Fractionally Integrated Models With ARCH Errors: With an Application to the Swiss 1-Month Euromarket Interest Rate |
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Authors: | Hauser Michael Kunst Robert |
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Institution: | (1) University of Economics and Business Administration, Augasse 2-6, A-1090 Vienna, Austria;(2) Institute for Advanced Studies, Stumpergasse 56, A-1060 Vienna, Austria;(3) Johannes Kepler University, Linz-Auhof, A-4040 Linz, Austria |
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Abstract: | We introduce ARFIMA-ARCH models, which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and we use it to construct the bias-corrected maximum (modified profile) likelihood estimator. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. Backus and Zin (1993) have motivated the existence of fractional integration in interest rates by the persistence of the short rate and the variability of the long end of the yield curve. An empirical investigation of a daily one-month Swiss Euromarket interest rate finds a difference parameter of 0.72. This indicates non-stationary behavior. In contrast to first-order integrated models, the long-run cumulative response of shocks to the series is zero. |
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Keywords: | Conditional heteroskedasticity autoregressive moving average model fractional differencing long memory |
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