Time Series and Stochastic Processes

The concept of basic number is applied to the development of a simple analogue of the Sturm–Liouville system of the second order. This is then employed to deduce a family of q -orthogonal functions, which leads to a generalization of the Fourier and Fourier–Bessel expansions. The numerical approximation of basic integrals is discussed and some aspects of the evaluation of C a (q; x) are mentioned. A few of the zeros of this function are listed, and, in conclusion, an indication is given of the possibility of applying the analysis presented in this paper to thé study of stochastic processes and time-series.

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Bibliography on Time Series and Stochastic Processes: An International Team Project.

Journal of the Royal Statistical Society Series C (Applied Statistics) ◽

10.2307/2985305 ◽

1966 ◽

Vol 15 (3) ◽

pp. 269

Author(s):

D. M. G. Wishart ◽

Herman O. A. Wold

Keyword(s):

Time Series ◽

Stochastic Processes ◽

International Team ◽

Team Project

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Comparison of two stationary stochastic processes using standardized time series

Proceedings of the 17th conference on Winter simulation - WSC '85 ◽

10.1145/21850.253095 ◽

1985 ◽

Cited By ~ 1

Author(s):

Bor-Chung Chen ◽

Robert G. Sargent

Keyword(s):

Time Series ◽

Stochastic Processes ◽

Stationary Stochastic Processes

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A METHOD FOR INFERRING HIERARCHICAL DYNAMICS IN STOCHASTIC PROCESSES

Advances in Complex Systems ◽

10.1142/s0219525908001507 ◽

2008 ◽

Vol 11 (01) ◽

pp. 1-16 ◽

Cited By ~ 13

Author(s):

OLOF GÖRNERUP ◽

MARTIN NILSSON JACOBI

Keyword(s):

Time Series ◽

Stochastic Processes ◽

A Priori ◽

Main Idea ◽

A Priori Knowledge ◽

Finite State Automaton ◽

State Spaces ◽

Markovian Dynamics ◽

Finite State ◽

Operational Algorithm

Complex systems may often be characterized by their hierarchical dynamics. In this paper we present a method and an operational algorithm that automatically infer this property in a broad range of systems — discrete stochastic processes. The main idea is to systematically explore the set of projections from the state space of a process to smaller state spaces, and to determine which of the projections impose Markovian dynamics on the coarser level. These projections, which we call Markov projections, then constitute the hierarchical dynamics of the system. The algorithm operates on time series or other statistics, so a priori knowledge of the intrinsic workings of a system is not required in order to determine its hierarchical dynamics. We illustrate the method by applying it to two simple processes — a finite state automaton and an iterated map.

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MANDELBROT’S ECONOMICS AFTER A QUARTER CENTURY

Fractals ◽

10.1142/s0218348x95000515 ◽

1995 ◽

Vol 03 (03) ◽

pp. 581-600 ◽

Cited By ~ 9

Author(s):

PHILIP MIROWSKI

Keyword(s):

Time Series ◽

Stochastic Processes ◽

Chaotic Dynamics ◽

Stable Distributions ◽

Economic Time Series ◽

Quarter Century ◽

Economics Profession ◽

Economic Time

A quarter century has passed since the bulk of Benoit Mandelbrot’s articles on economics were published. This paper outlines the broad reactions to Mandelbrot’s theses within the economics profession. There are two separate literatures which have responded skeptically to his innovations: that which considers the empirical possibility that economic time series are best described as stochastic processes based upon Levy stable distributions; and that which considers the possible evidence for chaotic dynamics in economic time series. The paper concludes that much of the skepticism in orthodox economics is founded upon inadequate empirical premises, especially when compared to the approach of physicists to similar issues.

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