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The thesis "Four Essays on the Econometric Modelling of Volatility and Durations" consists of four research papers in the area of financial econometrics on topics of the modelling of financial market volatility and the econometrics of ultra-high-frequency data. The aim of the thesis is to develop new econometric methods for modelling and hypothesis testing in these areas. The second chapter introduces a new model, the time-varying GARCH (TV-GARCH) model, in which volatility has a smooth time-varying structure of either additive or multiplicative type. To characterize smooth changes in the (un)conditional variance we assume that the parameters vary smoothly over time according to the logistic transition function. A data-based modelling technique is used for specifying the parametric structure of the TV-GARCH models. This is done by testing a sequence of hypotheses by Lagrange multiplier tests presented in the chapter. Misspecification tests are also provided for evaluating the adequacy of the estimated model. The third chapter addresses the issue of modelling deterministic changes in the unconditional variance over a long return series. The modelling strategy is illustrated with an application to the daily returns of the Dow Jones Industrial Average (DJIA) index from 1920 until 2003. The empirical results sustain the hypothesis that the assumption of constancy of the unconditional variance is not adequate over long return series and indicate that deterministic changes in the unconditional variance may be associated with macroeconomic factors. In the fourth chapter we propose an extension of the univariate multiplicative TV-GARCH model to the multivariate Conditional Correlation GARCH (CC-GARCH) framework. The variance equations are parameterized such that they combine the long-run and the short-run dynamic behaviour of the volatilities. In this framework, the long-run behaviour is described by the individual unconditional variances, and it is allowed to vary smoothly over time according to the logistic transition function. The effects of modelling the nonstationary variance component are examined empirically in several CC-GARCH models using pairs of seven daily stock return series from the S&P 500 index. The results show that the magnitude of such effect varies across different stock series and depends on the structure of the conditional correlation matrix. An important feature of financial durations is the evidence of a strong diurnal variation over the trading day. In the fifth chapter we propose a new parameterization for describing the diurnal pattern of trading activity. The parametric structure of the diurnal component allows the duration process to change smoothly over the time-of-day according to the logistic transition function. The empirical results suggest that the diurnal variation may not always have the inverted U-shaped pattern for the trade durations as documented in earlier studies.