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Gold Price Data Analysis Using Rescaled Range (R/S) Analysis

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Gold Price Data Analysis Using Rescaled Range (R/S) Analysis International Journal of Economics, Commerce and Research (IJECR) ISSN(P): 2250-0006; ISSN(E): 2319-4472 Vol. 4, Issue 1, Feb 2014, 7-14 © TJPRC Pvt. Ltd. GOLD PRICE DATA ANALYSIS USING RESCALED RANGE (R/S) ANALYSIS SHAIKH YUSUF H1, KAPSAE S. K.2, KHAN A R3 & G. RABBANI4 1Shivaji Arts, Commerce and Science College, Kannad, India 2S.B. Science College, Aurangabad, Maharashtra, India 3,4Maulana Azad College Dr. Rafiq Zakaria Campus, Dr. Rafiq Zakaria Marg, Aurangabad, Maharashtra, India ABSTRACT Gold has been at centre of attraction from various angles, particularly for value and financial importance and served as a reference. There has been a continuous rise in the international gold prices since for ages. Gold is a major part of savings of investors, this has caused concern as to whether any correction in gold prices will have destabilizing implications on the financial markets. With this backdrop, we make an attempt to analyze the gold prices over a period of more than last 32 years to explore the variability in the gold price in India. The gold market has recently attracted a lot of attention and the global price of gold is relatively higher than its historical changing pattern and trend. There has been a drastic increase in international gold prices in the last few years, though there was one large correction in 2008. The gold price data for about 32 years is divided into four sets for the purpose of implementation of Rescaled Range (R/S) Analysis. R/S analysis is an effective technique for analyzing random data in the form of time series in order to bring out trends and any memory effects present in the behavior of the changing data. Details of implementation of the R/S analysis technique and estimation of the Hurst exponent H and the fractal dimensions are presented and findings and results discussed, it is shown that the international gold prices exhibit a consistent trend of persistence and long term memory effect with fractal dimension close to unity. KEYWORDS: Gold Market, Gold Prices, Time Series, R/S Analysis, Fractal Dimension, Persistence, Memory Effect INTRODUCTION Like share prices the international gold prices exhibit a random variation and the parameters governing the gold prices can not exactly be enlisted. Randomly varying prices pose difficulties in predicting trends and future patterns which is of interest to investors and financial agencies. Such situations are at time handled using methods based on the concept of fractals and fractal dimensions and the approach is found to be effective for non-stationary signals such as stock market data [1 to 5]. These apparently irregularly changing signals are considered to be driven by external non stationary factors. Standard methods such as Fourier analysis assume that the signals are stationary in temporal windows. Such an assumption does not strictly apply for gold prices and stock market data as it changes constantly with an element of unpredictability and the factors governing the prices keep on changing from time to time. Such irregular phenomena are at times handled using the concept of fractals and fractal dimensions [6 to 8], fractals possess characteristics of self similarity and scale invariance. Fractal based methods such as rescaled range analysis does not impose the above assumption and therefore are better suited for the analyzing the data and has better predictability. In this paper, we use rescaled range analysis [9 to 15] to analyze gold price (in IRS) data for more than last 32 years which gives statistical insight into the trends and tendencies of fluctuations. The data spread over 32 years is divided into four part of approximately 8 years each (Set – I to IV). The four sets of data is independently subjected to R/S analysis and the findings are presented, it is shown that rescale 8 Shaikh Yusuf H, Kapsae S. K, Khan A R & G. Rabbani range analysis can be used for assessing any trends of persistence or anti persistence that can be used for predicting future trends. GOLD PRICE DATA Gold and Share market [16] form the fulcrum of economic trends in the market for ages and it has its own importance in establishing strength or weakness of the prevailing economic trends. It is known that domestic gold prices and international gold prices are closely interlinked. Variations in the international gold prices find almost similar echo in the domestic gold prices. For a long time, macro fundamental such as international commodity prices, US exchange rate and equity prices used to be the most dominating factors affecting the international gold prices and their impact used to be identical both in the long-run and short-run[17]. However this linkage started showing weakness and the mutual dependence was found to be more complex and the relative proportion of the two main deciding factors was found to appreciably change. Lot of standard software are available out there and for analyzing such data that in fact is a time series to evaluate the volatility and assess the variation patterns, however these try to forecast future prices based on statistical theories and historical weightages and at times are liked with news and technicals. Most of the times, statistically based parameters fail drastically if the prices drastically change due to economic events (also known as news) or issues like change of rule or Government, at times natural calamities and wars also shake the market drastically. RESCALE RANGE ANALYSIS OF TIME SERIES For the study natural phenomena possessing random character such as the flow of the Nile River in relation to long term correlation Hurst introduced approach. This approach was based on the statistical assessment of many observations of the natural phenomena. After studying 800 years of records, he showed that the flow of the Nile River was not random, but had a pattern. He introduced a constant, K, which measures the bias of the fractional Brownian motion. In 1968 Mandelbrot defined such pattern as fractal. There are many algorithms to calculate fractal characteristics such as fractal dimensions, which is a number that quantitatively describes how an object fills its space. He renamed the constant K to H in honor of Hurst. Rescaled range (R/S) analysis is a statistical method to analyse the records of natural phenomena in the form of a time series. The theory of the rescaled range analysis was first given by Hurst. Mandelbrot and Wallis further refined the method. Feder (1988) gives an excellent review of the analysis of data using time series [18, 19], history, theory and applications, and adds some more statistical experiments to establish the effectiveness of this approach. The parameter H, the Hurst exponent provides insight into the trends and patterns shown by the time series in respect of as to whether the time series is random or not. It is also related to the fractal dimension, the Rescaled range analysis (R/S) approach of estimating H is helpful in distinguishing a completely random time series from a correlated time series and. The value of H reveals persistence of trends in a given time series. METHODOLOGY The approach for estimation of the Hurst exponent ‘H’ follows simple statistical rules, for a time series like data, start with the whole observed data set Z (t) that covers a total duration and calculate its mean over the whole of the available data ‹Z›. 1 Z Z(t) t1 (1) Gold Price Data Analysis Using Rescaled Range (R/S) Analysis 9 Then Sum the differences from the mean to get the cumulative total of the deviation from mean at each time point, X ( t, ), from the beginning of the period up to any time t using X (t, ) Z t Z t1 (2) Then find the X max the maximum of X (t, ), X min the minimum of X(t, ) and calculate the self adjusted range R() defined as the difference between maximum and minimum accumulated influx X R ( ) = max X (t, ) - min X (t , ) (3) The standard deviation S, of the values, Z (t) of the observation over the period, 1 1 2 2 S( ) Z t Z t1 (4) Hurst used a dimension less ratio R/S where S( ) is the standard deviation as a function of (R/S) = ( / 2) H (5) Hurst exponent H can be found by plotting log (R/S) against log (/2), the slope of the resulting straight line is the Hurst exponent. The Hurst exponent gives a measure of the smoothness of a fractal object where H varies between 0 and 1. Low ‘H’ values indicate high levels of roughness or variability. High values of H indicate low value of roughness or high levels of smoothness. The fractal dimension D is related to H as H = 2 – D and higher the value of D, larger is the variability or complexity associated with the time series. We use H and D to analyze the gold price data as it has a broad applicability to signal processing due to its robustness. These parameters can be calculated by the rescaled range analysis method. It is useful to distinguish between random and nonrandom data points/time series. If H equals 0.5, then the data is determined to be random. If the H value is less than 0.5, it represents anti-persistence, meaning, if the signal is up/down in the last period then more likely it will go down/up in the next period (i.e. if H is between 0 and 0.5 then an increasing trend in the past implies a decreasing trend in the future and decreasing trend in past implies increasing trend in the future).
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