The Research Of Financial Time Series Adaptive Decomposition Prediction Based On Singular Spectrum Analysis

With the development of economy and financial industry, financial time series is gettingmore and more important and its analysis and prediction is very necessary and significant. Asa kind of special, more complex time-series data, financial time series is usually stochastic,nonlinear, noisy, etc. For the complexity of financial time series, people have proposed avariety of linear and nonlinear modeling methods to forecast and obtained better results.However, there are some shortcomings such as poor interpretability, parameter settings,depending on the model and so on. Singular Spectrum Analysis (SSA) is regarded as animportant method of component analysis of time series and has full freedom over selection ofcomponents, good explanation for components, no argument, model-independentcharacteristic, etc. which can decompose time-series data into many explicable components.Therefore, the singular spectrum analysis techniques are often used for pretreatment oftraditional prediction models, mainly for noise reduction for the time-series data. Nevertheless,non-noise components are subjectively determined by people in the noise reduction process,which makes de-noising time series loss too much energy or over-fitting, resulting in beingnot conducive to prediction. Here, the prediction of the time series which is de-noised by SSAis called direct prediction. Due to noise reduction process of direct prediction involves incertain subjective factors, the predicting results are not satisfactory. For this reason, weproposed a decomposition prediction based on singular spectrum analysis. The approach isthat we respectively predict high-frequency and low frequency component that is obtained bySSA with autoregressive (AR) and autoregressive integrated moving average (ARIMA) model,and the overall prediction can be achieved by composing these two predictors. Meanwhile, weintroduce the least mean square (LMS) algorithm in order to improve adaptive ability of themodel and achieve real-time tracking of financial time series. Experimental results show that,compared with LMS direct prediction, decomposition prediction in regardless of theprediction accuracy or the local depiction of sequence has a distinct advantage.On the other hand, in order to better capture local mutations of the sequence, reduceprediction delays and improve the prediction accuracy, allow for the actual prediction ofhigh-frequency components at the same time, the revised error-adjusted least mean square(EaLMS) algorithm is introduced. Simulation results indicate that, compared with LMS directprediction, the modified decomposition method has more obvious advantages.