Copulas, Chaotic Processes and Time Series: a Survey

In this work we summarize some of recent and classical results on the role played by copulas in the analysis of chaotic processes and univariate time series. We review some aspects of the copulas related to chaotic process, its properties and applications. We also present a review on classical and modern approaches to understand the relationship among random variables in Markov processes as well as short and long memory time series as well as ergodic properties of copula-based Markov processes

Explicit bivariate rate functions for large deviations in AR(1) and MA(1) processes with Gaussian innovations

We investigate the large deviations properties for centered stationary AR(1) and MA(1) processes with independent Gaussian innovations, by giving the explicit bivariate rate functions for the sequence of two-dimensional random vectors [...]. Via the Contraction Principle, we provide the explicit rate functions for the sample mean and the sample second moment. In the AR(1) case, we also give the explicit rate function for the sequence of two-dimensional random vectors [...], but we obtain an analytic rate function that gives different values for the upper and lower bounds, depending on the evaluated set and its intersection with the respective set of exposed points. A careful analysis of the properties of a certain family of Toeplitz matrices is necessary. The large deviations properties of three particular sequences of one-dimensional random variables will follow after we show how to apply a weaker version of the Contraction Principle for our setting, providing new proofs for two already known results on the explicit deviation function for the sample second moment and Yule-Walker estimators. We exhibit the properties of the large deviations of the first-order empirical autocovariance, its explicit deviation function and this is also a new result

Sinusoidal frequency modulated spectrum analysis

We will analyze the stationary frequency modulated (FM) process with the additive ambient noise Zt =Yi+t:t =Acos(wct+X(t)+<P)+t:t, fortE Z where X(t) = B sin(wo t + cp) (1.2) is the sinusoidalmodulatingprocess, A and B are constants, wc, wo E [0, 1r] are, respectively, the carrier· and the modulating frequencies and cp and <P are uniformly distributed random variables on ( -1r, 1r] independent of each other and of the noise process {t:t}tEZ· We will consider the noise process as being Gaussian and white for simplicity of the exposition. However, the results are similar for any stationary and ergodic process with continuous spectral density function. Here we will estimate the relevant parameters A, B, wc and w0 by an updating procedure based on HOC (higher order correlations) sequences in the fine tuning of parametric filters. \\7e will use two different parametric families of time invariant linear filters: the alpha and complex filters. Here we alleviate the assumption of Gaussianity for the signal and we prove its stationarity and ergodicity under appropriate conditions

Parameter estimation in Manneville–Pomeau processes

In this paper, we study a class of stochastic processes [...], where[...] is obtained from the iterations of the transformation , invariant for an ergodic probability[...] on [...] and a certain constant by partial function [...]. We consider here the family of transformations[...] indexed by a parameter , known as the Manneville–Pomeau family of transformations. The autocorrelation function of the resulting process decays hyperbolically (or polynomially) and we obtain efficient methods to estimate the parameter[...] from a finite time series. As a consequence, we also estimate the rate of convergence of the autocorrelation decay of these processes. We compare different estimation methods based on the periodogram function, the smoothed periodogram function, the variance of the partial sum, and the wavelet theory. To obtain our results we analyzed the properties of the spectral density function and the associated Fourier series

Trabalho e sobrevivência - o mundo da vida sob ameaça: racionalidade ou irracionalidade?

A condução da vida por uma racionalidade capitalista-instrumental é o tema aqui discutido sob o prisma de reconhecê-la em manifestações da vida, sem desconhecer o quanto afeta o chamado mundo do trabalho. A subjetividade comprometida do trabalhador nesse processo é um dos seus maiores efeitos. A construção do texto resgata as idéias weberianas sobre um processo racional-instrumental que absorve a vida moderna, apresentando, em seguida, o novo paradigma habermasiano da razão comunicativa como alternativa às conseqüências dessa lógica tipicamente capitalista. Ao analisar a invasão do mundo sistêmico sobre o mundo da vida e a continuidade desse processo, o artigo elabora uma reflexão sobre a racionalidade, colocando a indagação: nas condições da moderna produção flexível, marca das grandes e médias indústrias de caráter transnacional, está-se diante de uma racionalidade ou irracionalidade capitalista