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Mathematical Problems in Engineering
Volume 2018, Article ID 9280590, 12 pages
Research Article

Predicting Stock Price Trend Using MACD Optimized by Historical Volatility

Department of Mathematics, Korea University, Seoul 02841, Republic of Korea

Correspondence should be addressed to Junseok Kim;

Received 18 September 2018; Revised 13 November 2018; Accepted 21 November 2018; Published 25 December 2018

Academic Editor: Luis Martínez

Copyright © 2018 Jian Wang and Junseok Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


With the rapid development of the financial market, many professional traders use technical indicators to analyze the stock market. As one of these technical indicators, moving average convergence divergence (MACD) is widely applied by many investors. MACD is a momentum indicator derived from the exponential moving average (EMA) or exponentially weighted moving average (EWMA), which reacts more significantly to recent price changes than the simple moving average (SMA). Traders find the analysis of 12- and 26-day EMA very useful and insightful for determining buy-and-sell points. The purpose of this study is to develop an effective method for predicting the stock price trend. Typically, the traditional EMA is calculated using a fixed weight; however, in this study, we use a changing weight based on the historical volatility. We denote the historical volatility index as HVIX and the new MACD as MACD-HVIX. We test the stability of MACD-HVIX and compare it with that of MACD. Furthermore, the validity of the MACD-HVIX index is tested by using the trend recognition accuracy. We compare the accuracy between a MACD histogram and a MACD-HVIX histogram and find that the accuracy of using MACD-HVIX histogram is 55.55% higher than that of the MACD histogram when we use the buy-and-sell strategy. When we use the buy-and-hold strategy for 5 and 10 days, the prediction accuracy of MACD-HVIX is 33.33% and 12% higher than that of the traditional MACD strategy, respectively. We found that the new indicator is more stable. Therefore, the improved stock price forecasting model can predict the trend of stock prices and help investors augment their return in the stock market.