# On Prediction of Euro and Pound Sterling using Box-Jenkins Approach

## Keywords:

Forecasting, Exchange Rate, Box-Jenkins ARIMA Model, Model Selection Criteria.## Abstract

The purpose of this study is to determine ARIMA models for forecasting euro and pound sterling using secondary data of closed rates of euro and pound sterling in terms of the US. dollar at every 4-hour from the 00:00 (GMT) of September 23, 2019, to the 20:00 (GMT) of November 29, 2019. The first 270 observations of each exchange rate are used as training data to develop the forecasting models and the remaining 30 observations are used as validation data for model evaluation. The ARIMA(p,d,q) where p=1,10, d=0, q=9, and ARIMA(p,d,q) where p=0, d=1, q=9 are proposed as the potential forecasting models for the euro exchange rate. For pound sterling exchange rate, the ARIMA(p,d,q) where p=1,2, d=0, q=6, and ARIMA (p,d,q) where p=0, d=1, q=6 are proposed. Then, the likelihood estimation method is employed to estimate the parameters of the proposed models. The Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) are selectively used as the model selection criteria. The empirical results were found that the ARIMA(p,d,q) where p=1,10, d=0, q=9 is outstandingly selected to be the forecasting model of the euro exchange rate. In addition, the ARIMA(p,d,q) where p=1,2, d=0, q=6 is also determined as the forecasting model for the pound sterling exchange rate. We found that these forecasting models will be able to perform well only in a short time forecasting horizon. Therefore, the investor needs to modify the model with the incorporation of the actual observations when would like to perform a longer forecast horizon.

## References

Box, G.E.P. & Jenkins, G.M. (1976). Time Series Analysis: Forecasting and Control, Revised Edition, San Francisco: Holden-Day.

Chaiwan, S. (2007). Jewelry and Accessories Export Value Forecasting by ARIMA Method. Independent Studies of Economics, Faculty of Economic, Chiang Mai University, Chiang Mai.

Cheung, Y. (1993). Long Memory in Foreign-Exchange Rates. Journal of Business & Economic Statistics, 11(1), 93-101.

Fansiri, C. (2004). Forecasting of Rice Export Price by ARIMA Method. Independent Studies of Economics, Faculty of Economic, Chiang Mai University, Chiang Mai.

Foreign Exchange Market. (2020, December, 16). In Wikipedia. Retrieved December 25, 2020, from https://en.wikipedia.org/wiki/Foreign_exchange_market.

Fusion Media. (n.d.). Currencies. Retrieved December 25, 2020, from https://www.investing.com/currencies/gbp-usd-historical-data.

Kamruzzaman, J., & Sarker, R. (2003). Comparing ANN based Models with ARIMA for Prediction of Forex Rates. Asor Bulletin, 22(2), 2-11.

Khruachalee, K. (2017). Asian Currencies Forecasting and Modelling using a Time Series Analysis. International Journal of Computer, the Internet and Management, 25(2), 59-67.

Lion, S. (1997). Time Series Model of Systematic Risk of Banking Sector in The Stock Exchange of Thailand. Independent Studies of Applied Statistics, Faculty of Science, Silpakorn University, Nakorn Pathom.

Lorchirachoonkul, V. & Jitthavech, J. (2005). Forecasting Techniques. 3rd edition, Bangkok, National Institute of Development Administration (NIDA).

Madura, J. (2018). International Financial Management. 13th Edition, Boston, MA, Cengage Learning.

Pingmueang, A. (2012). Gold Price Forecasting by ARIMA Method. Independent Studies of Economics, Faculty of Economic, Chiang Mai University, Chiang Mai.

Remitr. (2020, October 16). What are the top 10 most traded currencies in the world?. Retrieved December 25, 2020, from https://remitr.com/blog/top-10-most-traded-currencies-2020/

Rungsuprangsi, C. (2007). Euro Currency Exchange Rate Forecast by ARIMA Model. Independent Studies of Economics, Faculty of Economic, Chiang Mai University, Chiang Mai.

Siriphanich, P. (2007). Time Series Forecasting Using a Combined of ARIMA and Artificial Neural Network Model. Independent Studies of Mathematics and Information Technology, Faculty of Science, Silpakorn University, Nakorn Pathom.

Udomsombatchai, B. (2004). Broiler Chicken Price Forecasting by ARIMA Method. Independent Studies of Economics, Faculty of Economic, Chiang Mai University, Chiang Mai.