The prediction of peak power load is a critical factor directly impacting the stability of power supply, characterized significantly by its time series nature and intricate ties to the seasonal patterns in electricity usage. Despite its crucial importance, the current landscape of power peak load forecasting remains a multifaceted challenge in the field. This study aims to contribute to this domain by proposing a method that leverages a combination of three primary models - the GRU model, self-attention mechanism, and Transformer mechanism - to forecast peak power load. To contextualize this research within the ongoing discourse, it’s essential to consider the evolving methodologies and advancements in power peak load forecasting. By delving into additional references addressing the complexities and current state of the power peak load forecasting problem, this study aims to build upon the existing knowledge base and offer insights into contemporary challenges and strategies adopted within the field. Data preprocessing in this study involves comprehensive cleaning, standardization, and the design of relevant functions to ensure robustness in the predictive modeling process. Additionally, recognizing the necessity to capture temporal changes effectively, this research incorporates features such as “Weekly Moving Average” and “Monthly Moving Average” into the dataset. To evaluate the proposed methodologies comprehensively, this study conducts comparative analyses with established models such as LSTM, Self-attention network, Transformer, ARIMA, and SVR. The outcomes reveal that the models proposed in this study exhibit superior predictive performance compared to these established models, showcasing their effectiveness in accurately forecasting electricity consumption. The significance of this research lies in two primary contributions. Firstly, it introduces an innovative prediction method combining the GRU model, self-attention mechanism, and Transformer mechanism, aligning with the contemporary evolution of predictive modeling techniques in the field. Secondly, it introduces and emphasizes the utility of “Weekly Moving Average” and “Monthly Moving Average” methodologies, crucial in effectively capturing and interpreting seasonal variations within the dataset. By incorporating these features, this study enhances the model’s ability to account for seasonal influencing factors, thereby significantly improving the accuracy of peak power load forecasting. This contribution aligns with the ongoing efforts to refine forecasting methodologies and addresses the pertinent challenges within power peak load forecasting.

Missing data which inevitably occurs in observed time series may lead to an erroneous result based on the correlation integral analysis. Effects of data, missing at regular and irregular times, on the analyzed result are estimated. A model estimation is obtained for the Lorenz time series. The effects of the missing data in economic and astronomical time series are estimated using the correlation integral analysis. A convenient method of choosing a time lag is proposed to minimize the effect of regularly missing data.

We proposed a new model for non-stationary time series analysis based on an inhomogeneous AR (autoregressive) equation. Time series data is regarded as white noise plus output of an AR system excited by non-stationary input sequence represented in terms of a set of basis. A method of model parameter estimation was presented when the set of basis and the AR order are given. In order to extend the method, we present a method of parameter estimation when the AR order is unknown: we set two new criteria 1) minimize the root mean square error of the output sequence, and 2) minimize scattering of estimated frequencies. Then, we derive a procedure for the estimation of the AR order and the other unknown parameters.

It is now known that a seemingly random irregular time series can be deterministic chaos (hereafter, chaos). However, there can be various kind of noise superimposed into signals from real systems. Other factors affecting a signal include sampling intervals and finite length of observation. Perhaps, there may be cases in which a chaotic time series is considered as noise. J. Theiler proposed a method of surrogating data to address these problems. The proposed method is one of a number of approaches for testing a statistical hypothesis. The method can identify the deterministic characteristics of a time series. In this approach, a surrogate data is formed to have stochastic characteristics with the statistic value associated with the original data. When the characteristics of the original data differs from that of a surrogate data, the null hypothesis is no longer valid. In other words, the original data is deterministic. In comparing the characteristics of an original time series data and that of a surrogate data, the maximum Lyapunov exponents, correlation dimensions and prediction accuracy are utilized. These techniques, however, can not calculate the structure in local subspaces on the attractor and the flow of trajectories. In deal with these issues, we propose the trajectory parallel measure (TPM) method to determine whether the null hypothesis should be rejected. In this paper, we apply the TPM method and the method of surrogate data to test a chaotic time series and a random time series. We also examine whether a practical time series has a deterministic property or not. The results demonstrate that the TPM method is useful for judging whether the original and the surrogate data sets are different. For illustration, the TPM method is applied to a practical time series, tap water demand data.

We proposed a new model for non-stationary time series analysis based on the IAR (inhomogeneous autoregressive) model, and a method for model parameter estimation when the set of basis is given. In this paper, we further propose a method for parameter estimation including that of basis set: we set a new condition that power of the input sequence is concentrated in low-frequency domain, and developed an iterative estimation method. We firstly select an initial set of basis, from which new sets are created in order to minimize the difference between the model and data. Among new sets of basis, we select a good one that gives minimum standard deviation of estimated frequencies.

A method is presented for detecting impulsive noises in chaotic time series, based on a new nonlinear prediction algorithm. A multi-dimensional trajectory is reconstructed from a time series using delay coordinates. The future value of a point on the trajectory is predicted using a local approximation technique revised by adding the Biweight estimation method and then the prediction error is calculated. Impulsive noises are detected by examining the prediction errors for all points on the trajectory. The proposed method is applied to the time series of the pupil area and the refractive power of the lens in the human eye. The Lyapunov exponent analysis for thses time series is conducted. As a result, it is shown that the proposed method is effective in detecting impulsive noises caused by blinking in these time series.

We present a framework for the unsupervised segmentation of time series. It applies to non-stationary signals originating from different dynamical systems which alternate in time, a phenomenon which appears in many natural systems. In our approach, predictors compete for data points of a given time series. We combine competition and evolutionary inertia to a learning rule. Under this learning rule the system evolves such that the predictors, which finally survive, unambiguously identify the underlying processes. The segmentation achieved by this method is very precise and transients are included, a fact, which makes our approach promising for future applications.

In this paper, we propose algorithm of deterministic nonlinear prediction, or a modified version of the method of analogues which was originally proposed by E.N. Lorenz (J. Atom. Sci., 26, 636-646, 1969), and apply it to the artificial time series data produced from nonlinear dynamical systems and further corrupted by superimposed observational noise. The prediction performance of the present method are investigated by calculating correlation coefficients, root mean square errors and signature errors and compared with the prediction algorithm of local linear approximation method. As a result, it is shown that the prediction performance of the proposed method are better than those of the local linear approximation especially in case that the amount of noise is large.

In this paper, a new time series analysis method is proposed. The proposed method uses the exponential (EXP) model. The residual signal is assumed to be identically and independently distributed (IID). To achieve accurate and efficient estimates, the parameter of the system model is calculated by maximizing the logarithm of the likelihood of the residual signal which is assumed to be IID t-distribution. The EXP model theoretically assures the stability of the system. This model is appropriate for analyzing signals which have not only poles, but also poles and zeroes. The asymptotic efficiency of the EXP model is addressed. The optimal solution is calculated by the Newton-Raphson iteration method. Simulation results show that only a small number of iterations are necessary to reach stationary points which are always local minimum points. When the method is used to estimate the spectrum of synthetic signals, by using small α we can achieve a more accurate and efficient estimate than that with large α. To reduce the calculation burden an alternative algorithm is also proposed. In this algorithm, the estimated parameter is updated in every sampling instant using an imperfect, short-term, gradient method which is similar to the LMS algorithm.