Empirical evaluation of a dimension-reduction method for time-series prediction - Ghorbani, Mahsa, author; Chong, Edwin K. P., advisor; Pezeshki, Ali, committee member; Young, Peter, committee member; Bradley, Thomas, committee member (Colorado State University. Libraries, 2020)
Stock price prediction is one of the most challenging problems in finance. The multivariate conditional mean is a point estimator to minimize the mean square error of prediction giver past data. However, the calculation of the condition mean and covariance involves the numerical inverse of a typically ill-conditioned matrix, leading to numerical issues. To overcome this problem, we develop a method based on filtering the data using principle components. Principal component analysis (PCA) identifies a small number of principle components that explain most of the variation in a data set. This method is often used for dimensionality reduction and analysis of the data. Our method bears some similarities with subspace filtering methods. Projecting the noisy observation onto a principle subspace leads to significantly better numerical conditioning. Our method accounts for time-varying covariance information. We first introduce our method for predicting future price values over a short period of time using just historical price values. The literature provides strong evidence that stock price values can be predicted from past price data. Different economic variables have also been used in the literature to estimate stock-price values with high accuracy. To accommodate using historical data for such economic variables, we build on our method to include multiple predictors. We use multichannel cross-correlation coefficient as a measure for selecting the most correlated set of variables for each stock. Then we apply our filtering operation based on the local covariance of the data. Our method is easily implemented and can be configured to include an arbitrary number of predictors, subject to computational constraints. Time-series prediction can be posed as a matrix completion problem. Matrix completion is an important problem in many fields and has been receiving considerable attention in recent years. Different approaches and algorithms have been proposed to solve this problem. We investigate the effectiveness of an iterative rank minimizing matrix completion algorithm for predicting financial time series. As a key performance to compare different schemes, we use computational complexity, which focuses on the computational burden of these schemes. We compare the prediction results from the iterative matrix completion method to our method in terms of asymptotic and empirical computational complexity. Both methods show similar performance for forecasting future stock price values in terms of different performance metrics, but our proposed method has lower computational complexity.
Keywords: matrix completion; principal component analysis; stock price forecasting; multiple predictors; covariance information; principal subspace