Abstract
A spline function is a curve constructed from polynomial segments that are subject to conditions of continuity at their joints. The chapter describes the algorithm of the cubic smoothing spline and its use in estimating trends in time series. Considerable effort has been devoted over several decades to developing the mathematics of spline functions. Much of the interest is because of the importance of splines in industrial design. In statistics, smoothing splines have been used in fitting curves to data ever since workable algorithms first became available in the late 1960s. The optimal degree of smoothing now becomes a function of the parameters of the underlying stochastic differential equation and of the parameters of the noise process; and therefore the element of judgment in fitting the curve is eliminated. This chapter provides a detailed exposition of the classical smoothing spline of which the degree of smoothness is a matter of choice. It also gives an account of a model-based method of determining an optimal degree of smoothing.
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