Online Sequential Model for Multivariate Time Series Prediction With Adaptive Forgetting Factor

Abstract

In the process of online prediction of multivariable non-stationary time series by kernel extreme learning machine (KELM), the dynamic characteristics of the system which are difficult to determine have always posed a big problem. We propose an online sequential prediction model with an adaptive forgetting factor (AFF) for multivariable time series to solve this problem. The multivariable time series instead of variable itself is reconstructed firstly. AFF is introduced into the objective function and can be adjusted iteratively and adaptively with the system changes. As a result, higher weight can be allocated for the fresh and more important samples while the old failure samples can be quickly forgotten. The model sparsification uses a fast leave-one-out cross-validation (FLOO-CV) method to set a prediction error threshold so that samples can be selected conditionally to form a dictionary. Besides, the dictionary parameters, including AFF and kernel parameters, are recursively updated simultaneously without increasing calculation complexity. The experimental results show that, compared with four fashionable KLEM methods, the proposed AFF-OSKELM has a better dynamic tracking ability and adaptability. Moreover, compared with single variable prediction, the spatial reconstructed multivariable has higher prediction accuracy and stability. INDEX TERMS Kernel extreme learning machine, adaptive forgetting factor, fast leave-one-out crossvalidation, online prediction, multivariable time series.

Dynamic Radio Map Using Statistical Hypothesis Testing

“…The second comparative method for the radio map updating is the forgetting factor [47], [48]. The database server calculates a new average value for the received signal power in each mesh using the following equation: (25) where¯f orget, , + [dBm] is the updated average received signal power value at time + of the th mesh and forget, , + −1 [dBm] is the updated average received signal power value at time + − 1, and is the forgetting factor.…”

Evolving multitask models for machine learning

“…9.2.2 PM2.5 time series of Beijing PM2.5 refers to the particles in the atmosphere with an aerodynamic equivalent diameter of less than 2.5 mm (Dai et al, 2020). Their presence in the air is directly related to pollution.…”

“…The concentration of PM2.5 was found to be inversely proportional to the change of wind speed. This experiment, extended from (Dai et al, 2020), aims to forecast PM2.5 values according to Beijing's historic PM2.5 time series and wind speed.…”

“…The number of 960 samples of PM2.5 (µg/m 3 ) and wind speed (m/s) was used, representing 40 days in Beijing from November 22 to December 31, 2014. The first 720 data points were used for training and the last 240 for testing, as prescribed by Dai et al (2020). The time delay was set to τ 1 = τ 2 = 1 h and the embedding dimension as m 1 = m 2 = 5.…”

“…A kernel Recursive Least Squares (KRLS) algorithm designed to multivariate chaotic time series is proposed by Han et al (2018), by combining approximate linear dependency, dynamic adjustment, coherence criterion and quantization. Founded on the kernel extreme learning machine, Dai et al (2020) proposed an improved version with adaptive forgetting factor introduced into the objective function, which guides the model development. The forgetting factor can be adjusted iteratively and adaptively according to data changes.…”