Stationary process ≈ Stationary process
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A Likelihood Approximation for Locally Stationary Processes Open
A new approximation to the Gaussian likelihood of a multivariate locally stationary process is introduced. It is based on an approximation of the inverse of the covariance matrix of such processes. The new quasi-likelihood is a generalisat…
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Stationary graph signals using an isometric graph translation Open
International audience
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The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis Open
Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intens…
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Non-Stationary Spectral Kernels Open
We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve …
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Ground roll attenuation using non-stationary matching filtering Open
Conventional approaches based on adaptive subtraction for ground roll attenuation first predict an initial model for ground rolls and then adaptively subtract it from the original data using a stationary matching filter (MF). Because of th…
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Non-stationary Extreme Value Analysis: a simplified approach for Earth science applications Open
Statistical approaches to study extreme events require by definition long time series of data. The climate is subject to natural and anthropogenic variations at different temporal scales, leaving their footprint on the frequency and intens…
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Non-Stationary Power System Forced Oscillation Analysis using Synchrosqueezing Transform Open
Non-stationary forced oscillations (FOs) have been observed in power system operations. However, most detection methods assume that the frequency of FOs is stationary. In this paper, we present a methodology for the analysis of nonstationa…
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Generation of fully non-stationary random processes consistent with target seismic accelerograms Open
In this paper, a method for generating samples of a fully non-stationary zero-mean Gaussian process, having a target acceleration time-history as one of its own samples, is presented. The proposed method requires the following steps: i) di…
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A comparative example of cyclostationary description of a non-stationary random process Open
The paper deals with cyclostationarity as a natural extension of stationarity as the key property in designing the widely-used models of random processes. The comparative example of two processes, one is wide-sense stationary and the other…
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Uniform convergence to the $Q$-process Open
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its $Q$-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a condi…
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A persistence‐based Wold‐type decomposition for stationary time series Open
This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based o…
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A Novel 3D Non-Stationary Vehicle-to-Vehicle Channel Model and its Spatial-Temporal Correlation Properties Open
In this paper, a new non-stationary Vehicle-to-Vehicle (V2V) channel model is proposed. It could generate more smooth fading phase between the adjacent channel states and guarantee more accurate Doppler frequency, which is a great improvem…
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Information Theory for Non-Stationary Processes with Stationary Increments Open
We describe how to analyze the wide class of non-stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability …
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Fatigue assessment of non-stationary random loading in the frequency domain by a quasi-stationary Gaussian approximation Open
The power spectral density (PSD) is a fundamental technique of random vibration fatigue providing an effective statistical characterization that can be processed by linear systems theory and load spectrum estimators. This lays the basis fo…
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Ergodic decompositions of stationary max-stable processes in terms of\n their spectral functions Open
We revisit conservative/dissipative and positive/null decompositions of\nstationary max-stable processes. Originally, both decompositions were defined\nin an abstract way based on the underlying non-singular flow representation. We\nprovid…
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Analysis of cyclostationary stochastic electromagnetic fields Open
Second order CS stochastic processes are non-stationary stochastic processes, where the TDCM depends on the global time and the time difference, and the dependence on the global time is periodic. This autocorrelation function can be repres…
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Detection of Non-Linearity in the Time Series Using BDS Test Open
The need to determine the status of the series is a very important issue that must be addressed before embarking on the statistical analysis of such series; this paper therefore, examines the status of the commercial bank savings in Nigeri…
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Minimal quasi-stationary distribution approximation for a birth and death process Open
In a first part, we prove a Lyapunov-type criterion for the $\\xi\\_1$-positive\nrecurrence of absorbed birth and death processes and provide new results on the\ndomain of attraction of the minimal quasi-stationary distribution. In a secon…
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Extending the validity of frequency domain bootstrap methods to general stationary processes Open
Existing frequency domain methods for bootstrapping time series have a limited range. Essentially, these procedures cover the case of linear time series with independent innovations, and some even require the time series to be Gaussian. In…
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Predictive, finite-sample model choice for time series under\n stationarity and non-stationarity Open
In statistical research there usually exists a choice between structurally\nsimpler or more complex models. We argue that, even if a more complex, locally\nstationary time series model were true, then a simple, stationary time series\nmode…
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Detection of distributed and localized faults in rotating machines using periodically non-stationary covariance analysis of vibrations Open
The covariance structure for vibrations of the noising mechanism for a port crane and a wind turbine with gear tooth breakage are studied on the basis of their models in the form of periodically non-stationary random processes (PNRPs). The…
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Prediction of functional ARMA processes with an application to traffic data Open
This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the fun…
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Over-Differencing and Forecasting with Non-Stationary Time Series Data Open
In time series analysis, over-differencing is a common phenomenon to make the data to be stationary. However, it is not always a good idea to take over-differencing in order to ensure the stationarity of time series data. In this paper, th…
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Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time Open
The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decom…
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Time-frequency analysis of locally stationary Hawkes processes Open
Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has recent…
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Predicting unemployment rates in Indonesia Open
The main purpose of this study is to predict the unemployment rate in Indonesia by using time series data from 1986 to 2015 using autoregressive integrated moving average (ARIMA). A differencing process is required due to the actual time s…
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Minimax Interpolation Problem for Random Processes with Stationary Increments Open
The problem of mean-square optimal estimation of the linear functional A_T ξ=\int_{0}^Ta(t) ξ(t)dt that depends on the unknown values of a continuous time random process ξ(t),t ∈ R, with stationary nth increments from observations of the p…
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Exact Run Length Computation on EWMA Control Chart for Stationary Moving Average Process with Exogenous Variables Open
The exponentially weighted moving average (EWMA) control chart is a popular tool used to monitor and identify slight unnatural variations in the manufacturing, industrial, and service processes.In general, control charts operate under the …
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Nonstationary Process Monitoring Based on Cointegration Theory and Multiple Order Moments Open
In industrial processes, process data often exhibit complex characteristics, such as nonstationarity and nonlinearity, which brings challenges to process monitoring. In this study, a monitoring strategy for nonstationary processes is propo…
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Optimal stationary self-triggered sampling for estimation Open
In this paper, we study optimal stationary sampling for transmission of measurements of a stochastic process from a source encoder to a source decoder through a costly communication channel. We measure information transferred over a time i…