AN ANALYSIS OF STABILITY OF TRENDS IN GOLD PRICES USING FRACTAL DIMENSION INDEX (FDI)COMPUTED FROM HURST EXPONENTS (original) (raw)

AN ANALYSIS OF STABILITY OF TRENDS IN GOLD PRICES USING FRACTAL DIMENSION INDEX (FDI)

Chaos is a nonlinear, dynamic system that appears to be random but is actually a higher form of order. All chaotic systems have a quantifying measurement known as a fractal dimension. The fractal dimension index (FDI) is a specialized tool that applies the principles of chaos theory and fractals. With FDI one can determine the persistence or anti-persistence of any equity or commodity. In this paper we study the data from gold rates by computing the fractal dimension index. The fractal dimension index is computed from the Hurst exponent and the Hurst exponent is computed from Rescaled Range R/S. Keywords: chaos, fractals, rescaled range, persistence.

Fractal Analysis of Currency Market: Hurst Index as an Indicator of Abnormal Events

2016

The article is devoted to analysis of currency quotes behavior on the currency market by defining dynamic changes over time. The main tool of fractal analysis is the Hurst under the hypothesis of fractal market. For 17 major currency pairs on closing prices and the prices maximum-minimum the Hurst index is calculated by formula for the adjusted R/S analysis. Values at the currency markets of different countries in different economic conditions are compared during 2008-2015. For currency pairs Hurst index tends to maintain its average value in stable economic situation, while it is an indicator of events affecting directly or indirectly on the state's economy and the rate of its national currency. Application of sliding window method allows to simulate the dynamics of Hurst index for the currency pairs USD/JPY, GBP/JPY, EUR/USD, GBP/USD and establish certain patterns of conduct series of quotes due to appropriate reaction to economic, political and natural disturbances.

Introducing fractal dimension algorithms to calculate the Hurst exponent of financial time series

In this paper, three new algorithms are introduced in order to explore long memory in financial time series. They are based on a new concept of fractal dimension of a curve. A mathematical support is provided for each algorithm and its accuracy is tested for different length time series by Monte Carlo simulations. In particular, in the case of short length series, the introduced algorithms perform much better than the classical methods. Finally, an empirical application for some stock market indexes as well as some individual stocks is presented.

Fractal Dimensional Analysis in Financial Time Series

A predictability index for time series of a financial market vector consisting of chosen market parameters is suggested providing a measure of long range predictability of the market. It is based on fractional Brownian motion that includes Brownian motion as a particular case followed by the time series of financial market parameters. By analysing respective time series, these indices are computed for parameters like volatility, FII investments in the local market, IIP numbers, CPI numbers, Dow Jones Index, different stock market indices, currency rates, and gold prices.

Fractal Analysis of US Financial Markets The Hurst Exponent as an indicator of regime shift

Our research goal is to apply fractal analysis to financial time series to gain insights on the type of market, the persistence of the market type, i.e. the presence of long term memory, and to identify if a possible regime change is in the making (by using the Hurst exponent as a proxy for volatility) in order to have an edge for the application of 2 basic trading strategies: momentum trading and mean reversion trading. In addition, we want to verify the applicability of the Fractal Market Hypothesis (FMH) vs the Efficient Market Hypothesis (EMH). The principal method of fractal analysis we will employ is the R/S statistic, introduced by Hurst in 1951, to estimate the fractal dimension (and the Hurst exponent, H), in order to classify time series in 3 main buckets: mean reverting (low volatility, anti-persistent) for H < 0.5, trending (higher volatility, series has long term memory, or persistence) for H > 0.5, and for H = 0.5 (or close to it), the EMH regime.

Multifractal characterization of gold market: A multifractal detrended fluctuation analysis

Physica A: Statistical Mechanics and its Applications, 2014

The multifractal detrended fluctuation analysis technique is employed to analyze the time series of gold consumer price index (CPI) and the market trend of three world's highest gold consuming countries, namely China, India and Turkey for the period: 1993July 2013. Various multifractal variables, such as the generalized Hurst exponent, the multifractal exponent and the singularity spectrum, are calculated and the results are fitted to the generalized binomial multifractal (GBM) series that consists of only two parameters. Special emphasis is given to identify the possible source(s) of multifractality in these series. Our analysis shows that the CPI series and all three market series are of multifractal nature. The origin of multifractality for the CPI time series and Indian market series is found due to a long-range time correlation, whereas it is mostly due to the fat-tailed probability distributions of the values for the Chinese and Turkey markets. The GBM model series more or less describes all the time series analyzed here.

Chaotic Analysis o f Gold Price Index

Journal of Engineering Science and Technology Review

This paper applies non linear methods to analyze the weekly gold prices close index .The aim of the analysis is to quantitatively show if the corresponding time series is a deterministic chaotic one and its predictable. For this purpose the correlation and minimum embedding dimensions of the corresponding strange attractor are calculated. Also the maximum Lyapunov exponent is estimated.

Fractal Analysis of Prime Indian Stock Market Indices

Fractals, 2013

The purpose of the present work is to study the fractal behaviour of prime Indian stock exchanges, namely Bombay Stock Exchange Sensitivity Index (BSE Sensex) and National Stock Exchange (NSE). To analyze the monofractality of these indices we have used Higuchi method and Katz method separately. By applying Mutifractal Detrended Fluctuation Analysis (MFDFA) technique we have calculated the generalized Hurst exponents, multifractal scaling exponents and generalized multifractal dimensions for the present indices. We have deduced Hölder exponents as well as singularity spectra for BSE and NSE. It has been observed that both the stock exchanges are possessing self-similarity at different small ranges separately and inhomogeneously. By comparing the multifractal behaviour of the BSE and NSE indices, we have found that the second one exhibits a richer multifractal feature than the first one.

Measuring the Complexity of Currency Markets by Fractal Dimension Analysis

International Journal of Theoretical and Applied Finance, 2003

We use the theory of nonlinear dynamical systems to measure the complexity of currency markets by estimating the correlation dimension of the returns of the Dollar/Pound and Dollar/Yen daily exchange rates (the spot rates). We test the significance of the results by comparing them to correlation dimension estimates for surrogate time series, i.e. stochastic linear time series with the same power spectrum and amplitude distribution as given by the original data. We find discernible nonlinear structure in the returns of the Dollar/Pound daily rate.