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