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Accurate detection of arrhythmia signal types is of great significance for the early detection of heart disease and its subsequent treatment. The primary purpose of this study is to explore an electrocardiogram (ECG) classification system to improve its performance and achieve excellent computing performance, especially for large sample datasets. We classified ECG signals using the Hurst exponent, which is an ECG feature extracted by multifractal detrended moving average cross-correlation analysis (MF-XDMA). In addition, we used multifractal methods such as multifractal detrended fluctuation analysis (MF-DFA), multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal detrended moving average (MF-DMA) to extract the features of ECG signals, and we used a support vector machine (SVM) to classify the four types of feature data. The experimental results show that MF-XDMA-SVM has the best classification performance for atrial premature beat (APB) and bigeminy signals, which indicates that MF-XDMA-SVM is the most effective for the extraction of ECG signal sequence features among the four multifractal models.

In this paper, we develop the multifractal detrending weighted average algorithm of historical volatility (MF-DHV) for one-dimensional multifractal measure based on the classical multifractal detrended fluctuation analysis (MF-DFA). In the calculation process of getting a local trend for MF-DHV, historical volatility is taken to develop an moving average algorithm, which is different from the simple moving average function in multifractal detrended moving average (MF-DMA). We assess the performance of three methods such as MF-DFA, MF-DMA, and MF-DHV based on the p-model multiplicative cascading constructed time series. The computational results show that all the estimated generalized Hurst exponent $H(q)$, the scaling exponent $\tau (q)$, and the singularity spectrum $f(\alpha )$ of MF-DHV are in good agreement with the theoretical values. In addition, we also calculate the standard deviations of $H_{\mathrm{\text{err}}}$ and ${\tau }_{\mathrm{\text{err}}}$ for three methods, and the lowest errors in MF-DHV provides the most accurate estimates. To avoid the accidental selection of parameters, we change the total length of the generated multifractal simulation data and p-value, respectively. It is found that in all the cases, the MF-DHV outperforms the other two methods.

To investigate difference of price's dynamic characteristics between different periods in different competitive electricity market, we applied multi fractal detrended moving average analysis (MF-DMA) to analyze multifractal natures of prices on-peak and off-peak of three typical localized electricity markets, namely, Canadian Alberta, Ontario and middle Columbia markets. The results demonstrate that there are huge differences multifractal natures of the prices between different periods in different markets. It provides a new view for uncovering dynamic features of prices in different periods.