This paper considers a continuous-time semi-parametric regression model to
test for the uncovered interest parity. The regression has two mean
components, one parametric and the other nonparametric, with error term
specified generally as a martingale differential. The parametric part in the
mean is linear and derived under no arbitrage condition. To deal with the
time-varying risk premium, we introduce an additional nonparametric term in
the regression mean, which specifies the time-varying risk premium as a
general smooth function of time. To effectively deal with stochastic volatility in
the general martingale differential regression error, we use a time change to
set sampling intervals. Once the samples are collected at appropriate sample
intervals, the uncovered interest parity condition is tested by a mixture of
series and IV estimation methods. As a result from our work, for Canada and
UK, the uncovered interest parity puzzle implying that interest rate differentials
seem often to be followed by exchange rate depreciation is not supportive in
our model. For Korea, we obtain more favorable coefficients for UIP
condition.