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Statistics for Finance by Erik Lindström, Henrik Madsen, Jan Nygaard Nielsen

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Chapter 6

Kernel estimators in time series analysis

6.1 Non-parametric estimation

Non-parametric methods are widely used in non-linear model building. Such methods are particularly useful if no prior information about the structure is available, since the estimation procedure is free of parameters and model structure (apart from a smoothing constant).

In this chapter we concentrate on kernel estimation. Some other non-parametric methods are based on splines, k nearest neighbour (k-NN) or orthogonal series smoothing. Each method has a specific weighting sequence {Ws(x); s = 1, ..., N}. These weighting sequences are related to each other and it can be argued (Härdle [1990]) that one of the simplest ways of computing a weighting sequence is kernel ...

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