Modeling and Predicting Time Series with Non-stationarity and Volatility

Abstract

The difficulty of time series prediction lies in how to handle non-stationarity and volatility. When dealing with non-stationarity, existing deep learning models adopt a method of stabilizing the input sequences before training, which has problems of weak ability to eliminate non-stationarity or loss of information. When dealing with volatility, LSTM models with a single-head attention mechanism are usually used, which have weak ability to capture global dependencies and affect prediction accuracy. To address these issues, in terms of dealing with non-stationarity, a Prophet-CEEMDAN secondary decomposition method that follows the principle of “extraction-decomposition” is proposed. By decomposing the original sequence into a set of components, this method ensures the integrity of trend and periodic characteristics while increasing the proportion of stationary components in the component set, providing more stable data for the prediction model. In terms of volatility, a long short-term memory model with multi-head self-attention mechanism (LSTM-MH-SA) is applied. The LSTM-MH-SA model stacks attention heads in parallel to capture the volatility characteristics of different time periods in the sequence and connect them, improving the ability to capture global volatility information. Combining Prophet CEEMDAN and LSTM-MH-SA, a PCLMS (Prophet-CEEMDAN decomposition and LSTM with multi-head self-attention) model that can simultaneously handle non-stationarity and high volatility in time series is proposed. Experiments on multiple stock datasets and synthetic datasets show that compared with the benchmark model, CNN-LSTM, and Informer models, the PCLMS model has the best average performance in various evaluation indicators and performs best on datasets with high volatility.

Keywords

• time series prediction; non-stationarity; high volatility; long short-term memory neural network; multi-head self-attention