Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development

The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.Comment: 46 pages, 7 figures, accepted for publication in Journal of Banking & Financ

Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development

The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.Scaling exponents; Time series analysis; Multi-fractals

Long Term Dependence of Popular and Neglected Stocks

In this study, we establish a connection between the levels of market attentions of a stock with its long memory features. We construct two portfolios of US equities based on Doyle et al’s (2006) criteria for neglected and popular stocks and measure the degrees of persistence for their daily returns from January 1, 2003 to December 31, 2007. We find that all stocks except for one display anti-persistence in the neglect portfolio; while the popular portfolio stocks uniformly display random walk returns. This suggests that there is a connection between the persistence features of stock return series and the levels of “neglect” of stocks. We use book to market ratio, analyst coverage, and transaction frictions to classify the levels of market neglect of stocks. Based on our study, while these criteria combined appear to contribute to the long memory features of daily returns of stocks, we also suspect the presence of other factors driving the persistence of stock returns

A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t1−1/γ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3e1/t1−1/γ scaling law, where γ\u3e0 role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eγ\u3e0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values

Financial power laws: Empirical evidence, models, and mechanism

Financial markets (share markets, foreign exchange markets and others) are all characterized by a number of universal power laws. The most prominent example is the ubiquitous finding of a robust, approximately cubic power law characterizing the distribution of large returns. A similarly robust feature is long-range dependence in volatility (i.e., hyperbolic decline of its autocorrelation function). The recent literature adds temporal scaling of trading volume and multi-scaling of higher moments of returns. Increasing awareness of these properties has recently spurred attempts at theoretical explanations of the emergence of these key characteristics form the market process. In principle, different types of dynamic processes could be responsible for these power-laws. Examples to be found in the economics literature include multiplicative stochastic processes as well as dynamic processes with multiple equilibria. Though both types of dynamics are characterized by intermittent behavior which occasionally generates large bursts of activity, they can be based on fundamentally different perceptions of the trading process. The present chapter reviews both the analytical background of the power laws emerging from the above data generating mechanism as well as pertinent models proposed in the economics literature. --

Theoretical Insight in Financial Decision and Brain as Fractal Computer Architecture

The purpose of this paper is to examine the theoretical interaction of brain dynamics using fractal information tools, fractal geometry in fnancial decision making. This paper concludes a scientific analytical observatory focusing on financial decision making. Through the integration of neuroscien-tific approach to the brain as a fractal and financial decision-making with the concept of fractal fi-nancial market, we open the analytical framework through two interrelated approaches that can in-crease information on making financial decisions and improve effective financial decisions in times of uncertainty. In order to achieve the aim of the work, the concept of “organized business forms” and the analogue of neurons in the financial market is the fractal – the price of a financial asset, to summarize theoretical basics, multifraktal and financial market / fractal trading, fractal computing architecture. Time series of property prices are dental lines, Fractal Computing Architectur

Application of the Fractal Market Hypothesis for Modelling Macroeconomic Time Series

This paper explores the conceptual background to financial time series analysis and financial signal processing in terms of the Efficient Market Hypothesis. By revisiting the principal conventional approaches to market analysis and the reasoning associated with them, we develop a Fractal Market Hypothesis that is based on the application of non-stationary fractional dynamics using an operator of the type ∂2 / ∂x2 − σq(t) * ∂ q(t)/ ∂tq(t) where σ−1 is the fractional diffusivity and q is the Fourier dimension which, for the topology considered, (i.e. the one-dimensional case) is related to the Fractal Dimension 1 \u3c DF \u3c 2 by q = 1 − DF + 3/2. We consider an approach that is based on the signal q(t) and its interpretation, including its use as a macroeconomic volatility index. In practice, this is based on the application of a moving window data processor that utilises Orthogonal Linear Regression to compute q from the power spectrum of the windowed data. This is applied to FTSE close-of-day data between 1980 and 2007 which reveals plausible correlations between the behaviour of this market over the period considered and the amplitude fluctuations of q(t) in terms of a macroeconomic model that is compounded in the operator above

MATLAB

This excellent book represents the final part of three-volumes regarding MATLAB-based applications in almost every branch of science. The book consists of 19 excellent, insightful articles and the readers will find the results very useful to their work. In particular, the book consists of three parts, the first one is devoted to mathematical methods in the applied sciences by using MATLAB, the second is devoted to MATLAB applications of general interest and the third one discusses MATLAB for educational purposes. This collection of high quality articles, refers to a large range of professional fields and can be used for science as well as for various educational purposes