Abstract: Nonparametric kernel density estimation has recently been used to
estimate and test shortterm 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 shortrate
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 AitSahalia'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
CoxIngersollRoss models relative to a conditional momentbased
specification test.
Keywords: Interest rate, nonparametric, bandwidth, specification test
Full paper (1020 KB PDF)
 Full paper (2045 KB Postscript)
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Last update: December 12, 1997
