On detecting and modeling periodic correlation in financial data

For many economic problems standard statistical analysis, based on the notion of stationarity, is not adequate. These include modeling seasonal decisions of consumers, forecasting business cycles and - as we show in the present article - modeling wholesale power market prices. We apply standard methods and a novel spectral domain technique to conclude that electricity price returns exhibit periodic correlation with daily and weekly periods. As such they should be modeled with periodically correlated processes. We propose to apply periodic autoregression (PAR) models which are closely related to the standard instruments in econometric analysis - vector autoregression (VAR) models.periodic correlation, sample coherence, electricity price, periodic autoregression, vector autoregression

Induced stationary process and structure of locally square integrable periodically correlated processes

A one-to-one correspondence between locally square integrable periodically correlated (PC) processes and a certain class of infinite-dimensional stationary processes is obtained. The correspondence complements and clarifies Gladyshev's known result [3] describing the correlation function of a continuous periodically correlated process. In contrast to Gladyshev's paper, the procedure for explicit reconstruction of one process from the other is provided. A representation of a PC process as a unitary deformation of a periodic function is derived and is related to the correspondence mentioned above. Some consequences of this representation are discussed

Innovation and factorization of the density of a regular PC sequence

In this paper we study an innovation representation of a periodically correlated PC sequence and describe the factorization of the densities of a regular PC sequence generated by its innovation. As a byproduct we obtain a certain factorization of vector analytic functions which may be of interest in the theory of Hardy spaces. In this paper we study an innovation representation of a periodically correlated PC sequence and describe the factorization of the densities of a regular PC sequence generated by its innovation. As a byproduct we obtain a certain factorization of vector analytic functions which may be of interest in the theory of Hardy spaces

Characterization of the Spectra of Periodically Correlated Processes

A complete characterization of the spectrum of a locally square integrable periodically correlated (PC) processes is obtained. The result makes use of the author's recent theorem establishing a one to one correspondence between PC processes and a certain class on infinite dimensional stationary processes. In terms of distributions it is proved that the Fourier transform of a positive definite distribution on the plane which is the sum of complex uniformly bounded measures supported on equidistant lines parallel to diagonal is a locally square integrable function.periodically correlated process correlation function spectrum positive definite distribution

On the hellinger square integral with respect to an operator valued measure and stationary processes

A construction of the Hellinger square integral with respect to a semispectral measure in a Banach space B is given. It is proved that the space of values of a B-valued stationary stochastic process is unitarily isomorphic to the space of all B*-valued measures that are Hellinger square integrable with respect to the spectral measure of the process. Some applications of the above theorem in the prediction theory (especially to interpolation problem) are also considered.Hellinger square integral semispectral measure dilation of a semispectral measure stationary process linear prediction

Spectrum of Periodically Correlated Fields

The paper deals with Hilbert space valued fields over any locally compact Abelian group G, in particular over G = Zn ×Rm, which are periodically correlated (PC) with respect to a closed subgroup of G. PC fields can be regarded as multi-parameter extensions of PC processes. We study structure, covariance function, and an analogue of the spectrum for such fields. As an example a weakly PC field over Z2 is thoroughly examined.

Foundations of the Theory of Strongly Periodically Correlated Fields over Z2

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