of the implications for purchasing power parity. In particular are real exchange rates best characterized as stationary and non‐persistent; nonstationary but non‐persistent; or nonstationary and persistent? Most assessments of this issue use the I(0)/I(1) paradigm, which only allows the first and last of these options. In contrast, in the I(d) paradigm, d fractional, all three are possible, with the crucial parameter d determining the long‐run properties of the process. This study includes estimation of d by three methods of semi‐parametric estimation in the frequency domain, using both local and global (Fourier) frequency estimation, and maximum likelihood estimation of ARFIMA models in the time domain. We give a transparent assessment of the key selection parameters in each method, particularly estimation of the truncation parameters for the semi‐parametric methods. Two other important developments are also included. We implement Tanaka's locally best invariant parametric tests based on maximum likelihood estimation of the long‐memory parameter and include a recent extension of the Dickey–Fuller approach, referred to as fractional Dickey–Fuller (FD‐F), to fractionally integrated series, which allows a much wider range of generating processes under the alternative hypothesis. With this more general approach, we find very little evidence of stationarity for 10 real exchange rates for developed countries and some very limited evidence of nonstationarity but non‐persistence, and none of the FD‐F tests leads to rejection of the null of a unit root.

Suggested Citation

  • Saeed Heravi & Kerry Patterson, 2005. "Optimal And Adaptive Semi‐Parametric Narrowband And Broadband And Maximum Likelihood Estimation Of The Long‐Memory Parameter For Real Exchange Rates," Manchester School, University of Manchester, vol. 73(2), pages 165-213, March.
  • Handle: RePEc:bla:manchs:v:73:y:2005:i:2:p:165-213
    DOI: 10.1111/j.1467-9957.2005.00441.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9957.2005.00441.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1467-9957.2005.00441.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    3. Friberg, Richard, 2001. "Two monies, two markets?: Variability and the option to segment," Journal of International Economics, Elsevier, vol. 55(2), pages 317-327, December.
    4. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    5. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    6. Pinelopi Koujianou Goldberg & Michael M. Knetter, 1997. "Goods Prices and Exchange Rates: What Have We Learned?," Journal of Economic Literature, American Economic Association, vol. 35(3), pages 1243-1272, September.
    7. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April.
    8. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
    9. Wu, Yangru, 1996. "Are Real Exchange Rates Nonstationary? Evidence from a Panel-Data Test," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(1), pages 54-63, February.
    10. Taylor, Mark P & Peel, David A & Sarno, Lucio, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1015-1042, November.
    11. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    12. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February.
    13. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
    14. Papell, David H., 1997. "Searching for stationarity: Purchasing power parity under the current float," Journal of International Economics, Elsevier, vol. 43(3-4), pages 313-332, November.
    15. Sarno, Lucio & Taylor, Mark P., 1998. "Real exchange rates under the recent float: unequivocal evidence of mean reversion," Economics Letters, Elsevier, vol. 60(2), pages 131-137, August.
    16. Mark, Nelson C., 1990. "Real and nominal exchange rates in the long run: An empirical investigation," Journal of International Economics, Elsevier, vol. 28(1-2), pages 115-136, February.
    17. Anderson, Simon P & Ginsburgh, Victor A, 1999. "International Pricing with Costly Consumer Arbitrage," Review of International Economics, Wiley Blackwell, vol. 7(1), pages 126-139, February.
    18. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive Semiparametric Estimation of the Memory Parameter," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 183-207, February.
    19. Clifford M. Hurvich & Willa W. Chen, 2000. "An Efficient Taper for Potentially Overdifferenced Long‐memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 155-180, March.
    20. Pinelopi Koujianou Goldberg & Frank Verboven, 2001. "The Evolution of Price Dispersion in the European Car Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(4), pages 811-848.
    21. MacDonald, Ronald, 1996. "Panel unit root tests and real exchange rates," Economics Letters, Elsevier, vol. 50(1), pages 7-11, January.
    22. Taylor, Mark P. & Sarno, Lucio, 1998. "The behavior of real exchange rates during the post-Bretton Woods period," Journal of International Economics, Elsevier, vol. 46(2), pages 281-312, December.
    23. Abuaf, Niso & Jorion, Philippe, 1990. "Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 45(1), pages 157-174, March.
    24. Oh, Keun-Yeob, 1996. "Purchasing power parity and unit root tests using panel data," Journal of International Money and Finance, Elsevier, vol. 15(3), pages 405-418, June.
    25. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-511, August.
    26. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    27. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive semiparametric estimation of the memory parameter," LSE Research Online Documents on Economics 2082, London School of Economics and Political Science, LSE Library.
    28. Coakley, Jerry & Fuertes, Ana Maria, 1997. "New panel unit root tests of PPP," Economics Letters, Elsevier, vol. 57(1), pages 17-22, November.
    29. Fleissig, Adrian R. & Strauss, Jack, 2000. "Panel unit root tests of purchasing power parity for price indices," Journal of International Money and Finance, Elsevier, vol. 19(4), pages 489-506, August.
    30. Clifford M. Hurvich, 2001. "Model Selection for Broadband Semiparametric Estimation of Long Memory in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 679-709, November.
    31. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
    32. Liudas Giraitis & Peter M. Robinson & Alexander Samarov, 1997. "Rate Optimal Semiparametric Estimation Of The Memory Parameter Of The Gaussian Time Series With Long‐Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(1), pages 49-60, January.
    33. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    34. Adler, Michael & Lehmann, Bruce, 1983. "Deviations from Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 38(5), pages 1471-1487, December.
    35. Kuo, Biing-Shen & Mikkola, Anne, 2001. "How Sure Are We about Purchasing Power Parity? Panel Evidence with the Null of Stationary Real Exchange Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 33(3), pages 767-789, August.
    36. Clifford M. Hurvich & Kaizo I. Beltrao, 1994. "Automatic Semiparametric Estimation Of The Memory Parameter Of A Long‐Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 285-302, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:rdg:wpaper:em-dp2013-02 is not listed on IDEAS
    2. Derek Bond & Michael J. Harrison & Niall Hession & Edward J. O'Brien, 2006. "Some Empirical Observations on the Forward Exchange Rate Anomaly," Trinity Economics Papers tep2006, Trinity College Dublin, Department of Economics.
    3. Saeed Heravi & Kerry Patterson, 2013. "Log-Periodogram Estimation of the Long-Memory Parameter: An Evaluation of Competing Estimators," Economics Discussion Papers em-dp2013-02, Department of Economics, University of Reading.
    4. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers tep200615, Trinity College Dublin, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Miguel Carvalho & Paulo Júlio, 2012. "Digging out the PPP hypothesis: an integrated empirical coverage," Empirical Economics, Springer, vol. 42(3), pages 713-744, June.
    2. Okimoto, Tatsuyoshi & Shimotsu, Katsumi, 2010. "Decline in the persistence of real exchange rates, but not sufficient for purchasing power parity," Journal of the Japanese and International Economies, Elsevier, vol. 24(3), pages 395-411, September.
    3. Tatsuyoshi Okimoto & Katsumi Shimotsu, 2007. "Financial Market Integration And World Economic Stabilization Toward Purchasing Power Parity," Working Paper 1138, Economics Department, Queen's University.
    4. Choi, Chi-Young, 2004. "Searching for evidence of long-run PPP from a post-Bretton Woods panel: separating the wheat from the chaff," Journal of International Money and Finance, Elsevier, vol. 23(7-8), pages 1159-1186.
    5. Lucio Sarno & Mark P. Taylor, 2002. "Purchasing Power Parity and the Real Exchange Rate," IMF Staff Papers, Palgrave Macmillan, vol. 49(1), pages 1-5.
    6. Chiu, Ru-Lin, 2002. "Testing the purchasing power parity in panel data," International Review of Economics & Finance, Elsevier, vol. 11(4), pages 349-362.
    7. Maican, Florin G. & Sweeney, Richard J., 2013. "Real exchange rate adjustment in European transition countries," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 907-926.
    8. Jean Imbs & Haroon Mumtaz & Morten O. Ravn & Hélène Rey, 2005. "PPP Strikes Back: Aggregation And the Real Exchange Rate," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 1-43.
    9. Cushman, David O. & Michael, Nils, 2011. "Nonlinear trends in real exchange rates: A panel unit root test approach," Journal of International Money and Finance, Elsevier, vol. 30(8), pages 1619-1637.
    10. Caporale, Guglielmo Maria & Cerrato, Mario, 2004. "Panel Data Tests of PPP. A Critical Overview," Economics Series 159, Institute for Advanced Studies.
    11. Hwa-Taek Lee & Gawon Yoon, 2013. "Does purchasing power parity hold sometimes? Regime switching in real exchange rates," Applied Economics, Taylor & Francis Journals, vol. 45(16), pages 2279-2294, June.
    12. Cheung, Yin-Wong & Lai, Kon S., 2001. "Long memory and nonlinear mean reversion in Japanese yen-based real exchange rates," Journal of International Money and Finance, Elsevier, vol. 20(1), pages 115-132, February.
    13. Chen, Show-Lin & Wu, Jyh-Lin, 2000. "A Re-Examination of Purchasing Power Parity in Japan and Taiwan," Journal of Macroeconomics, Elsevier, vol. 22(2), pages 271-284, April.
    14. Syed A. Basher & Josep Lluís Carrion-i-Silvestre, 2007. "Another Look at the Null of Stationary RealExchange Rates. Panel Data with Structural Breaks and Cross-section Dependence," IREA Working Papers 200710, University of Barcelona, Research Institute of Applied Economics, revised May 2007.
    15. Lean Hooi Hooi & Russell Smyth, 2007. "Are Asian real exchange rates mean reverting? Evidence from univariate and panel LM unit root tests with one and two structural breaks," Applied Economics, Taylor & Francis Journals, vol. 39(16), pages 2109-2120.
    16. Franses, Ph.H.B.F. & van Dijk, D.J.C., 2002. "A simple test for PPP among traded goods," Econometric Institute Research Papers EI 2002-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Alan M. Taylor & Mark P. Taylor, 2004. "The Purchasing Power Parity Debate," Journal of Economic Perspectives, American Economic Association, vol. 18(4), pages 135-158, Fall.
    18. Cheung, Yin-Wong & Lai, Kon S., 2000. "On cross-country differences in the persistence of real exchange rates," Journal of International Economics, Elsevier, vol. 50(2), pages 375-397, April.
    19. Tolga Omay & Furkan Emirmahmutoglu & Mubariz Hasanov, 2018. "Structural break, nonlinearity and asymmetry: a re-examination of PPP proposition," Applied Economics, Taylor & Francis Journals, vol. 50(12), pages 1289-1308, March.
    20. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:manchs:v:73:y:2005:i:2:p:165-213. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/semanuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.