Artificially Intelligent Forecasting of Stock Market Indexes

Transcription

1 Artificially Intelligent Forecasting of Stock Market Indexes Loyola Marymount University Math 560 Final Paper Daniel McGrath Advisor: Dr. Benjamin Fitzpatrick

2 Contents I. Introduction II. III. IV. Model Network Design Results V. Conclusions VI. References

3 Introduction The task of predicting a random value or series of random values is one that has posed a great challenge to mankind for centuries. Knowing the exact weather patterns of several weeks in the future, for example, requires the incorporation of a wide range of factors and inter-dependent variables. The winds affect temperature, which affects pressure, which in turn can have effects on temperature, with all three of these things undergoing constant interaction with the Sun and Moon, not to mention disruptive human air traffic and resulting pollutants. One can easily recognize the difficulty surrounding this sort of record keeping and vigilance. For this reason, the problem must be simplified using higher mathematical techniques, particularly statistical analyses made possible by artificially intelligent structures. In predicting the future value of a stock market index, typically a real valued quantity that takes on a single value at the close of each day of trading, such techniques are particularly well suited. The following document describes the implementation of a multilayer, artificial neural network (ANN) trained to forecast the daily closing price of the NASDAQ index and analyzes the results that were obtained. The forecasting process is referred to herein as, Index Price Point Prediction (IP3). Model To reiterate and provide a more thorough understanding of the system, consider the notion of forecasting a real valued, time variant signal, in a similar fashion to an analog voltage signal receiver, which determines the value of the received signal while accounting for random noise, typically additive white Gaussian noise. The value of the signal at a given time instant, in this case the price of a particular stock index, undergoes fluctuations due to buyer activity in a similar manner to the analog voltage signal, which is attenuated by or added to the voltage level of the noise at a given instance. Because of the presence of this noise in the stock market, simple linear regression and analysis of the standard deviation, variance, or mean value of an index are insufficient in determining its future value, necessitating the error minimizing properties of an ANN. Network Design The objective of the ANN implementation is to train the network on ten prior days of NASDAQ closing values and forecast the daily closing of the next five days using the neural network toolbox available in MATLAB-R2017b, specifically a feedforwardnet. This methodology is referred to by the

4 author as two for one reinforcement due to the two week training data, which yields one week of forecasted data. The training algorithm that was ultimately chosen was the Levenberg-Marquardt technique, due primarily to its suitability for curve fitting applications and best performance in testing when compared to the the gradient descent, back-propagation, and one step secant methods as well as all other training functions available in MATLAB. Parameter sweeps of each network attribute converged at the optimal values shown in Table 1, using an accuracy threshold requirement and iterative training technique. Table 1: Optimal ANN Attributes Attribute Value Epoch Count 51 Learning Rate Hidden Layer Count 6 Accuracy Goal 1E-05 Results Using the two for one reinforcement technique ultimately yielded positive results. Figure 1 shows a sample forecast of the NASDAQ over a period of five days from March 3rd, 2018 to April 2nd, Figure 1: Predicted NASDAQ vs. Actual 3/26/18-4/02/18

5 The forecasted and actual values shown in Figure 1 are tabulated in Table 2. Table 2: 3/26/18-4/02/18 Forecast Error Analysis 3/26/18 3/27/18 3/28/18 3/29/18 4/02/18 Actual Predicted % error A textual indicator program was also developed that indicates the weekly trend of the NASDAQ as well as daily price point fluctuations based on the forecasted data. Example outputs of this program are shown below. Weekly Trend: The NASDAQ is on an upward trend Day By Day: The NASDAQ will grow by :0.666%, grow by :0.879%, decline by :2.95%, grow by : 1.641% An additional simulation was carried out over a three year span, from April 15, 2015 to April 17, 2018 using the same approach, as if the values in the series were unknown. The results are shown in Figure 2. Figure 2: Predicted NASDAQ vs. Actual 4/15/15-4/17/18

6 As is shown in Figure 2, the ANN exhibited some anomalous behavior at the beginning of the series, which is to be expected given the randomness of the NASDAQ or of any such index. Such anomalies can be ignored in practice when buying and selling stocks based on the ANN predictions; it is unlikely that the NASDAQ would undergo as sharp a decline, i.e. by more than 6 %, as the ones shown in the 0th - 180th day range of Figure 2. The largest daily NASDAQ fluctuations in the entire history of the index range from 3 to 14%. Table 3 reports the mean squared error and coefficient of determination for the predicted and actual datasets plotted in Figure 2. The mean squared error (MSE) was calculated according to, where Yi are the actual values and Yi(hat) are the predicted values. The coefficient of determination, R 2, was calculated by, where SStot is the actual data sum of squares, SSreg is the predicted sum of squares, and SSres is the residual sum of squares which gives the error sum of squares. Table 3: 4/15/15-4/17/18 Forecast Error Analysis % Mean Squared Error R

7 As is reported in Table 3, the ANN performed well in a simulation of 3 years of prediction. Conclusions In summation, the findings provide the insight that is necessary in order to move forward with a systematic approach to investing in the NASDAQ composite that surpasses simple market intuition. By providing specific price points along with a close measure of the index trend with IP3, an investor is able to make decisive buying timelines for each week of trading. Judging by the accuracy of the results obtained for a sample one week prediction, the profits gained by the investor would not deviate by more than 4.1% of the total potential profits that could be earned if the investor was actually able to predict the closing value of the NASDAQ with zero error. Similarly, over a 3 year period, the error of the ANN appears to be minimal enough to ensure portfolio growth.

8 References 1. ^IXIC Historical Prices NASDAQ Composite Stock. Yahoo! Finance, Yahoo!, 1 May 2018, finance.yahoo.com/quote/%5eixic/history? period1= &period2= &interval=1d&filter=history&frequency=1d. 2. Kshirsagar,Gaurav, Chandel,Mohit, Kakade,Shantanu, Amaria,Rukshad Stock Market Prediction Using Artificial Neural Networks. International Journal of Advanced Research in Computer Engineering & Technology (IJARCET), Volume 5, Issue 5, May List of Largest Daily Changes in the Nasdaq Composite. Wikipedia, Wikimedia Foundation, 10 Apr. 2018, en.wikipedia.org/wiki/ List_of_largest_daily_changes_in_the_Nasdaq_Composite. 4. Moghaddam, Amin Hedayati, et al. Stock Market Index Prediction Using Artificial Neural Network. Journal of Economics, Finance and Administrative Science, vol. 21, no. 41, 2016, pp