基于深度学习和小波分析的LSTM-Wavelet模型股价预测

针对股价数据具有高噪声、非线性和非平稳性等特征,使得股价精确预测非常困难的问题,提出小波-长短记忆网络(LSTM-Wavelet)模型应用于股价预测。首先,利用小波(Wavelet)分解降低金融时间序列的不稳定性,并分析小波系数的细节特征;接着,发挥长短记忆网络(LSTM)模型的优势,深层挖掘小波系数中的长期依赖关系,对分解后的各层小波系数分别建模预测;最后进行预测小波系数的数据重构。使用中石油近两年的股价数据进行实证分析,以每个交易日的开盘价、最高价、最低价、交易量为特征输入,预测当日中石油的收盘价。结果表明:相较于标准LSTM模型和小波-ARIMA(ARIMA-Wavelet)模型,提出的LSTM-Wavelet模型有更好的预测效果;通过小波分析将复杂股票数据,分解为长短记忆网络(LSTM)容易识别的小波系数,根据各层小波系数不同的数据特征进行分层预测,提高了预测精度。

Research on runoff variations based on wavelet analysis and wavelet neural network model： A case study of the Heihe River drainage basin （1944-2005）

The Heihe River drainage basin is one of the endangered ecological regions of China. The shortage of water resources is the bottleneck, which constrains the sustainable development of the region. Many scholars in China have done researches concerning this problem. Based on previous researches, this paper analyzed characteristics, tendencies, and causes of annual runoff variations in the Yingluo Gorge （1944-2005） and the Zhengyi Gorge （1954-2005）, which are the boundaries of the upper reaches, the middle reaches, and the lower reaches of the Heihe River drainage basin, by wavelet analysis, wavelet neural network model, and GIS spatial analysis. The results show that： （1） annual runoff variations of the Yingluo Gorge have principal periods of 7 years and 25 years, and its increasing rate is 1.04 m^3/s.10y; （2） annual runoff variations of the Zhengyi Gorge have principal periods of 6 years and 27 years, and its decreasing rate is 2.25 m^3/s.10y; （3） prediction results show that： during 2006-2015, annual runoff variations of the Yingluo and Zhengyi gorges have ascending tendencies, and the increasing rates are respectively 2.04 m^3/s.10y and 1.61 m^3/s.10y; （4） the increase of annual runoff in the Yingluo Gorge has causal relationship with increased temperature and precipitation in the upper reaches, and the decrease of annual runoff in the Zhengyi Gorge in the past decades was mainly caused by the increased human consumption of water resources in the middle researches. The study results will provide scientific basis for making rational use and allocation schemes of water resources in the Heihe River drainage basin.

WAVELET ESTIMATION FOR JUMPS IN A HETEROSCEDASTIC REGRESSION MODEL

Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.

JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS

Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.

Network traffic prediction by a wavelet-based combined model

Network traffic prediction models can be grouped into two types, single models and combined ones. Combined models integrate several single models and thus can improve prediction accuracy. Based on wavelet transform, grey theory, and chaos theory, this paper proposes a novel combined model, wavelet-grey-chaos （WGC）, for network traffic prediction. In the WGC model, we develop a time series decomposition method without the boundary problem by modifying the standard à trous algorithm, decompose the network traffic into two parts, the residual part and the burst part to alleviate the accumulated error problem, and employ the grey model GM（1,1） and chaos model to predict the residual part and the burst part respectively. Simulation results on real network traffic show that the WGC model does improve prediction accuracy.

Analytical Polarizable Continuum Model for Wavelets on NURBS Patches

This article concerns the application of wavelet techniques on molecular surfaces constituted of four-sided patches. The Polarizable Continuum Model, which is governed by the Poisson-Boltzmann equation, is treated by means of boundary integral equations. The media inside and outside the molecular surface consist respectively of the solute and the solvent. For a given electrically charged molecule, the principal unknown is the electrostatic solvation energy when the permittivity is specified. The wavelet basis functions are constructed on the unit square which are subsequently mapped onto the patches that are assumed to be isotropically shaped and to admit similar surface areas. The initial transmission problem is recast as an integral equation in term of both the single and the double layers. Domain decomposition preconditioner serves as acceleration of the linear solver of the single layer which is badly conditioned.

Application of Wavelet Random Coupling Model in Monthly Rainfall Prediction

A Trous algorithm of wavelet transform was used to decompose wavelet signal, and the cross-correlation analysis was used to analyze the sequence of each wavelet transform, and then the mathematical model correspond with wavelet transform sequence was established, finally wavelet random coupling model was obtained by wavelet reconstruction algorithm. Then, according to the rainfall data in crop growth period of Farm Chahayang from 1956 to 2008, the wavelet random coupling model was established to fit the model prediction test. The results showed that the prediction and fitting accuracy of the model was high, the model could reflect the rainfall variation regulation in the region, and it was a practical prediction model. It was very important for us to determine reasonably irrigation schedule and to use efficiency coefficient of precipitation resource.

Wavelet Neural Network Based on NARMA-L2 Model for Prediction of Thermal Characteristics in a Feed System

Research of thermal characteristics has been a key issue in the development of high-speed feed system. Most of the work carried out thus far is based on the principle of directly mapping the thermal error against the temperature of critical machine elements irrespective of the operating conditions. But recent researches show that different sets of operating parameters generated significantly different error values even though the temperature of the machine elements generated was similar. As such, it is important to develop a generic thermal error model which is capable of evaluating the positioning error induced by different operating parameters. This paper ultimately aims at the development of a comprehensive prediction model that can predict the thermal characteristics under different operating conditions （feeding speed, load and preload of ballscrew） in a feed system. A novel wavelet neural network based on feedback linearization autoregressive moving averaging （NARMA-L2） model is introduced to predict the temperature rise of sensitive points and thermal positioning errors considering the different operating conditions as the model inputs. Particle swarm optimization（PSO） algorithm is brought in as the training method. According to ISO230-2 Positioning Accuracy Measurement and ISO230-3 Thermal Effect Evaluation standards, experiments under different operating conditions were carried out on a self-made quasi high-speed feed system experimental bench HUST-FS-001 by using Pt100 as temperature sensor, and the positioning errors were measured by Heidenhain linear grating scale. The experiment results show that the recommended method can be used to predict temperature rise of sensitive points and thermal positioning errors with good accuracy. The work described in this paper lays a solid foundation of thermal error prediction and compensation in a feed system based on varying operating conditions and machine tool characteristics.

Wavelet Density Estimation and Statistical Evidences Role for a GARCH Model in the Weighted Distribution

We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.

WAVELET MODELING AND FORECASTING AND ITS APPLICATION IN THE CHINESE MONETARY MULTIPLIER

In this paper, a time_varying AR model is constructed by using the vector_space algorithm of compactly_supported biorthonormal wavelet transform. It is developed for forecasting narrow monetary multipliers in China .

VARIABLE SELECTION BY PSEUDO WAVELETS IN HETEROSCEDASTIC REGRESSION MODELS INVOLVING TIME SERIES

A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.

MANDARIN TONE RECOGNITION BASED ON WAVELET TRANSFORM AND HIDDEN MARKOV MODELING

This paper presents a method of tone recognition for Mandarin speech by using combination of wavelet transform and hidden Markov modeling techniques. A pitch detector based on singularity detection and multi-resolution analysis of wavelet transform is employed for estimation of pitch periods, and hidden Markov modeling with partition Gaussian mixtures probability density function is used for the tone recognition. The algorithm can provide recognition accuracy of 97.22% and 94.47% for speaker-dependent and speaker-independent tone recognition, respectively.

Analysis of the Meteorological Variables for Puebla City 2011-2012 Applying the Modeling Ion-Wavelets in a Hypothetical Manner

This work presents the results of the analysis of meteorological variables applying the modeling Ion-Wavelets in a hypothetical manner. In this case the Morlet wavelet transform is used, which is the result of a huge number of researches made in the80’s and applied to various physical phenomena derived from natural chaotic processes;the data were processed using the phenomenon “El Nino” and CO2 (Carbon dioxide) due to the fact that these are the meteorological phenomena which best adapt to our object of study correlating with distribution of Gauss and Morlet during the study period in the Puebla Valley.

Hybrid Model Based on Wavelet Decomposition for Electricity Consumption Prediction

The effective supply of electricity is the basis of ensuring economic development and people's normal life. It is difficult to store electricity, as leading to the production and consumption must be completed simultaneously. Therefore, it is of great significance to accurately predict the demand for electricity consumption for the production planning of electricity and the normal operation of the society. In this paper, a hybrid model is constructed to predict the electricity consumption in China. The structural breaks test of monthly electricity consumption in China from January 2010 to December 2016 is carried out by using the structural breaks unit root test. Based on the existence of structura breaks, the electricity consumption data are decomposed into low-frequency and high-frequency components by wavelet model, and the separated low frequency signal and high frequency signal are predicted by autoregressive integrated moving average(ARIMA) and nonlinear autoregressive neural network(NAR), respectively. Therefore the wavelet-ARIMA-NAR hybrid model is constructed. In order to compare the effect of the hybrid model, the structural time series(STS) model is applied to predicting the electricity consumption. The results of prediction error test show that the hybrid model is more accurate for electricity consumption prediction.

Use of the Wavelet Transform for Digital Terrain Model Edge Detection (Special Issue—Wavelet Analysis)

The purpose of this work is to analyze the feasibility of using the wavelet transform in the edge detection of digital terrain models (DTM) obtained by Laser Scanner. The Haar wavelet transform and the edge detection method called Wavelet Transform Modulus Maxima (WTMM), both implemented in Matlab language, were used. In order to validate and verify the efficiency of WTMM, the edge detection of the same DTM was performed by the Roberts, Sobel-Feldman and Canny methods, chosen due to the wide use in the scientific community in the area of Image Processing and Remote Sensing. The comparison of the results showed superior performance of WTMM in terms of processing time.

Image denoising using statistical model based on quaternion wavelet domain

Image denoising is the basic problem of image processing. Quaternion wavelet transform is a new kind of multiresolution analysis tools. Image via quaternion wavelet transform, wavelet coefficients both in intrascale and in interscale have certain correla- tions. First, according to the correlation of quaternion wavelet coefficients in interscale, non-Ganssian distribution model is used to model its correlations, and the coefficients are divided into important and unimportance coefficients. Then we use the non-Gaussian distribution model to model the important coefficients and its adjacent coefficients, and utilize the MAP method estimate original image wavelet coefficients from noisy coefficients, so as to achieve the purpose of denoising. Experimental results show that our al- gorithm outperforms the other classical algorithms in peak signal-to-noise ratio and visual quality.

Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge

The wind-rain induced vibration phenomena in the Dongting Lake Bridge (DLB) can be observed every year, and the field measurements of wind speed data of the bridge are usually nonstationary. Nonstationary wind speed can be decomposed into a deterministic time-varying mean wind speed and a zero-mean stationary fluctuating wind speed component. By using wavelet transform (WT), the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed in this paper. The wind characteristics of turbulence intensity, integral scale and probability distribution of the bridge are calculated from the typical wind samples recorded by the two anemometers installed on the DLB using the proposed nonstationary wind speed model based on WT. The calculated results are compared with those calculated by the empirical mode decomposition (EMD) and traditional approaches. The compared results indicate that the wavelet-based nonstationary wind speed model is more reasonable and appropriate than the EMD-based nonstationary and traditional stationary models for characterizing wind speed in analysis of wind-rain-induced vibration of cables.

Using of Color Model and Contrast Variation in Wavelet Ideology for Study <i>Megaloblastic Anemia Cells</i>

Processing and analyzing of medical images is one of the priority research areas. At the same time, the processing of images of cells occupies a special place. This is due to the fact that such studies allow for a comprehensive diagnosis of the state of human health, identify and prevent the development of diseases in the early stages. We investigate the effectiveness of using wavelet analysis in color models, taking into account the preliminary change in the contrast of the input image. We consider the HSV color model and the image contrast modification procedure, which is based on the histogram change in the specified range with gamma correction. As a criterion for choosing parameters for changing the contrast of the image, we consider the entropy of the image. We also showed the advisability of using the value of the entropy index for the subsequent improvement of image analysis based on the wavelet ideology. We examined the general sequence of action for the analysis of image of megaloblastic anemia cells. This sequence is based on the choice of parameters for changing the contrast of the image and application of wavelet ideology.

海域重力异常模型的多尺度分析

不同于传统的重力异常模型精度分析方法,本文以马里亚纳海沟区域(140°E—150°E,10°N—20°N)为例,利用DOG球面小波提取了DTU10、DTU17和SIO V32.1模型在不同波段内的重力异常信号,对模型间的差异进行了深入分析,并对基于径向基函数的不同深度、不同分辨率的多尺度分析进行了尝试。利用DOG球面小波对各模型多尺度分析的结果表明,随着尺度变小,模型间的差异在变大;DTU10、DTU17模型间的差异主要集中在10.9~43.6 km的波段内,分布在海岸、海沟、海底山附近,体现了Cryosat-2、Jason-1/GM观测数据和FES2014海潮模型的贡献;受模型构建方法不同、观测数据增多和波形重跟踪的影响,DTU17、SIO V32.1模型的差异大于DTU10、DTU17之间的差异。对传统径向基函数进行了改进,实现了多深度、多空间分辨率情况下径向基函数多尺度分析,结果略优于单一深度、单一空间分辨率径向基函数构建结果,有望应用于多源数据的重力场模型构建。