Related papers: Likelihood-Based Ergodicity Transformations in Tim…
We suggest employing log-ergodic processes to simulate the velocity of money in an ergodic manner. Our approach sheds light on economic behavior, policy implications, and financial dynamics by maintaining long-term stability. By bridging…
Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for…
Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…
This study concerns problems of time-series forecasting under the weakest of assumptions. Related results are surveyed and are points of departure for the developments here, some of which are new and others are new derivations of previous…
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…
This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient…
We obtain the lower bounds for ergodic convergence rates, including spectral gaps and convergence rates in strong ergodicity for time-changed symmetric L\'{e}vy processes by using harmonic function and reversible measure. As direct…
We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit…
Prediction for high dimensional time series is a challenging task due to the curse of dimensionality problem. Classical parametric models like ARIMA or VAR require strong modeling assumptions and time stationarity and are often…
We consider the problem of finding confidence intervals for the risk of forecasting the future of a stationary, ergodic stochastic process, using a model estimated from the past of the process. We show that a bootstrap procedure provides…
We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…
This paper examines some probabilistic properties of the class of periodic GARCH processes (PGARCH) which feature periodicity in conditional heteroskedasticity. In these models, the parameters are allowed to switch between different…
Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such…
Irregularly sampled time series are increasingly prevalent, particularly in medical domains. While various specialized methods have been developed to handle these irregularities, effectively modeling their complex dynamics and pronounced…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
Parameterized optimization and parameter estimation is of great importance in almost every branch of modern science, technology and engineering. A practical issue in the problem is that when the parameter space is large and the available…
We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…