A hybrid artificial neural network-GJR modeling approach to forecasting currency exchange rate volatility
Introduction
A major phenomenon that has rapidly transformed and improved the socio-economic status of individual corporations, institutions and our world in its entirety is globalization. In fact, financial globalization is in particular widely regarded as inevitably central to the survival of financial institutions and national economies. With its key drivers including the liberalization of national financial and capital markets as well as rapid improvements in information technology, it has become a mainstay of the world economy while its reach and associated impact is expected to keep increasing [1], [2]. In recent decades, as a direct consequence of the aforementioned drivers, there has been a rapid spurt in the growth of foreign exchange markets through the increased cross-border capital. Thus unsurprisingly, the foreign exchange market is the largest and most liquid of the current financial markets. A number of economic indices exist for this market but perhaps the most crucial is exchange rates [3]. Primarily, the foreign exchange market comprises of three inter-related parts; spot transactions, forward transactions, and derivative contracts. As traders react to new information, currency markets can be volatile and exhibit periods of volatility clustering [4]. When compared to the volatility of inflation rates and relative price levels, exchange rates and their rates of change with time are more volatile [5], [6]. In the context of international trade, the impact of this volatility on national monetary policies especially for countries whose economic growth is largely dependent on export growth has been identified by national governments as worthy of consideration [1], [7], [8]. Accordingly, central banks often monitor exchange rate movements and periodical fluctuations for macroeconomic analysis and market surveillance purposes. The subject of effectively monitoring and managing exchange rate fluctuations and movements has attracted not only the interests of national policy makers but also financial economists, investors and corporate managers who given the growth of the number of international portfolios have embraced the need to address exchange rate volatility related risks [9], [10].
In academia, contributions to this all-important subject can be categorized into two collective empirical modeling approaches. The first and relatively more modern approach involves time series modeling. This approach focuses on time series analysis of financial returns such as leverage effects, and volatility clustering and persistence. In this regard, the univariate Autoregressive Conditional Heteroscedasticity (ARCH) / Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models, the "work-horse" of financial and economic time series modeling have been successfully employed in modeling volatilities of foreign exchange rates. The works of [11] and [12] are two earlier examples of the applications of such models. More recent applications of these univariate models can be found in other studies such as that of [13] who utilized data from 30/06/2003 to 31/03/2008 in evaluating volatility forecasts of the United States Dollar (USD) to Mauritius Rupee (MUR) i.e. USD/MUR exchange rate using GARCH (1, 1) models with GED and Student's error distributions. Their findings indicated that the GARCH (1, 1) model with GED errors slightly outperformed the other models in their study. Also using daily data from a different time period i.e., 03/07/2006 to 30/04/2012, [14] analyzed the Bangladesh Taka ((BDT) to USD (BDT/USD) exchange rate volatility using GARCH-type models and discovered on the basis of their empirical findings that current volatility is significantly affected by past volatilities. In yet another recent study, the in-sample and out-of-sample forecast performance of Log-Linear Realized GARCH was found to be superior to other models as reported by Xu et al. [15].
Prior to the deployment of time series models, earlier attempts often focused on the premise that a number of macroeconomic variables such as inflation, gross domestic product (GDP), and interest rates can in general help in the explanation of exchange rates movements and fluctuations. For instance, while employing a multivariate approach, Meese, and Rogoff [16] identified macroeconomic variables including trade nominal income, trade balance, and money supply as determinants of exchange rate changes. Their findings are popularly referred to as exchange rate disconnect puzzle in literature as their proposed macroeconomic variables proved to be weaker predictors while higher predictive power was instead realized for a random walk model. Cheung et al. [17] analyzed the forecasting ability of four models namely Behavioral Equilibrium Exchange Rate (BEER), Stick-price monetary model, Balassa-Samuelson and Uncovered Interest Rate Parity adopting the criterion of mean squared error. They used exchange rates data for CAD/USD, GBP/USD, DM/USD, CHF/USD, JPY/USD, spanning the second quarter of 1973 to fourth of 2004. Cheung et al. [17] however found that whiles none of the tested models outperforms the random walk on forecasting, over longer horizons, structural models however presented, on mean, a higher forecasting power than the random walk hypothesis.
Lately, there has been growing interest in the adoption of artificial neural networks (ANNs) to analyze historical data and provide predictions on future movements in the foreign exchange market. Researchers have revealed increasingly improved performance using artificial neural network models which have proven to outperform other models in time series forecasts [1], [18], [19], [20]. Multiple distinguishing features of ANNs make them valuable and attractive in forecasting. One of such is the fact that they are non-linear. In addition, ANNs are data-driven and can generalize. Previous studies to forecast exchange rate volatility with Neural Networks include the work of Podding [21] who investigated the problem of predicting the trend of the United States Dollar to German Deutsche Mark (USD/DEM) in comparison with results from the regression analysis. On the other hand, considerable research effort has gone into ANNs for forecasting exchange rates directly as against predicting volatility, Kuan and Liu [22] use both feed-forward (FFNN) and recurrent neural networks (RNN) to forecast British Pound to United States Dollar (GBP/USD), Canada Dollar to United States Dollar (CAD/USD), German Deutsche Mark to United States Dollar (DEM/ USD), Japanese Yen to United States Dollar (JPY/ USD), Swiss Franc to United States Dollar (CHF/ USD). Wu [23] also compares neural networks with Autoregressive integrated moving average (ARIMA) models in forecasting Taiwan New Dollar to United States Dollar (TWD/USD) exchange rates. Hann, and Steurer[24] make comparisons between the neural network and linear model in USD/DEM forecasting.
In spite of the numerous research conducted in the area of foreign exchange rate volatility forecast, to the best of our knowledge, previous studies on the use of neural network-based hybrid approaches is scanty. Other areas of finance are replete with successful implementations of such hybrid models which generally improve the forecasting ability of traditional models. For instance, Tseng et al. [25] used an asymmetric hybrid volatility forecast model together with a Neural Network to improve the forecasting power of the financial derivatives prices in the Taiwanese stock market. Based on their findings, they concluded that the Grey-Exponential generalized autoregressive conditional heteroskedastic (Grey -EGARCH) model has the highest forecasting power compared to the other models used in their study. In a recent application, Kristjanpoller and Minutolo [26] successfully employed a hybrid artificial neural network – GARCH model to forecast the volatility of oil price. They found that their proposed hybrid model improves the forecasting precision of the traditional models by up to 30% in terms of their adopted performance criterion. Various GARCH models have been applied in the modeling of the volatility of exchange rates in different countries. However, asymmetric GARCH models by addressing the challenge of heavy tails in financial data have gained significant attention. Brownlees et al. [27] introduced the Glosten Jagannathan and Runkle (GJR) model as a threshold autoregressive conditional heteroskedasticity (TARCH) model and reported that it was the best forecaster among asymmetric models and GARCH for one step or multi-step ahead forecasting. In more recent studies this observation is further confirmed [28], [29], [30], [31]. Therefore the GJR model has promising prospect for incorporation in hybrid systems/models for the task of volatility forecasting.
In this paper, we seek to improve the foreign exchange rates volatility forecast precision of traditional models by the use of a hybrid ANN-GJR model. Exchange rates data for five (5) major currencies i.e., British Pound to United States Dollar (GBP/USD), Euro to United States Dollar (EUR/USD), Canada Dollar to United States Dollar (CAD/USD), Swiss Franc to United States Dollar (CHF/ USD), and Japanese Yen to United States Dollar (JPY/ USD) are utilized for the purpose of the study. Using heteroskedastically modified mean standard (HMSE) and absolute errors (HMAE) we assess the relative performance of the proposed hybrid model vis a vis a GARCH (1,1) model and a GJR (1,1) model. The study employs the GARCH (1,1) owing to its popularity and use in several previous works as a benchmark model. Since improving the asymmetric GARCH variant i.e., the GJR model is a direct target of the study it is also employed as a benchmark. We adopt a moving window approach for which the calculations are based on some suggested innovations in previous volatility related forecasting studies [26], [32]. The moving window calculations are applied in generating both forecasts from the benchmark models as well as the neural network. A base model with GJR estimates and squared returns is firstly built. Followed by assessing the impact of two major commodity prices i.e., Oil and Gold as external input variables on the forecasting performance of the hybrid model. We finally investigate the best architecture for forecasting using the hybrid model by varying number of hidden layer sizes/nodes of the neural network. To determine the superiority of models generated from these combinations we also apply the Model Confidence Set (MCS) test procedure [33], [34], [35].
The need to improve exchange rate volatility forecast is very crucial thus reflecting the significance of the current work. Our study provides an extension to the field of expert systems, exchange rate volatility modeling and forecasting by applying an artificial neural network to an asymmetric GJR model in developing a hybrid ANN-GJR model. In general, understanding and estimating exchange rate volatility is important for asset pricing, portfolio allocation, and risk management. More specifically, improved forecast from the proposed ANN-GJR model will be useful to multinational firms, financial institutions as well as traders who wish to hedge currency risks. Most traders of foreign currency options often attempt to make profits from either buying options on the basis of expectations that exchange rate volatility will rise or be writing options based on expectations that it will drop relative to that currently implied in currency option premiums [4]. Moreover, knowledge of exchange rate volatility is also important because exchange-rate risk may increase transaction costs and reduce gains to international trade.
The organization of this paper is as follows: section one provides an introduction which includes illustrations of the state of the art in this subject. Section two gives the methodology and provides details on the models utilized in the study. We also define the methods of comparison for measuring the accuracy of the models. In the following section, we discuss the characteristics of the employed data sets. The fourth section contains presentation and analysis of the obtained results and we finally follow that up with a summary of our key findings and their implications in the last section.
Section snippets
Methodology
Modeling and forecasting volatility is undoubtedly one of the most essential developments in empirical finance. The rising popularity of this field is albeit a direct consequence of the rapid growth in financial derivatives, quantitative trading and risk modeling. It is worth noting however that volatility modeling is quite demanding with associated difficulties derived from the latent nature of financial market volatility. An effective volatility study will require a prior determination of
Data
The analysis was conducted using data sets for foreign exchange rates of five (5) major currencies against the US Dollar. The currency pairings studied are the AUD/USD, CAD/USD, CHF/USD, EUR/USD and GBP/USD. Each of the data sets obtained from investing.com covered a sample period starting from January 2001 to November 2013. Descriptive statistics of the returns for each exchange rate pairing are provided in Table 1. The daily mean return for AUD, CAD, CHF and EUR against the USD are all above
Results
In this section, we report the findings of our empirical analysis by firstly examining the results for each exchange rate pairing and subsequently discuss existing general trends and probable deviations that may aid in explaining the strengths or weakness of the models developed herein. To assess the performance of the hybrid model we deploy the traditional GARCH (1,1) model as well as the GJR (1,1) model as benchmarks. The more advanced APGARCH model is also adopted as an additional benchmark.
Conclusion
This paper examines the implementation of a hybrid neural network model in forecasting currency exchange rate volatility. The currency pairings utilized are the AUD/USD, CAD/USD, CHF/USD, EUR/USD and GBP/USD. The empirical evidence firstly suggests that the hybrid ANN-GJR, developed in this study is remarkably superior to all applied benchmark models. In terms of the MSE, the MAD and the MAPE measures, a significant improvement of the measured forecast accuracy was found when using the ANN
CRediT authorship contribution statement
Alexander Amo Baffour: Conceptualization, Data curation, Writing - original draft, Writing - review & editing, Formal analysis. Jingchun Feng: Conceptualization, Data curation, Writing - original draft, Writing - review & editing, Formal analysis. Evans Kwesi Taylor: Conceptualization, Data curation, Writing - original draft, Writing - review & editing, Formal analysis.
Declaration of Competing Interest
None.
Acknowledgments
This work was supported by (1) The National Social Science Fund (Key Project of the 2014 Grant No. 14AZD024; (2) The Fundamental Research Funds for the Central Universities (2014B09014); (3) The National Social Science Fund (Youth Project of 2015, Grant No. 15CJL023).
Alexander Amo Baffour is Ph.D. student and a research assistant at the Business School, Hohai University, China. He received his first degree from University of Ghana & MBA in Finance & Investment from London School of Business & Finance/University of Wale, UK. His research interest is application of Artificial Intelligent in data mining in the area of Management science and Project Investment Financing.
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Alexander Amo Baffour is Ph.D. student and a research assistant at the Business School, Hohai University, China. He received his first degree from University of Ghana & MBA in Finance & Investment from London School of Business & Finance/University of Wale, UK. His research interest is application of Artificial Intelligent in data mining in the area of Management science and Project Investment Financing.
Feng Jingchun is a Professor & Director of Engineering, Master Education Center at the Business School, Hohai University, China. He received his B.Sc. from Tianjin University and both M.Sc. and Ph.D. from Hohai University, 1987–1991 and 1993–1997 respectively. His research interest is in the area of Management Engineering and Project Management; Project System and Information Management. He has published more than 60 papers in Water Science and Engineering, Hydraulic Engineering, China Investment, Intelligent Information Management, etc. and many of his works have been abstracted in SCI, EI, CITIC and CSSCI.
Evans Kwesi Taylor is a PHD student at the College of Mechanics, Hohai University, China. He obtained his undergraduate degree in Materials Science and Engineering from KNUST, Ghana and Masters in the same field at Hohai University. His research interests include the application of machine learning algorithms in the field of corrosion engineering. He has expertise in a wide range of programming languages and software.
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The authors contributed equally to this work.