6533b82bfe1ef96bd128ddc7

RESEARCH PRODUCT

Aliasing-Free and Additive Error in Mixed Spectra for Stable Processes. Application: Sound of a Bird just captivated in stress

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Consider a symmetric continuous time α stableprocess observed with an additive constant error. Theobjective of this paper is to give a non-parametric estimatorof this error by using discrete observations. As the time ofprocess is continuous and the observations are discrete, weencountered the aliasing phenomenon. Our process sampleis taken in a way to circumvent the difficulty related toaliasing and we smoothed the periodogram by using JacksonKernel. The rate of convergence of this estimator is studiedwhen the spectral density is zero at origin. Few long memoryprocesses are taken here as examples. We have applied ourestimator to the concrete case of modeling noise of a birdcaptured under stress