Evaluating the Performance of Autoregressive Model for Solar Radiation Forecasting

The solar radiation data taken from 14 meteorological stations in Nigeria has been analyzed. The periodic component of the data which covered a period of 13 (mostly 1977-1989) years was removed via Fourier analysis while the residual series was subjected to autoregressive analysis. It was evident from the t-test and autocorrelation plots of the modified (i.e. without the periodic component) series that there exist significant persistence at nine stations including Sokoto, Nguru, Kano, Maiduguri, Bauchi, Yola, Minna, Ibadan, and Benin. The autocorrelation at Jos, Bida, Ikeja, Enugu and Port Harcourt were however found to be insignificant. As the sample partial autocorrelation function cuts off after lag 1, a non-seasonal autoregressive model of order 1, AR (1), was identified for stations with autocorrelation. The Q-statistic of error series suggested that the models were adequate as identified. Moreover, the exploratory plots of the model residual series showed agreement with the quantitative statistics and thus enforces the inference that the models were adequate for monthly mean daily global solar radiation forecasts at some of the study stations. It is interesting to note that all the stations within the sub-sahelian region showed significant persistence whereas all the stations in the coastal region except Benin were found with insignificant autocorrelation. Expectedly, the performance evaluation of the model gave impressive result for the stations within the sub-sahelian region but a relatively weak result for the coastal region. The result for the midland region was mixed whereas it was difficult to conclude on the Guinea savannah region with result from only one station.

Development of a Hybrid Method to Predict the Slope Surface Deformation Utilizing the Time Series and GA-Elman Models

A reliable prediction of the surface deformation of slopes is vital to better assess the fatalities and economic losses caused by landslides. Many prediction methods have been proposed to estimate the surface deformation of landslides with nonlinear characteristics. However, these methods have low accuracy and poor applicability. In this paper, a new hybrid method for surface deformation prediction was proposed, which was deduced from the Wavelet Analysis, Genetic Algorithm (GA), and Elman Algorithm. In this method, the slope surface deformation was decomposed into a trend component and a periodic component using the time series model, which were trained and predicted utilizing the GA-Elman model. The predicted slope surface deformation was the combination of the trend component and the periodic component. Then, the predicted results of slope surface deformation through GA-Elman were compared with the predicted results through Support Vector Machines (SVM), Extreme Learning Machine (ELM), Back Propagation (BP), and Genetic Algorithm-Back Propagation (GA-BP) models. The comparison was made with reference to the data retrieved from the on-site slopes and the laboratory tests. The results revealed that the proposed method highlighted reliability and could be used with higher accuracy to forecast the slope surface deformation in the process of landslides.

Periodic Components of the Fatou Set of Three Transcendental Entire Functions and Their Compositions

We prove that there exist three different transcendental entire functions that can have infinite number of domains which lie in the different periodic component of each of these functions and their compositions.

Isolation of a periodic component by singular wavelet decomposition

In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results.

Dynamics on the Pre-periodic Components of the Fatou Set of Three Transcendental Entire Functions and Their Compositions

We prove that there exist three entire transcendental functions that can have an infinite number of domains which lie in the pre-periodic component of the Fatou set each of these functions and their compositions.

Evaluation of Short-Term Freeway Speed Prediction Based on Periodic Analysis Using Statistical Models and Machine Learning Models

Accurate prediction of traffic information (i.e., traffic flow, travel time, traffic speed, etc.) is a key component of Intelligent Transportation System (ITS). Traffic speed is an important indicator to evaluate traffic efficiency. Up to date, although a few studies have considered the periodic feature in traffic prediction, very few studies comprehensively evaluate the impact of periodic component on statistical and machine learning prediction models. This paper selects several representative statistical models and machine learning models to analyze the influence of periodic component on short-term speed prediction under different scenarios: (1) multi-horizon ahead prediction (5, 15, 30, 60 minutes ahead predictions), (2) with and without periodic component, (3) two data aggregation levels (5-minute and 15-minute), (4) peak hours and off-peak hours. Specifically, three statistical models (i.e., space time (ST) model, vector autoregressive (VAR) model, autoregressive integrated moving average (ARIMA) model) and three machine learning approaches (i.e., support vector machines (SVM) model, multi-layer perceptron (MLP) model, recurrent neural network (RNN) model) are developed and examined. Furthermore, the periodic features of the speed data are considered via a hybrid prediction method, which assumes that the data consist of two components: a periodic component and a residual component. The periodic component is described by a trigonometric regression function, and the residual component is modeled by the statistical models or the machine learning approaches. The important conclusions can be summarized as follows: (1) the multi-step ahead prediction accuracy improves when considering the periodic component of speed data for both three statistical models and three machine learning models, especially in the peak hours; (2) considering the impact of periodic component for all models, the prediction performance improvement gradually becomes larger as the time step increases; (3) under the same prediction horizon, the prediction performance of all models for 15-minute speed data is generally better than that for 5-minute speed data. Overall, the findings in this paper suggest that the proposed hybrid prediction approach is effective for both statistical and machine learning models in short-term speed prediction.