Monofractal and Multifractal Analysis of Indian Agricultural Commodity Prices

Abstract

The Indian commodity market is characterized by high volatility. When considering the agro-based commodity market, the prices may sometimes vary on a daily basis and regional basis. For the purpose of our research, we have restricted our region of study to the Indian national capital New Delhi. This paper aims to find out whether commodity markets follow a pattern with respect to prices, and if they do, then whether this could be determined by using basic fractal theory and determination of Hurst exponent. We have followed a suitable algorithm to find the Hurst exponent using statistical methods, specifically linear regression and time series analysis, wherein time is the independent variable and price of the commodity considered is dependent. The reason why time series analysis is chosen is because of the tendency of a time series to regress strongly to its mean. A statistical measure chosen to classify time series is the Hurst exponent. Initially, we have focused on onion prices for the years 2013 to 2017. The data set has been derived from the official website of the Consumer Affairs Department of the Government of India. The daily retail prices for Delhi for the month of June were observed and analyzed. We eventually aim to investigate if the market for onions has a long-term memory and will it be suitable to extend this conclusion to all other agro-based commodities. Our study has been motivated by the Fractal Market Hypothesis (FMH) that analyses the daily randomness of the market. We seek to find out whether the commodity market follows such a pattern provided that external factors remain constant. By external factors, we mean the variations that occur in the market with time, which include the demand, inflation, global price change, changes in the economy, etc. Keeping this in mind, we have attempted a time series analysis, using the monofractal analysis, at the end of which we would be estimating the Hurst exponent. The determination of Hurst exponent will help us to classify the time series as persistent or anti-persistent, i.e., how strong is the tendency of the time series to revert to its long-term mean value. Further, the multifractal analysis has been used to detect small as well as large fluctuations within the time series taken into consideration. This result would thus lead us to understand if prices in the commodity market could be remotely predicted, and what is the strength of the time series to return to its long-term mean value. Hence, this fractal analysis can be used to determine the characteristics of the prices in an agro-based economy.