An Approximate Wavelet MLE of Short and Long Memory Parameters
By design a wavelet's strength rests in its ability to simultaneously localize a process in time-scale space. The wavelet's ability to localize a time series in time-scale space directly leads to the computational efficiency of the wavelet representation of a N X N matrix operator by allowing the N largest elements of the wavelet represented operator to adequately represent the matrix operator. This property allos many dense matrices to have sparse representation when transformed by wavelets. In this paper we generalize the long-memory parameter estimator of McCoy and Walden (1996) to simultaneously estaimte short and long-memory parameters. Using the sparse wavelet representation of a matrix operator, we are able to adequately approximate an ARFIMA models likelihood function with the series wavelet coefficients and their variances. Maximization of this approximate likelihood function over the short and long-memory parameter space results in the approximate wavelet maximum likelihood estimator of the ARFIMA model. By simultaneously maximizing the likelihood function over both the short and long-memory parameters, and using only the wavelet coefficient's variances, the approximate wavelet MLE provides an equally fast alternative to the frequency-domain MLE. Futhermore, the simulation studies reveal the approximate wavelet MLE to be robust over the invertible parameter region of the ARFIMA model's moving average parameter, whereas the frequency-domain MLE dramatically deteriorates as the moving average parameter approaches the boundaries of invertibility.
|Date of creation:||16 Feb 1998|
|Date of revision:||21 Jun 1999|
|Note:||Type of Document - PostScript; prepared on LaTeX Sun Ultra 1; to print on PostScript; pages: 23 ; figures: included|
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- Mark J. Jensen, 1997.
"Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter,"
- Jensen, Mark J, 1999. "Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter," MPRA Paper 39152, University Library of Munich, Germany.
- Lo, Andrew W. (Andrew Wen-Chuan), 1989.
"Long-term memory in stock market prices,"
3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Ramsey, James B. & Zhang, Zhifeng, 1997. "The analysis of foreign exchange data using waveform dictionaries," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 341-372, December.
- Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
- David K. Backus, 1993.
"Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates,"
93-04, New York University, Leonard N. Stern School of Business, Department of Economics.
- Backus, David K & Zin, Stanley E, 1993. "Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(3), pages 681-700, August.
- David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
- David K. Backus & Stanley E. Zin, 1993. "Long-memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," NBER Technical Working Papers 0133, National Bureau of Economic Research, Inc.
- Diebold, Francis X & Rudebusch, Glenn D, 1991.
"Is Consumption Too Smooth? Long Memory and the Deaton Paradox,"
The Review of Economics and Statistics,
MIT Press, vol. 73(1), pages 1-9, February.
- Francis X. Diebold & Glenn D. Rudebusch, 1989. "Is consumption too smooth? Long memory and the Deaton paradox," Finance and Economics Discussion Series 57, Board of Governors of the Federal Reserve System (U.S.).
- Baillie, R.T. & Bollerslev, T., 1993.
"Cointegration, Fractional Cointegration, and Exchange RAte Dynamics,"
9103, Michigan State - Econometrics and Economic Theory.
- Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-45, June.
- Yin-Wong Cheung & Francis X. Diebold, 1990.
"On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean,"
Discussion Paper / Institute for Empirical Macroeconomics
34, Federal Reserve Bank of Minneapolis.
- Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June.
- Yin-Wong Cheung & Francis X. Diebold, 1993. "On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean," Working Papers 93-5, Federal Reserve Bank of Philadelphia.
- Baillie, Richard T & Chung, Ching-Fan & Tieslau, Margie A, 1996. "Analysing Inflation by the Fractionally Integrated ARFIMA-GARCH Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(1), pages 23-40, Jan.-Feb..
- 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.
- Ramsey James B. & Lampart Camille, 1998. "The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(1), pages 1-22, April.
- 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.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Mark J. Jensen, 1997.
"An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets,"
- Jensen, Mark J., 2000. "An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 361-387, March.
- 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.
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