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In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be another standard tool of the applied statistician rather than a research novelty. With that in mind, this paper gives a relatively accessible introduction to(More)
S We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the model explains well the common characteristics of(More)
We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since the parameters are changing over time, a successful estima-tor(More)
Using the asymptotical minimax framework, we examine convergence rates equivalency between a continuous functional deconvolution model and its real-life discrete counterpart over a wide range of Besov balls and for the L 2-risk. For this purpose, all possible models are divided into three groups. For the models in the first group, which we call uniform, the(More)
This article shows how a non-decimated wavelet packet transform (NWPT) can be used to model a response time series, Ø, in terms of an explanatory time series, Ø. The proposed computational technique transforms the explanatory time series into a NWPT representation and then uses standard statistical modelling methods to identify which wavelet packets are(More)
This paper considers the use of wavelet methods in relation to a common signal processing problem, that of detecting transient features in sound recordings which contain interference or distortion. In this particular case, the data are various types of underwater sounds, and the objective is to detect intermittent departures (potentiaìsignals') from the(More)
We show how a recently developed wavelet packet modelling methodology could be useful for infant sleep state classification using heart rate data. The suggested approach produces adequate classification rates when applied to recordings from an infant who was placed to bed at night at different ages. As well as classification, this approach gives us valuable(More)
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation.(More)