Stock market forecasting using LASSO Linear Regression model

Abstract The forecasting of stock price movement in general is considered to be a thought-provoking and essential task for financial time series' exploration. In this paper, a Least Absolute Shrinkage and Selection Operator (LASSO) method based on a linear regression model is proposed as a novel method to predict financial market behavior. LASSO method is able to produce sparse solutions and performs very well when the numbers of features are less as compared to the number of observations. Experiments were performed with Goldman Sachs Group Inc. stock to determine the efficiency of the model.

Why is prediction of stock market crucial ? Stock market helps in flourishing commerce and industry that ultimately has an effect on the country's economy. Moreover, it provides a generic platform for the sellers and buyers of stocks listed on the stock market. The buyers and sellers are basically retail and institutional investors. If the stock’s future price can be predicted, it can resist the significant losses and can certainly increase the profits

Related Works J. L. Ticknor proposed a Bayesian Regularized Artificial Neural Network as the prediction model. Daily market prices and financial technical indicators were used as inputs. This technique reduces the potential for over-fitting and over-training and hence improves the quality of prediction. S. Deng, Takashi M., Kei S., Tatsuro S., and Akito Sakurai proposed a prediction model which extracts features from time series data and social networks. Using features such as frequency of news and comments, a multiple kernel learning regression framework was used as the model. Paul D. Yoo, Maria H. Kim, and Tony Jan made a survey of various machine learning techniques for the task of prediction. They concluded that incorporating event information with prediction model plays important role for accurate prediction.

Related Works M. P. Naeini, et al. proposed neural networks for prediction. They used two kinds of neural networks. The first being a feed-forward multi-layer perceptron(MLP) and the other being an Elman recurrent network to predict the stock price. They inferred that the latter can predict the direction of the changes of the stock value better than MLP. S. Aseervatham, et al. proposed a new model selection method which tried to approach the Ridge regression method’s results. This method first computes the Ridge solution and then performs feature selection. B. B. Nair, et al. proposed an automated decision tree-adaptive neuro-fuzzy hybrid stock market prediction system. It used technical analysis for feature extraction and decision tree for feature selection.

Proposed model – LASSO model Least Absolute Shrinkage and Selection Operator (LASSO) is based on linear regression. It is able to produce sparse solutions and performs very well when the number of features are less as compared to the number of observations. For a general linear regression model, the cost function 𝐽 w = 1 𝑁 𝑖=0 𝑁 ℎ x 𝑖 − 𝑦 𝑖 2 = 1 𝑁 Xw−y 2 For LASSO we add a l1-norm to the cost function 𝐽 w = 1 𝑁 𝑖=0 𝑁 ℎ x 𝑖 − 𝑦 𝑖 2 +𝜆 𝑗=1 𝑑 𝑤 𝑗 2 = 1 𝑁 Xw−y 2 + 𝜆 𝑗=1 𝑑 𝑤 𝑗 2

Data Preparation Research data utilized for prediction was gathered for Goldman Sachs Group, Inc. The total number of instances composed of 3686 trading days. The features taken into consideration are, Date Opening Price High Price Low Price Close Price Trading Volume The target variable is “Adjusted Close Price”.

Data Preparation Two kinds of analysis were performed on the data set: A comparison study for analyzing the model which we have proposed, with the Ridge regression model. The Ridge model incorporates regularization with the original least squares approach. For this, all the available instances were utilized. Analysis of our algorithm with Bayesian Regularized Artificial Neural Networks as proposed by J.N. Ticknor in [6]. Here, identical trading days (as taken in [6]) were taken as the instances.

Evaluation metrics The performance of LASSO and Ridge linear regression method was measured by computing RMSE and MAPE Root mean squared error(RMSE) RMSE = 𝑖=1 𝑛 ( 𝑦 𝑖 − 𝑝 𝑖 ) 2 𝑛 Mean Absolute Percentage Error(MAPE) MAPE = 𝑖=1 𝑛 | 𝑦 𝑖 − 𝑝 𝑖 | 𝑦 𝑖 𝑛 ×100%

Results

Evaluation on full data set between Ridge and LASSO Results Method Training RMSE Test RMSE Training MAPE Test MAPE Ridge 1.7648 3.2272 1.3028 1.8065 LASSO 1.1403 2.5401 0.9304 1.4726 Evaluation on full data set between Ridge and LASSO

Results LASSO Ridge

Bayesian Regularized ANN Results Method Training MAPE (%) Testing MAPE (%) Bayesian Regularized ANN 1.5235 1.3291 LASSO 0.1806 0.6869 Comparison with J.L. Ticknor’s method

Conclusion The results indicate that the proposed model outperforms Ridge linear regression model and Bayesian Regularized ANN model. The technique proposed here is a different approach which can provide traders a dependable technique for estimating future prices.

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