By building on the work of Conley et al. (1997), we investigate the stationarity of riskless short-term interest rate processes, analyzing generalized stochastic volatility models with level effects and examine the compatibility of stationarity of short-term interest rates with the popular dynamic term structure of models of interest rates, such as ATSM and QTSM. We extend extant stochastic volatility models with level effects crucial in characterizing the stationarity of a continuous time stochastic process, estimate the extended models using an efficient simulation-based MCML(Monte Carlo Maximum Likelihood) estimation method using importance sampling and implement model diagnostics using the inverse of standard normal distribution of the dynamic probability integral transform obtained via an auxiliary particle filter. Empirical estimation results indicate that TB3M and Call1d exhibit drift-induced stationarity compatible with both ATSM and QTSM, and that ED1M, KTB3M, MMF7d, CD91d and CP91d are of volatility-induced stationarity. Consequently, the results imply that, without careful consideration for the nature of stationarity of a short-term interest rate, indiscriminate application of theoretical models assuming the drift-induced stationarity of short-term interest rates may cause serious failure in derivative pricing and risk management.