Features affecting hurst exponent estimation on time series

Abstract

Forecasting is becoming increasingly relevant to producers and consumers in all markets today. Both for producers and consumers, forecasts are necessary to develop bidding strategies as well as negotiating skills at the market in order for both parties to maximize benefits. Due to fluctuations of the Kenya shilling strength, weather conditions, politics and many other variables in the markets, prices of goods are highly volatile. The volatility of prices following a pattern makes it a time series phenomenon. Everyone with a new prediction method wants to try it out on returns from a speculative asset, such as stock market prices. Papers continue to appear attempting to forecast stock returns usually with very little success. This project is aimed at estimating the amount of predictability of a time series data using the Hurst exponent index. The Hurst exponent (H) is a dimensionless estimator for the predictability of a time series. Initially defined by Harold Edwin Hurst to develop a law for regularities of the Nile water level, it now finds applications in financial data such as stock prices. The Hurst Exponent can be interpreted as a measure of the trendiness: To be more specific, different values of Hurst exponent imply fundamentally different price behaviors. It is a statistical measure used to classify time series into either a random series or a trend reinforcing series. The larger the index value is, the stronger the trend. In this study we have investigated the features of time series associated with different estimates of Hurst exponent. It is shown that series with large Hurst exponent can be predicted more accurately than those series with Hurst exponent value close to 0:50. The main focus of this study is therefore to determine: Why Hurst exponent index swings from persistence to anti-persistence. Estimating of the Hurst exponent for time series data plays a very important role in research of processes which show properties of auto-correlation.