Identification is the most important stage of all stages modeling process. This research identifies a suitable order for two different time series models ARIMA and GARCH. For GARCH distributions that GARCH-STD GARCH-GED with sample sizes in fitting forecasting stationary non-stationary data structures was considered. The study recommends use smallest information criterion like AIC BIC to select...

 This paper deals with a short term forecasting non-stationary time series using wavelets and splines. Wavelets can decompose the series as the sum of two low and high frequency components. Aminghafari and Poggi (2007) proposed to predict high frequency component by wavelets and extrapolate low frequency component by local polynomial fitting. We propose to forecast non-stationary process u...

We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the interparticle gap-length distribution in the critical one-dimensional contact process. We also find evidence for power-law decay of the interparticle distance distri...

Diagnostic plots are an important part of extreme value statistics. This paper provides a theoretical basis for such plots by proving weak convergence of the tail empirical process for a large class of stationary processes. The conditions needed for convergence are (i) restrictions on the long-range dependence (mixing), (ii) moment restrictions on the amount of clustering of extremes, and (iii)...

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate o...

I define a process over all stationary covariance kernels. I show how one might be able to perform inference that scales as O(nm) in a GP regression model using this process as a prior over the covariance kernel, with n datapoints and m < n. I also show how the stationarity assumption can be relaxed.

The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, which is the probability distributions on finite binary strings. In our previous paper [1] we propose a definition of effective complexity in precise terms of algorithmic information theory. Here we ...