A5001383921- Coastal and Marine Dynamics
- Financial Risk and Volatility Modeling
- Geological formations and processes
- Statistical Methods and Inference
- Geology and Paleoclimatology Research
- Complex Systems and Time Series Analysis
- Stochastic processes and financial applications
- Stochastic processes and statistical mechanics
- Aeolian processes and effects
- Coastal wetland ecosystem dynamics
- Probability and Risk Models
- Bayesian Methods and Mixture Models
- Market Dynamics and Volatility
- Tropical and Extratropical Cyclones Research
- Monetary Policy and Economic Impact
- Fault Detection and Control Systems
- Maritime and Coastal Archaeology
- Time Series Analysis and Forecasting
- Paleontology and Stratigraphy of Fossils
- Neural Networks and Applications
- Advanced Statistical Process Monitoring
- Complex Network Analysis Techniques
- Methane Hydrates and Related Phenomena
- Random Matrices and Applications
- Cephalopods and Marine Biology
Columbia University
2014-2025
Aarhus University
2020
University of South Florida
1997-2019
Colorado State University
1997-2016
Texas A&M University – Corpus Christi
2011-2016
Chinese University of Hong Kong
2013
ACT Government
2012
Barclays (United Kingdom)
2011
Capital University
2011
City College of New York
2009
Preface 1 INTRODUCTION 1.1 Examples of Time Series 1.2 Objectives Analysis 1.3 Some Simple Models 1.3.3 A General Approach to Modelling 1.4 Stationary and the Autocorrelation Function 1.4.1 The Sample 1.4.2 Model for Lake Huron Data 1.5 Estimation Elimination Trend Seasonal Components 1.5.1 in Absence Seasonality 1.5.2 Both 1.6 Testing Estimated Noise Sequence 1.7 Problems 2 STATIONARY PROCESSES 2.1 Basic Properties 2.2 Linear Processes 2.3 Introduction ARMA 2.4 Mean 2.4.2 $\gamma(\cdot)$...
Let $\{Z_k, -\infty < k \infty\}$ be iid where the $Z_k$'s have regularly varying tail probabilities. Under mild conditions on a real sequence $\{c_j, j \geq 0\}$ stationary process $\{X_n: = \sum^\infty_{j=0} c_jZ_{n-j}, n 1\}$ exists. A point based $\{X_n\}$ converges weakly and from this, host of weak limit results for functionals ensue. We study sums, extremes, excedences first passages as well behavior sample covariance functions.
Let $X_t = \sum^\infty_{j=-\infty} c_jZ_{t-j}$ be a moving average process where the $Z_t$'s are iid and have regularly varying tail probabilities with index $\alpha > 0$. The limit distribution of sample covariance function is derived in case that has finite variance but an infinite fourth moment. Furthermore, $(0 < \alpha 2)$, correlation shown to converge ratio two independent stable random variables indices $\alpha$ $\alpha/2$, respectively. This result immediately gives for least...
We study the sample ACVF and ACF of a general stationary sequence under weak mixing condition in case that marginal distributions are regularly varying. This includes linear bilinear processes with varying noise ARCH processes, their squares absolute values. show distributional limits can be random, provided variance distribution is infinite process nonlinear. contrast to processes. If has finite second but fourth moment, then consistent scaling rates grow at slower rate than standard...
Let $\{\xi_j\}$ be a strictly stationary sequence of random variables with regularly varying tail probabilities. We consider, via point process methods, weak convergence the partial sums, $S_n = \xi_1 + \cdots \xi_n$, suitably normalized, when satisfies mild mixing condition. first give characterization limit processes for $N_n$ mass at points $\{\xi_j/a_n, j 1,\ldots,n\}$, where $a_n$ is $1 - n^{-1}$ quantile distribution $|\xi_1|$. Then $0 < \alpha 1 (-\alpha$ exponent regular variation),...
We consider the problem of model selection for geospatial data. Spatial correlation is often ignored in explanatory variables, and this can influence results. For example, importance particular variables may not be apparent when spatial ignored. To address problem, we Akaike Information Criterion (AIC) as applied to a geostatistical model. offer heuristic derivation AIC context provide simulation results that show using superior often-used traditional approach ignoring variables. These ideas...
We establish the equivalence between multivariate regular variation of a random vector and univariate all linear combinations components such vector. According to classical result Kesten [Acta Math. 131 (1973) 207-248], this implies that stationary solutions stochastic recurrence equations are regularly varying. Since GARCH processes can be embedded in their finite-dimensional distributions
An estimate of the upper tail a distribution function which is based on $m$ order statistics from sample size $n(m \rightarrow \infty, m/n 0$ as $n \infty)$ shown to be consistent for wide class functions. The empirical mean residual life $\log$ transformed data and $1 - m/n$ quantile play key role in estimate. joint asymptotic behavior determined rates convergence are derived.
We consider a strictly stationary sequence of random vectors whose finite-dimensional distributions are jointly regularly varying with some positive index. This class processes includes, among others, ARMA noise, GARCH normally or Student-distributed noise and stochastic volatility models multiplicative noise. define an analog the autocorrelation function, extremogram, which depends only on extreme values in sequence. also propose natural estimator for extremogram study its asymptotic...
ABSTRACT Beach and inner nearshore areas of Lake Michigan are basically the same as northern Massachusetts except for scale morphologic features tidal range; in spring tides reach 0.25 feet whereas they 13 feet. Ridge runnel topography is developed zone at both locations result storm activity. These ridges migrate shoreward during low energy conditions eventually weld onto beach. Overall morphology, surface internal structures quite similar areas. The only appreciable differences between two...
Journal Article A negative binomial model for time series of counts Get access Richard A. Davis, Davis Department Statistics, Columbia University, New York, York 10027, U.S.A.rdavis@stat.columbia.edu Search other works by this author on: Oxford Academic Google Scholar Rongning Wu Statistics and Computer Information Systems, Baruch College, The City University 10010, U.S.A.rongning.wu@baruch.cuny.edu Biometrika, Volume 96, Issue 3, September 2009, Pages 735–749,...
The effect of changes in atmospheric carbon dioxide concentrations and sulphate aerosols on near-surface temperature is investigated using a version the Hadley Centre model coupled to mixed layer ocean. scattering sunlight by represented appropriately enhancing surface albede. On doubling concentrations, global mean increases 5.2 K. An integration with 39% increase CO2, giving estimated change radiative heating due greenhouse gases since 1900, produced an equilibrium warming 2.3 K, which,...
The problem of testing whether or not a change has occurred in the parameter values and order an autoregressive model is considered. It shown that if white noise AR weakly stationary with finite fourth moments, then under null hypothesis no changepoint, normalized Gaussian likelihood ratio test statistic converges distribution to Gumbel extreme value distribution. An asymptotically distribution-free procedure for either coefficients model, variance also proposed. asymptotic this obtained...
A max-autoregressive moving average (MARMA( p, q )) process { X t } satisfies the recursion for all where φ i , and Z is i.i.d. with common distribution function Φ 1,σ ( ): = exp {–σ x –1 . Such processes have finite-dimensional distributions which are max-stable hence examples of processes. We provide necessary sufficient conditions existence a stationary solution to MARMA we examine reducibility MARMA( p′, q′ ) p′ <p or < After introducing natural metric between two jointly random...