Random spectral measure for non Gaussian moving averages

We study the distribution of phases and amplitudes for the spectral representation of weighted moving averages of a general noise measure. The simple independent structure, known for the Gaussian case, and involving Rayleigh amplitude and uniform phase distributions, is lost for the non Gaussian noise case. We show that the amplitude/phase distributions exhibit a rich and more complex structure depending not just on the covariance of the process but specifically on the form of the kernel and the noise distribution. We present a theoretical tool for studying these distributions that follows from a proof of the spectral theorem that yields an explicit expression for the spectral measure. The main interest is in noise measures based on second-order Lévy motions since such measures are easily available through independent sampling. We approximate the spectral stochastic measure by independent noise increments which allows us to obtain amplitude/phase distributions that is of fundamental interest for analyzing processes in the frequency domain. For the purpose of approximating the moving average process through sums of trigonometric functions, we assess the mean square error of discretization of the spectral representation. For a specified accuracy, the approximation is explicitly given. We illustrate the method for the moving averages driven by the Laplace motion.

Podgórski, KrzysztofLund University,Lunds universitet,Matematisk statistik,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Statistics,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)mats-ksp (författare)
University of CyprusMatematisk statistik (creator_code:org_t)

Ingår i:Communications in Statistics - Theory and Methods: Informa UK Limited47:2, s. 448-4620361-09261532-415X

Om ämnet

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.