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Varyingcoefficient linear models arise from multivariate nonparametric regression, nonlinear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an <i>index</i>. To enlarge the modelling capacity substantially, this paper explores a class of varyingcoefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and/or other variables. We search for the index such that the derived varyingcoefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternating iteration between estimating the index through a onestep scheme

Value-at-risk measures the worst loss to be expected of a portfolio over a given time horizon at a given confidence level. Calculation of VaR frequently involves estimating the volatility of return processes and quantiles of standardized returns. In this paper, several semiparametric techniques are introduced to estimate the volatilities. In addition, both parametric and nonparametric techniques are proposed to estimate the quantiles of standardized return processes. The newly proposed techniques also have the flexibility to adapt automatically to the changes in the dynamics of market prices over time. The combination of newly proposed techniques for estimating volatility and standardized quantiles yields several new techniques for evaluating multiple period VaR. The performance of the newly proposed VaR estimators is evaluated and compared with some of existing methods. Our simulation results and empirical