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Non-stationary Extensions of the Diffusion-Based Gaussian Matérn Field for Ecological Applications
The use of statistical methods informed by partial differential equations (PDEs) and in particular reaction–diffusion PDEs such as ecological...
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Correlation Integral for Stationary Gaussian Time Series
The correlation integral of a time series is a normalized coefficient that represents the number of close pairs of points of the series lying in...
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Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components
In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single...
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On the existence of stationary threshold bilinear processes
This article investigates some statistical and probabilistic properties of general threshold bilinear processes. Sufficient conditions for the...
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Time Series and Stationary Processes
This chapter introduces basic concepts such as time series, stationary process and covariance function. Subsequently, the time domain of a stationary...
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Stationary Time Series Models
This chapter first introduces the backshift operator, which is widely used for model simplicity and differencing, which is one way to make a...
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Kac-Ornstein-Uhlenbeck Processes: Stationary Distributions and Exponential Functionals
We study Ornstein-Uhlenbeck processes whose parameters are modulated by an external two-state Markov process. The conditional means of such a process...
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On Some Non-stationary Bivariate INAR(p) Models with Applications to Intra-day Stock Transaction Series
This paper introduces a non-stationary bivariate integer-valued auto-regressive process of order p (BINAR( p ) with non-stationary moments. The BINAR( p )...
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Multivariate frequency polygon for stationary random fields
The purpose of this paper is to investigate the multivariate frequency polygon as a density estimator for stationary random fields indexed by...
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Extremes for stationary regularly varying random fields over arbitrary index sets
We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient...
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Information Theoretic Results for Stationary Time Series and the Gaussian-Generalized von Mises Time Series
This chapter presents some novel information theoretic results for the analysis of stationary time series in frequency domain. In particular, the...
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Sieve bootstrap** the memory parameter in long-range dependent stationary functional time series
We consider a sieve bootstrap procedure to quantify the estimation uncertainty of long-memory parameters in stationary functional time series. We use...
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Robust Local Likelihood Estimation for Non-stationary Flood Frequency Analysis
As changes to the environment, both human and non-human made, continue to occur, the assumption of stationarity in flood frequency analysis is seldom...
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Extremal clustering in non-stationary random sequences
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically...
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Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays
For Gaussian stationary triangular arrays, it is well known that the extreme values may occur in clusters. Here we consider the joint behaviors of...
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Stationary GE-Process and its Application in Analyzing Gold Price Data
In this paper we introduce a new discrete time and continuous state space stationary process { X n ; n = 1,2,…}, such that X n follows a two-parameter...
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Estimation methods for stationary Gegenbauer processes
This paper reviews alternative methods for estimation for stationary Gegenbauer processes specifically, as distinct from the more general long memory...
