Informatics Publishing Limited

E. Priyadarshini ¹, A. Chandra Babu ²

Affiliations
1 Sathyabama University Chennai - 600119, IN
2 Department of Mathematics MNM Jain Engineering College Chennai - 600097, IN

Abstract

Accuracy in forecasting the foreign exchange rate and predicting the trend correctly is of crucial importance for any future investments. Over the last few decades, the foreign exchange market has experienced unprecedented growth. The purpose of this paper is to apply rescaled range analysis to foreign exchange market data in an attempt to establish the presence of long term memory and market cycles. It also identifies the fractal dimension of the market by using rescaled range analysis and an estimated Hurst exponent.

Keywords

Chaos, Fractals, Rescaled Range, Persistence, Foreign Exchange Market

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E. Priyadarshini ¹, A. Chandra Babu ²

Affiliations
1 Department of Mathematics, Sathyabama University, Chennai, IN
2 Department of Mathematics, M.N.M. Jain Engineering College, Chennai, IN

Abstract

The exchange rates play a vital role in controlling the dynamics of the exchange market. As a result, the appropriate prediction of exchange rate is a crucial factor for the success of many businesses and fund managers. For more than twenty decades, Box Jenkin's Auto Regressive Integrated Moving Average (ARIMA) technique is one of the most sophisticated extrapolation method for forecasting. It predicts the values in a time series as a linear combination of its own past values, past errors and current and past values of other time series. Artificial Neural Network (ANN) is a modern non linear technique used for prediction that involves learning and pattern recognition. The historical monthly data for the years 1999-2009 (10 years) for five exchange rates namely US Dollar (USD), Great Britain Pound (GBP), Kuwaiti Dinar (KWD), Japanese Yen (JPY), and Hong Kong Dollar (HKD) were modeled using these two techniques and the Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE) Mean Absolute Percentage Error (MAPE) are used to evaluate the accuracy of the models. Results show that ANN model performs much better than the traditional ARIMA model. The main focus of this paper is to forecast the monthly exchange rates using various ARIMA models and ANN models and the future exchange rates is forecasted for the succeeding months.

Keywords

Auto Regressive Moving Average (ARIMA), Artificial Neural Networks (ANN), Forecasting, Stationary.

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E. Priyadarshini ¹

Affiliations
1 Maths Department, Sathyabama University, Chennai – 600119, Tamil Nadu, IN

Abstract

This research paper focuses on the persistence level of earthquakes in and around Indonesia by using Rescaled Range Analysis. In the past, the long-term memories in many natural phenomena like floods, hurricanes, sunspots have been found using Rescaled Range Analysis. The Hurst exponent computed from the Rescaled Range determines the level of persistence. The test sample employed for conducting this analysis was taken from the seismic data of Indonesia for the period from 1943 to 2013 (70 years). The result analysis indicates that there is a fair level of persistence in the occurrences of earthquakes in Indonesia. It also suggests that this time series has long term memory and the intensity and recurrence of earthquakes in this area may increase in the coming years.

Keywords

Hurst Constant, Periodic, Persistence, Rescaled Range, Time Series.

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