Study On Multivariate Timeseries Based On Lasso Penalty

With the coming of big data era, the amount of data has increased dramatically in various fields. Data analysis and data mining are facing new opportunities and challenges.The application of traditional vector auto regression for multivariate time series is no limited. So the problem of how to expand the traditional model to the high-dimensional time series requires urgent settlement. Translating the high-dimensional into lower dimension by taking certain technology is a very effective and feasible way. In this paper,a novel method that adding different penalty functions on the basis of the traditional VAR model in order to reduce dimensions reduction is proposed.First, we introduced a new model called Lasso-VAR which is combining VAR model and Lasso penalty function. The method to solve is coordinate descent. Experimental results of air quality forecast in several groups with different dimensions proved that the model can be effectively applied in high-dimensional time series, and it can overcomes the limitations of traditional VAR model.Then, Ordered Lasso, adding the monotonically non-increasing constraints on Lasso,converts the vector equation scalar equation, and the specific process of the adjacent gradient method to solve the model is given. Apply Ordered Lasso model to the problem of order selection and prediction,we can demonstrate that Ordered Lasso can be obtained a more easily explainable model.Finally, a new class of regularized VAR models is introduced, called Hierarchical Vector Auto Regression(HVAR). The key convex modeling tool is a group lasso with hierarchically nested groups. We provide computationally efficient algorithms for solving HVAR problems. The experiments results in financial and EEG data proves that the model can not only describe relationships of multivariate time series more effectively, but also can obtained lower mean square error. So we can draw a conclusion that HVAR has a good applicability for high-dimensional time series.