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Maximum Likelihood Estimation of a Unit Root Bilinear Model with an Application to Prices

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Author Info
Daniela Hristova
Abstract

We estimate a unit root bilinear process using the Maximum Likelihood method with log-likelihood function constructed by means of the Kalman filter, and evaluate the finite sample properties of this estimator. One hundred and six world-wide price series are tested for unit root bilinearity applying the test suggested by Charemza et al. (2002b). Applying the Maximum Likelihood estimator based on the Kalman filter, the null hypothesis of no bilinearity is rejected for 40 out of 106 series at the 5% level of significance. Most of the significant unit root bilinear coefficient estimates are explosive

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 47.

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Date of creation: 11 Aug 2004
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Handle: RePEc:sce:scecf4:47

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Keywords: unit root bilinear process; non-linear process; Kalman filter; Simulated Annealing; prices;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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  1. Maravall, Agustin, 1983. "An Application of Nonlinear Time Series Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 66-74, January.
  2. Hinich, Melvin J & Patterson, Douglas M, 1985. "Evidence of Nonlinearity in Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(1), pages 69-77, January.
  3. Peel, David & Davidson, James, 1998. "A non-linear error correction mechanism based on the bilinear model1," Economics Letters, Elsevier, vol. 58(2), pages 165-170, February. [Downloadable!] (restricted)
  4. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99. [Downloadable!] (restricted)
  5. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July. [Downloadable!] (restricted)
  6. Charemza, Wojciech W. & Lifshits, Mikhail & Makarova, Svetlana, 2005. "Conditional testing for unit-root bilinearity in financial time series: some theoretical and empirical results," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 63-96, January. [Downloadable!] (restricted)
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  7. Byers, J D & Peel, D A, 1995. "Bilinear Quadratic ARCH and Volatility Spillovers in Inter-war Exchange Rates," Applied Economics Letters, Taylor and Francis Journals, vol. 2(7), pages 215-19, July. [Downloadable!] (restricted)
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