Some convergence results on quadratic forms for random fields and application to empirical covariances

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our limit theorems and those of Ginovian (99) to obtain the asymptotic behavior of the empirical covariances of Gaussian fields, which is a particular example of quadratic forms. We show that it is possible to obtain a Gaussian limit when the spectral density is not in $L^2$. Therefore the dichotomy observed in dimension $d=1$ between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in $d>1$

Random sampling of long-memory stationary processe

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the effects of deterministic sampling on seasonal long-memory

A two-sample test for comparison of long memory parameters

We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L., Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit roots for a wide class of dependent errors. Econometric Theory 21, 989--1029]. The two samples have the same length and can be mutually independent or dependent. In the latter case, the test statistic is modified to make it asymptotically free of the long-run correlation coefficient between the samples. To diminish the sensitivity of the test on the choice of the bandwidth parameter, an adaptive formula for the bandwidth parameter is derived using the asymptotic expansion in [Abadir, K., Distaso, W., Giraitis, L., 2009. Two estimators of the long-run variance: Beyond short memory. Journal of Econometrics 150, 56--70]. A simulation study shows that the above choice of bandwidth leads to a good size of our comparison test for most values of fractional and ARMA parameters of the simulated series

On particle filters applied to electricity load forecasting

We are interested in the online prediction of the electricity load, within the Bayesian framework of dynamic models. We offer a review of sequential Monte Carlo methods, and provide the calculations needed for the derivation of so-called particles filters. We also discuss the practical issues arising from their use, and some of the variants proposed in the literature to deal with them, giving detailed algorithms whenever possible for an easy implementation. We propose an additional step to help make basic particle filters more robust with regard to outlying observations. Finally we use such a particle filter to estimate a state-space model that includes exogenous variables in order to forecast the electricity load for the customers of the French electricity company \'Electricit\'e de France and discuss the various results obtained

Consistency of the posterior distribution and MLE for piecewise linear regression

We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with regard to the break- point parameter induces technical difficulties that we overcome by creating a regularised version of the problem at hand. We first recover the strong consistency of the quantities of interest for the regularised version, using results about the MLE, and we then prove that the regularised version and the original version of the problem share the same asymptotic properties

Characterisation of collaborative decision making processes

This paper deals with the collaborative decision making induced or facilitated by Information and Communication Technologies (ICTs) and their impact on decisional systems. After presenting the problematic, we analyse the collaborative decision making and define the concepts related to the conditions and forms of collaborative work. Then, we explain the mechanisms of collaborative decision making with the specifications and general conditions of collaboration using the modelling formalism of the GRAI method. Each specification associated to the reorganisation of the decisional system caused by the collaboration is set to the notion of decision-making centre. Finally, we apply this approach to the e-maintenance field, strongly penetrated by the ICTs, where collaborations are usual. We show that the identified specifications allow improving the definition and the management of collaboration in e-maintenance

Estimation of Scale and Hurst Parameters of Semi-Selfsimilar Processes

The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter $\lambda$ and the Hurst index of such processes is one of the fundamental problem in the literature. We present some iterative method for estimation of the scale and Hurst parameters which is addressed for semi-selfsimilar processes with stationary increments. This method is based on some flexible sampling scheme and evaluating sample variance of increments in each scale intervals $[\lambda^{n-1}, \lambda^n)$, $n\in \mathbb{N}$. For such iterative method we find the initial estimation for the scale parameter by evaluating cumulative sum of moving sample variances and also by evaluating sample variance of preceding and succeeding moving sample variance of increments. We also present a new efficient method for estimation of Hurst parameter of selfsimilar processes. As an example we introduce simple fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary increments. We present some simulations and numerical evaluation to illustrate the results and to estimate the scale for sfBm as a semi-selfsimilar process. We also present another simulation and show the efficiency of our method in estimation of Hurst parameter by comparing its performance with some previous methods.Comment: 15 page