Is Long Memory Necessary? An Empirical Investigation of Nonnegative Interest Rate Processes

This paper analyzes a class of nonnegative processes for the short-term interest rate. The dynamics of interest rates and yields are driven by the dynamics of the conditional volatility of the pricing kernel. We study Markovian interest rate processes as well as more general non-Markovian processes that display “short”and “long”memory. These processes also display heteroskedasticity patterns that are more general than those of existing models. We …nd that deviations from the Markovian structure signi…cantly improve the empirical performance of the model. Certain aspects of the long memory e¤ect can be captured with a (less parsimonious) short memory parameterization, but a simulation experiment suggests that the implied term structures corresponding to the estimated longand short-memory speci…cations are very di¤erent. We also …nd that the choice of proxy for the short rate a¤ects the estimates of heteroskedasticity patterns. JEL Classi…cation: G12 Keywords: Interest Rate, GARCH, Heteroskedasticity, Long Memory, Nonnegativity, Term Structure. Duan: Risk Management Institute and Department of Finance and Accounting, National University of Singapore, and Rotman School of Management, University of Toronto. Jacobs: Desautels Faculty of Management, McGill University, CIRANO and CIREQ. Duan acknowledges support from a Direct Allocation Grant from the Hong Kong University of Science and Technology and a grant from the Research Grants Council of Hong Kong (HKUST6017/99H). Jacobs acknowledges FQRSC of Quebec and SSHRC of Canada for …nancial support. We would like to thank Peter Christo¤ersen, Nour Meddahi and Angelo Melino for helpful comments. The paper has also bene…ted from presentations at CIRANO, the 1999 NFA Meetings, the 1999 North American Summer Meetings of the Econometric Society and the 2000 North American Winter Meetings of the Econometric Society. Xiaofei Li provided excellent research assistance.