Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models

Finance and Economics Discussion Series 97-26

49 Pages Posted: 26 Nov 1997

See all articles by Matt Pritsker

Matt Pritsker

Federal Reserve Bank of Boston

Abstract

Nonparametric kernel density estimation has recently been used to estimate and test short-term interest rate models, but inference has been based on asymptotics. We derive finite sample properties of kernel density estimates of the ergodic distribution of the short-rate when it follows a continuous time AR(1) as in Vasicek. We find that the asymptotic distribution substantially understates finite sample bias, variance, and correlation. Also, estimator quality and bandwidth choice depend strongly on the persistence of the interest rate process and on the span of the data, but not on sampling frequency. We also examine the size and power of one of Ait-Sahalia's nonparametric tests of continuous time interest rate models. The test rejects too often. This is probably because the quality of the nonparametric density estimate depends on persistence, but the asymptotic distribution of the test does not. After critical values are adjusted for size, the test has low power in distinguishing between the Vasicek and Cox-Ingersoll-Ross models relative to a conditional moment-based specification test.

JEL Classification: C12, C14, G12

Suggested Citation

Pritsker, Matthew G., Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models. Finance and Economics Discussion Series 97-26, Available at SSRN: https://ssrn.com/abstract=36891 or http://dx.doi.org/10.2139/ssrn.36891

Matthew G. Pritsker (Contact Author)

Federal Reserve Bank of Boston ( email )

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617-973-3191 (Phone)

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