Using Power Laws and the Hurst Exponent to Identify Stock Market Trading Bubbles

Many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. However a series of power laws in economics do count as true and nontrivial quantitative laws—and they are not only established empirically, but also understood theoretically. I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock market. I summarize some of the theoretical explanations that have been proposed. I suggest that power laws help us explain many economic phenomena, including aggregate economic fluctuations. I hope to clarify why power laws are so special, and to demonstrate their utility. In conclusion, I list some power-law-related economic enigmas that demand further exploration. A formal definition may be useful.

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Cellular automata: a decision support system for stock market trading

International Journal of Computational Economics and Econometrics ◽

10.1504/ijcee.2016.079531 ◽

2016 ◽

Vol 6 (4) ◽

pp. 366

Author(s):

Tessy Mathew ◽

U. Srinivasa Rao ◽

L. Jeganathan

Keyword(s):

Decision Support ◽

Cellular Automata ◽

Stock Market ◽

Decision Support System ◽

Support System ◽

Stock Market Trading

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Stock Market Trading Volume

Handbook of Financial Econometrics: Applications ◽

10.1016/b978-0-444-53548-1.50007-6 ◽

2010 ◽

pp. 241-342 ◽

Cited By ~ 15

Author(s):

Andrew W. Lo ◽

Jiang Wang

Keyword(s):

Stock Market ◽

Trading Volume ◽

Stock Market Trading

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Searching for long memory effects in time series of central Europe stock market indices

Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis ◽

10.11118/actaun200856030187 ◽

2008 ◽

Vol 56 (3) ◽

pp. 187-200

Author(s):

Luboš Střelec

Keyword(s):

Time Series ◽

Stock Market ◽

Central Europe ◽

Long Memory ◽

Hurst Exponent ◽

Financial Time Series ◽

Memory Effects ◽

Stock Index ◽

Source Data ◽

Independent Process

This article deals with one of the important parts of applying chaos theory to financial and capital markets – namely searching for long memory effects in time series of financial instruments. Source data are daily closing prices of Central Europe stock market indices – Bratislava stock index (SAX), Budapest stock index (BUX), Prague stock index (PX) and Vienna stock index (ATX) – in the period from January 1998 to September 2007. For analysed data R/S analysis is used to calculate the Hurst exponent. On the basis of the Hurst exponent is characterized formation and behaviour of analysed financial time series. Computed Hurst exponent is also statistical compared with his expected value signalling independent process. It is also operated with 5-day returns (i.e. weekly returns) for the purposes of comparison and identification nonperiodic cycles.

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Single step estimation of ARMA roots for non-fundamental nonstationary fractional models

Econometrics Journal ◽

10.1093/ectj/utac001 ◽

2022 ◽

Author(s):

Ignacio N Lobato ◽

Carlos Velasco

Keyword(s):

Stock Market ◽

Strong Evidence ◽

Long Memory ◽

Trading Volume ◽

Moving Average ◽

Single Step ◽

Arma Process ◽

Dow Jones Industrial Average ◽

Fractional Models ◽

Stock Market Trading

Abstract We propose a single step estimator for the autoregressive and moving-average roots (without imposing causality or invertibility restrictions) of a nonstationary Fractional ARMA process. These estimators employ an efficient tapering procedure, which allows for a long memory component in the process, but avoid estimating the nonstationarity component, which can be stochastic and/or deterministic. After selecting automatically the order of the model, we robustly estimate the AR and MA roots for trading volume for the thirty stocks in the Dow Jones Industrial Average Index in the last decade. Two empirical results are found. First, there is strong evidence that stock market trading volume exhibits non-fundamentalness. Second, non-causality is more common than non-invertibility.

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