4,781 research outputs found
On the entropy production of time series with unidirectional linearity
There are non-Gaussian time series that admit a causal linear autoregressive
moving average (ARMA) model when regressing the future on the past, but not
when regressing the past on the future. The reason is that, in the latter case,
the regression residuals are only uncorrelated but not statistically
independent of the future. In previous work, we have experimentally verified
that many empirical time series indeed show such a time inversion asymmetry.
For various physical systems, it is known that time-inversion asymmetries are
linked to the thermodynamic entropy production in non-equilibrium states. Here
we show that such a link also exists for the above unidirectional linearity.
We study the dynamical evolution of a physical toy system with linear
coupling to an infinite environment and show that the linearity of the dynamics
is inherited to the forward-time conditional probabilities, but not to the
backward-time conditionals. The reason for this asymmetry between past and
future is that the environment permanently provides particles that are in a
product state before they interact with the system, but show statistical
dependencies afterwards. From a coarse-grained perspective, the interaction
thus generates entropy. We quantitatively relate the strength of the
non-linearity of the backward conditionals to the minimal amount of entropy
generation.Comment: 16 page
Noise recovery for L\'evy-driven CARMA processes and high-frequency behaviour of approximating Riemann sums
We consider high-frequency sampled continuous-time autoregressive moving
average (CARMA) models driven by finite-variance zero-mean L\'evy processes. An
L^2-consistent estimator for the increments of the driving L\'evy process
without order selection in advance is proposed if the CARMA model is
invertible. In the second part we analyse the high-frequency behaviour of
approximating Riemann sum processes, which represent a natural way to simulate
continuous-time moving average processes on a discrete grid. We shall compare
their autocovariance structure with the one of sampled CARMA processes, where
the rule of integration plays a crucial role. Moreover, new insight into the
kernel estimation procedure of Brockwell et al. (2012a) is given.Comment: 26 pages, 2 figure
Algorithms for Linear Time Series Analysis: With R Package
Our ltsa package implements the Durbin-Levinson and Trench algorithms and provides a general approach to the problems of fitting, forecasting and simulating linear time series models as well as fitting regression models with linear time series errors. For computational efficiency both algorithms are implemented in C and interfaced to R. Examples are given which illustrate the efficiency and accuracy of the algorithms. We provide a second package FGN which illustrates the use of the ltsa package with fractional Gaussian noise (FGN). It is hoped that the ltsa will provide a base for further time series software.
On a flexible construction of a negative binomial model
This work presents a construction of stationary Markov models with
negative-binomial marginal distributions. A simple closed form expression for
the corresponding transition probabilities is given, linking the proposal to
well-known classes of birth and death processes and thus revealing interesting
characterizations. The advantage of having such closed form expressions is
tested on simulated and real data.Comment: Forthcoming in "Statistics & Probability Letters
Computational Aspects of Maximum Likelihood Estimation of Autoregressive Fractionally Integrated Moving Average Models
We discuss computational aspects of likelihood-based estimation of univariate ARFIMA (p,d,q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.Long memory, Bias, Modified profile likelihood, Restricted maximum likelihood estimator, Time-series regression model likelihood
Recursive Estimation in Econometrics
An account is given of recursive regression and of Kalman filtering which gathers the important results and the ideas that lie behind them within a small compass. It emphasises the areas in which econometricians have made contributions, which include the methods for handling the initial-value problem associated with nonstationary processes and the algorithms of fixed-interval smoothing.Recursive regression, Kalman filtering, Fixed-interval smoothing, The initial-value problem
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