Asymptotic Results for an Extreme Value Estimator of the Autocorrelation Coefficient for a First Order Autoregressive Sequence

1989 ◽  
pp. 166-180 ◽  
Author(s):  
W. P. McCormick ◽  
G. Mathew
Keyword(s):  
Extreme Value ◽  
Autocorrelation Coefficient ◽  
Asymptotic Results ◽  
First Order

scholarly journals Sorting using complete subintervals and the maximum number of runs in a randomly evolving sequence: Extended abstract.

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Order Term ◽  
Combinatorial Problem ◽  
Random Order ◽  
Priority Queues ◽  
Sorting Algorithm ◽  
Asymptotic Results ◽  
First Order ◽  
Asymptotically Normal ◽  
International Audience ◽  
Space Requirements

International audience We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a string of 0's, and then evolves by changing each 0 to 1, with the n changes done in random order. What is the maximal number of runs of 1's? We give asymptotic results for the distribution and mean. It turns out that, as in many problems involving a maximum, the maximum is asymptotically normal, with fluctuations of order $n^{1/2}$, and to the first order well approximated by the number of runs at the instance when the expectation is maximized, in this case when half the elements have changed to 1; there is also a second order term of order $n^{1/3}$. We also treat some variations, including priority queues and sock-sorting.

scholarly journals Realized Semicovariances

Econometrica ◽  
2020 ◽  
Vol 88 (4) ◽  
pp. 1515-1551
Author(s):  
Tim Bollerslev ◽  
Jia Li ◽  
Andrew J. Patton ◽  
Rogier Quaedvlieg
Keyword(s):  
High Frequency ◽  
Asymptotic Properties ◽  
Sampling Interval ◽  
Asymptotic Results ◽  
First Order ◽  
Economic Information ◽  
Stochastic Correlation ◽  
Realized Covariance ◽  
Return Variance ◽  
Portfolio Return

We propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high‐frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first‐order asymptotic results highlight how the same‐sign and mixed‐sign components load differently on economic information related to stochastic correlation and jumps. The second‐order asymptotic results reveal the structure underlying the same‐sign semicovariances, as manifested in the form of co‐drifting and dynamic “leverage” effects. In line with this anatomy, we use data on a large cross‐section of individual stocks to empirically document distinct dynamic dependencies in the different realized semicovariance components. We show that the accuracy of portfolio return variance forecasts may be significantly improved by exploiting the information in realized semicovariances.

Extreme value theory for a class of discrete distributions with applications to some stochastic processes

1970 ◽  
Vol 7 (01) ◽  
pp. 99-113 ◽  
Author(s):  
C. W. Anderson
Keyword(s):  
Stochastic Processes ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Discrete Distributions ◽  
Independent Random Variables ◽  
Asymptotic Results ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Positive Integers

Let ξn be the maximum of a set of n independent random variables with common distribution function F whose support consists of all sufficiently large positive integers. Some of the classical asymptotic results of extreme value theory fail to apply to ξn for such F and this paper attempts to find weaker ones which give some description of the behaviour of ξn as n → ∞. These are then applied to the extreme value theory of certain regenerative stochastic processes.

Estimating Parameters of the Autocorrelated Current Effects Model from Temporally Aggregated Data

1986 ◽  
Vol 23 (4) ◽  
pp. 379-386 ◽  
Author(s):  
Vinay Kanetkar ◽  
Charles B. Weinberg ◽  
Doyle L. Weiss
Keyword(s):  
Monte Carlo ◽  
Simple Procedure ◽  
Monte Carlo Experiment ◽  
Good Recovery ◽  
Autocorrelation Coefficient ◽  
Aggregated Data ◽  
First Order ◽  
Level Of Aggregation

The authors briefly review the literature associated with the autocorrelated current effects model and present a simple procedure that recovers its parameters from time-aggregated data when the level of aggregation is known. The procedure is based partly on the estimation of a first-order autocorrelation coefficient. The procedure is illustrated and its properties are compared with those of a GLS procedure by means of a Monte Carlo experiment. In many of the tested cases, there is good recovery of the microparameters with aggregated data.

Stochastic properties of scalar quantities advected by a non-buoyant plume

1978 ◽  
Vol 89 (2) ◽  
pp. 209-222 ◽  
Author(s):  
Edward E. O'Brien
Keyword(s):  
Single Point ◽  
Field Measurements ◽  
Similarity Solutions ◽  
Asymptotic Results ◽  
First Order ◽  
Point Density ◽  
Model Probability ◽  
Intermittency Factor ◽  
Stochastic Properties ◽  
Density Equation

A model probability density equation is obtained by approximating the convective and diffusive terms in a single-point density formulation of homogeneous turbulent scalar transport, with first-order reaction, in a plume. The equation, which includes the intermittency factor of the scalar field explicitly, is then shown to support similarity solutions under some constraining assumptions. Comparison of the similarity solutions with field measurements of conditioned concentrations shows that they can reproduce the general features of the data for both low intermittency and high intermittency measurement regimes. On the basis of these asymptotic results a speculative modelling of the terms representing entrainment at the plume interface is proposed and a class of similarity solutions for the intermittency factor is obtained by numerical integration.

Micro-Inertia Effects in Material Flow

2019 ◽  
Vol 44 (3) ◽  
pp. 235-246
Author(s):  
Paul M. Mwasame ◽  
Norman J. Wagner ◽  
Antony N. Beris
Keyword(s):  
Evolution Equation ◽  
Material Flow ◽  
Constitutive Models ◽  
Material Behavior ◽  
Asymptotic Results ◽  
Simple Modification ◽  
Inertia Effects ◽  
First Order ◽  
Inertial Flow ◽  
Conformation Tensor

Abstract The mechanics of understanding a new application of the bracket theory of Non-Equilibrium Thermodynamics that allows for the incorporation of microstructural inertia effects within conformation tensor-based constitutive models of macroscopic material behavior is presented. Introducing inertia effects generally requires the replacement of a first order in time evolution equation for the conformation tensor by a second order one. Through the analysis of a simple damped oscillator we bring forward here the close connection to the structural dissipation brackets present in the two cases, with the weights being inverted as one transitions from the inertialess to the inertial description. Moreover, one may also describe inertial effects in material flow in certain situations through a simple modification of the first order evolution equation for the conformation tensor, which consists of adding a new non-affine term that couples the conformation and the vorticity tensors, as detailed in a recent publication (P. M. Mwasame, N. J. Wagner and A. N. Beris, Phys. Fluids, 30 (2018), 030704). As shown there, when applied to the low particle Reynolds flow of dilute emulsions, this reduced inertial flow model provides predictions consistent with literature-available microscopically based asymptotic results.

Extreme value theory for a class of discrete distributions with applications to some stochastic processes

1970 ◽  
Vol 7 (1) ◽  
pp. 99-113 ◽  
Author(s):  
C. W. Anderson
Keyword(s):  
Stochastic Processes ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Discrete Distributions ◽  
Independent Random Variables ◽  
Asymptotic Results ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Positive Integers

Let ξn be the maximum of a set of n independent random variables with common distribution function F whose support consists of all sufficiently large positive integers. Some of the classical asymptotic results of extreme value theory fail to apply to ξn for such F and this paper attempts to find weaker ones which give some description of the behaviour of ξn as n → ∞. These are then applied to the extreme value theory of certain regenerative stochastic processes.

scholarly journals Extreme value theory for anomaly detection – the GPD classifier

Extremes ◽  
2020 ◽  
Vol 23 (4) ◽  
pp. 501-520
Author(s):  
Edoardo Vignotto ◽  
Sebastian Engelke
Keyword(s):  
Anomaly Detection ◽  
Extreme Value Theory ◽  
Recognition Task ◽  
Real Data ◽  
Value Theory ◽  
Extreme Value ◽  
Data Sets ◽  
Asymptotic Results ◽  
Long Time ◽  
Classification Tasks

Abstract Classification tasks usually assume that all possible classes are present during the training phase. This is restrictive if the algorithm is used over a long time and possibly encounters samples from unknown new classes. It is therefore fundamental to develop algorithms able to distinguish between normal and abnormal test data. In the last few years, extreme value theory has become an important tool in multivariate statistics and machine learning. The recently introduced extreme value machine, a classifier motivated by extreme value theory, addresses this problem and achieves competitive performance in specific cases. We show that this algorithm has some theoretical and practical drawbacks and can fail even if the recognition task is fairly simple. To overcome these limitations, we propose two new algorithms for anomaly detection relying on approximations from extreme value theory that are more robust in such cases. We exploit the intuition that test points that are extremely far from the training classes are more likely to be abnormal objects. We derive asymptotic results motivated by univariate extreme value theory that make this intuition precise. We show the effectiveness of our classifiers in simulations and on real data sets.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

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