White Noise Test Research Articles

White noise testing for functional time series

We review white noise tests in the context of functional time series, and compare many of them using a custom developed R package wwntests. The tests are categorized based on whether they are conducted in the time domain or spectral domain, and whether they are valid for i.i.d. or general uncorrelated noise. We also review and extend several residual-based goodness-of-fit tests of popular models used in functional data analysis. Through numerous simulation experiments and a data application, we demonstrate the use of these tests, and are able to provide practical guidance on their implementation, benefits, and drawbacks.

Functional spherical autocorrelation: A robust estimate of the autocorrelation of a functional time series

We propose a new autocorrelation measure for functional time series that we term “spherical autocorrelation”. It is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere. This new measure enjoys several complimentary advantages compared to existing autocorrelation measures for functional data, since it both 1) describes a notion of “sign” or “direction” of serial dependence in the series, and 2) is more robust to outliers. The asymptotic properties of estimators of the spherical autocorrelation are established, and are used to construct confidence intervals and portmanteau white noise tests. These confidence intervals and tests are shown to be effective in simulation experiments, and demonstrated in applications to model selection for daily electricity price curves, and measuring the volatility in densely observed asset price data.

A Dynamic Learning Interest Model for a Personalized Learning Requirement Analysis of College Students

The randomness in college students’ participation of online learning causes common problems such as improper learning resource allocation or unbalanced supply and demand to online education platforms, thus scientifically predicting college students’ learning requirements, triggering their dynamic learning interest, and effectively improving their learning effect are important prerequisites for ensuring these platforms to develop stably, efficiently, and sustainably. Existing prediction models generally ignored the progressing process of learning and failed to comprehensively model or analyze from multiple dimensions such as resource utilization, learning behavior, learning pattern, teaching mode, and teaching management, etc. To fill in this research gap, this paper proposed a Dynamic Learning Interest (DLI) model for analyzing the personalized learning requirements of college students. Based on the college students’ online learning cycles and the learning cycle division results, a time series DLI model was established for studying the prediction of college students’ personalized learning requirements, and short-term prediction and comparative experiment were carried out accordingly. Then, the proposed model was subject to stability test and white noise test to determine the model structure and estimate it parameters. At last, significance test was performed on the proposed model and its parameters, and the results verified the effectiveness of the model.

Research on Short-Time Wind Speed Prediction in Mountainous Areas Based on Improved ARIMA Model

In rugged mountain areas, the lateral aerodynamic force and aerodynamic lift caused by strong winds are the main reasons for the lateral overturning of trains and the destruction of buildings and structures along the railroad line. Therefore, it is important to build a strong wind alarm system along the railroad line, and a reasonable and accurate short-time forecast of a strong wind is the basis of it. In this research, two methods of constructive function and time-series decomposition are proposed to pre-process the input wind speed for periodic strong winds in mountainous areas. Then, the improved Auto-Regressive Integrated Moving Average model time-series model was established through the steps of a white noise test, data stationarity test, model recognition, and order determination. Finally, the effectiveness of the improved wind speed prediction was examined. The results of the research showed that rational choice of processing functions has a large impact on wind speed prediction results. The prediction accuracy of the improved ARIMA model proposed in this paper is better than the results of the traditional Seasonal Auto-Regressive Integrated Moving Average model, and it can quickly and accurately realize the short-time wind speed prediction along the railroad line in rugged mountains. In addition, the improved ARIMA model has verified its universality in different mountainous places.

Application of Autoregressive Moving Average Model in the Prediction of COVID-19 of China

Objective: To establish ARIMA model through time series analysis to understand the occurrence law of newly confirmed cases of novel coronavirus pneumonia and provide references for taking epidemic prevention and control measures.
 Methods: The cumulative confirmed and cured cases of COVID-19 are collected through the official website of the National Health Commission, and the number of newly confirmed and cured cases per week are sorted out. We analyze the time series of newly diagnosed and cured COVID-19 cases every week from April 12, 2020 to December 5, 2021 by IBM SPSS 25.0 software. The model is established through model identification, parameter estimation and model fitting.
 Results: The number of reported cases of COVID-19 has no obvious seasonal characteristics. The ARIMA(2,1,1) model well fitted the time series, R2 = 0.542/0.617. Through the residual white noise test, all parameters of the model have statistical significance, Ljung box q = 9.095/9.651, P > 0.05. We predict the cases and cures in the four weeks after December 5, 2021 by ARIMA(2,1,1). The measured values in the first week and the second week are within the predicted 95% CI range.
 Discussion and Conclusion: The epidemiological characteristics of COVID-19 need a longer time series for validation and analysis. ARIMA model can predict the incidence of COVID-19 in a short term, and the model should be constantly revised according to the actual situation.

Multiple Sequence Long and Short Memory Network Model for Corner Gas Concentration Prediction on Coal Mine Workings.

To further improve the accuracy of recurrent neural network in predicting the gas concentration in the upper corner of the mine tunnel, this paper proposes a method to construct a gas concentration prediction model based on multiple sequence long and short memory network, considering the spatial correlation between the gas concentration in the return airway and upper corner. The reliability of the model construction is improved by using the white noise test and smoothness test to verify the interpretability of the data in this paper and constructing supervised learning type data for gas concentration prediction model training and testing by means of data set division and data windowing. Through experimental comparison, grid search, and time series decomposition, the model algorithm, training parameters, and experimental results were combined to make an in-depth analysis of the influence of each parameter on the model training and the prediction. A training model of the spatially fused gas concentration prediction model with a network layer of 1 and a number of neurons of 32 as the model structure, Adam as the optimization algorithm, and a learning rate of 0.001 and a batch size of 32 as the training parameters was finally determined. The gas concentration prediction model trained in this paper performed well in the test set with a mean square error (MSE) of 0.0013, and its superiority was verified by comparing it with other models to provide some experience and basis for subsequent studies on gas concentration prediction in the upper corner.

Spectral measure of empirical autocovariance matrices of high-dimensional Gaussian stationary processes

Consider the empirical autocovariance matrices at given non-zero time lags, based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain statistical problems, such as those related to testing for white noise. We study the behavior of their spectral measure in the asymptotic regime where the time series dimension and the observation window length both grow to infinity, and at the same rate. Following a general framework in the field of the spectral analysis of large random non-Hermitian matrices, at first the probabilistic behavior of the small singular values of a shifted version of the autocovariance matrix is obtained. This is then used to obtain the asymptotic behavior of the empirical spectral measure of the autocovariance matrices at any lag. Matrix orthogonal polynomials on the unit circle play a crucial role in our study.

Prediction of the Best Portfolio for Bitcoin and Gold based on the ARIMA Model

With the prosperity of the financial market, more and more people are involved in securities trading. How to combine investment in bitcoin and gold to achieve the highest profit is one of the issues that market traders think about. To solve this problem, we build a model that predicts future prices in order to better help investors. We constructed an ARIMA model through differential stationarity processing, AEC, white noise test and other methods, and used the data of the current day and the previous day to predict the price of the next day. At the same time, we use the model to predict the average for the next N days. If it is predicted that the price of the asset will decrease in the future, it will be sold on the same day. If the price of the asset will increase in the future, and the income obtained is greater than the transaction cost and the expected income of the investor, the purchase will continue until the end. Last until the last day $323841.52. Finally, it can be verified that the accuracy of the ARIMA model is the highest by comparing other mainstream machine learning models. In other words, the ARIMA model is the best strategy for this problem.

Quantitative trading portfolio optimization based on machine learning

The capital asset pricing model (CAPM) is to study the quantitative relationship between the expected return rate of assets and risky assets in the securities market. With the development of computer network technology and the trading market, quantitative trading has gradually become a new way of investment. Its essence lies in the decision of trading strategy. This paper obtains the relative price data of the subsequent short-term investment period through the time series method, then uses the PA algorithm in machine learning to update the portfolio and verify the effectiveness of the strategy in the data set. Based on the exchange rate change trend of the US dollar, gold, and bitcoin within five years given in the question, we constructed dynamic portfolio models for the three assets to ensure maximum profits. First, we use the time series model to predict the relative price data of the next period in a continuous trading period. Then, we implement the PA passive attack algorithm by calling the Sklearn package in Python to update the asset components in real-time every day and calculate the average annual return rate in 5 years. Based on the above analysis, we used the ADF unit root to test the stationarity of the time series. Meanwhile, we also carried out a white noise test of time series. The specific test indexes include: According to CAPM's theory, this product has a high yield, with an annual interest rate of 195.849%, which is entirely objective. However, the annual standard deviation reached 0.919164, and the maximum retractable rate exceeded 50%, indicating a sizeable overall risk. Despite this, the composite product's Calmar ratio is 3.556, Sharpe ratio is 2.104623, and its return per unit risk is still high. Compared with other quantitative trading models, this paper combines time series, machine learning, Monte Carlo, and other algorithms to effectively solve the portfolio investment optimization problem of nonlinear time-varying correlation structure among multiple assets. It enriches the results of portfolio investment structure decisions.

Acoustical testing of face coverings using an artificial acoustic head with speech audio

The COVID-19 pandemic has caused many communities to require or at least recommend the wearing of face coverings, masks, and/or shields inside indoor public spaces to reduce the transmission rate of the virus. Several types of face coverings are studied, including standardized N95 and KN95, assorted cloth, and clear plastic face shields. They are evaluated on an acoustical head and torso simulator (HATS) setup in a classroom with two different locations for monitoring via a sound level meter. The HATS is used as a controlled and repeatable artificial voice or sound source, which reproduces the ITU-T artificial speech signals as well as playback of real speech signals for American English, male and female voices. The signals are recorded with a sound level meter at a distance of 2 and 6 m between source and receiver in a classroom environment. These signals evaluated in time and frequency domains to better understand the acoustical difference between the no-mask and various masks conditions. These are compared with the same classroom environment but using white noise test signals.

Shaking table test on a novel mega-frame suspended structural system

This paper designed a 1/20 scaled two-segment 19-story mega-frame suspended structure. The seismic behaviors of the structure equipped with viscous dampers (named damping suspended structure, DSS) or rigid connecting rods (named normal suspended structure, NSS) were studied and evaluated by a series of shaking table tests, where three seismic ground motions with two intensities were selected as input motions. Both acceleration and displacement responses of the primary and suspended structures were recorded. The results revealed that the mega-frame suspended system showed good seismic behaviors and viscous dampers could effectively improve its energy dissipation capacities. For DSS, the maximal acceleration and displacement reduction of suspended structures were 75.4% and 39.8% while those of the primary structure were 29.4% and 35.3% respectively. White noise tests showed all models were at the elastic stage under all cases. Evident relative displacements between the primary and subordinate structures were observed for DSS, in this case, the suspended floors were considered as the additional mass of the primary structure and the energy could be dissipated by the swing of suspended floors. The energy dissipation mechanism of DSS was theoretically analyzed while the effect of connection forms on vibration reduction was discussed.

White Noise Test from Ordinal Patterns in the Entropy–Complexity Plane

SummaryThis article serves two purposes. Firstly, it surveys the Bandt and Pompe methodology for the statistical community, stressing topics that are open for research. Secondly, it contributes towards a better understanding of the statistical properties of that approach for time series analysis. The Bandt and Pompe methodology consists of computing information theory descriptors from the histogram of ordinal patterns. Such descriptors lie in a 2D manifold: the entropy–complexity plane. This article provides the first proposal of a test in the entropy–complexity plane for the white noise hypothesis. Our test is based on true white noise sequences obtained from physical devices. The proposed methodology provides consistent results: It assesses sequences of true random samples as random (adequate test size), rejects correlated and contaminated sequences (sound test power) and captures the randomness of generators previously analysed in the literature.

Bootstrap Tests for High-Dimensional White-Noise

The testing of white-noise (WN) is an essential step in time series analysis. In a high dimensional set-up, most existing methods either are computationally infeasible, or suffer from highly distorted Type-I errors, or both. We propose an easy-to-implement bootstrap method for high-dimensional WN test and prove its consistency for a variety of test statistics. Its power properties as well as extensions to WN tests based on fitted residuals are also considered. Simulation results show that compared to the existing methods, the new approach possesses much better power, while maintaining a proper control over the Type-I error. They also provide proofs that even in cases where our method is expected to suffer from lack of theoretical justification, it continues to outperform its competitors. The proposed method is applied to the analysis of the daily stock returns of the top 50 companies by market capitalization listed on the NYSE, and we find strong evidence that the common market factor is the main cause of cross-correlation between stocks.

Comparative investigation: Closed versus semi-closed vertical cylinder-shaped fish cage in waves

A comparative analysis between a closed cage (CC) and a semi-closed/open-bottom cage (OC) in regular, white-noise and irregular waves is presented. Both cages consist of a vertical circular free surface-piercing cylinder with an external toroidal floater. A main target is to examine experimentally and theoretically the similarities and differences of the hydrodynamic behavior between the two cages. Transfer functions obtained from regular and white-noise waves test show that the two cages have similar performance in surge motion, ovalizing deformations, interior wave elevation and mean drift loads in shorter waves (wavelength to cage diameter ratio λ/D<1). This is not the case for heave, with OC experiencing much larger heave. A clear sinkage (minus average heave) is also observed for OC, which is almost proportional to the square of the incident wave amplitude. The linear potential flow solver WAMIT can provide a reasonable prediction of surge and pitch motions, and mean drift loads for OC in shorter waves (λ/D<1.5), but is unsatisfactory in longer waves and, in general, for heave motion.From the analysis of irregular wave tests, there is a small difference in the standard deviations of the surge motion (wave-frequency component) and interior waves for the semi-closed and closed cages. The slow-drift component is dominant in surge for both cages, with OC having a smaller value due to larger viscous damping associated with flow separation at the bottom. Theoretical evaluations of standard deviations based on transfer functions from a white-noise test and from WAMIT are performed, assuming that the linear superposition principle applies. Reasonable agreement against results from experiments in irregular waves is achieved except for response variables with strong nonlinear effects.Survival conditions for both cages are determined through systematic evaluations. The platform freeboard is identified as the most critical parameter. The minimum freeboard for the closed and semi-closed cage should be at least 1.05 and 1.3 m, respectively, to operate at moderate exposure sea states. The standard deviation of vertical acceleration due to rigid body motions and interior waves could reach 0.72 m/s2 for both cages at high exposure sea states, which might be of concern for fish inside.

A Statistical Study of Lead-Lag Relationship between BCG and DPT Vaccinations in Anambra State: A Cross Spectrum Analysis

This study examined the lead-lag relationship between between Bacille Calmette-Guerin (BCG) and Diphtheria, Pertussis and Tetanus (DPT) vaccinations in Anambra State using cross spectrum analysis with BCG as the input series. The monthly data on the number of vaccinations for BCG and DPT were collected from Expanded Programmes on Immunization office in Awka, Anambra State for the period of January, 2012 to December, 2020. The Fisher’s Kappa and Bartlett Komolgorov-Smirnov white noise tests showed that both series were white noise. The series were differenced stationary using Augumented Dickey-fuller test. The coherence squared presented a strong relationship between BCG and DPT vaccinations, though it did not show consistent pattern of relationship, however identified pattern of relationship existed at both lower and higher frequencies. In addition, the phase showed that at lower frequencies BCG led DPT, while at higher frequencies BCG lagged DPT. The analysis showed that there is a high awareness for both vaccinations in the State and it should be sustained by the state government.

White Noise Tests on the LSTM Model Trained with Double Pendulum

This paper describes the intrinsic qualities of a simple double pendulum (DP), with a visual representation, a rigorous deduction of the Lagrangian equation, and a concrete factor analysis. LSTM model was utilized to simulate the double pendulum’s periodic and chaotic behaviors and evaluates the effectiveness of the model. The auto-correlation coefficients was calculated. Meanwhile, Box-Pierce test and Ljung-Box tests for various state-dependent time series were conducted to give various initial conditions to explore the DP system’s random characteristics. The research results are as follows: 1) Chaos did not lead to direct randomness; 2) seasonality could coexist with chaos; 3) the highly auto-regressive nature of DP’s time series data are found. Therefore, it can be concluded that the chaos in a double pendulum has particular patterns (such as the positive relationship with the likelihood of being a random white noise series) that could be further explored.

Wind Speed Prediction in the Hexi Corridor Region of China Using an Enhanced Multiscale Nonlinear Ensemble Model

Accurate wind speed prediction has become more and more popular. Herein, an enhanced multi‐scale nonlinear ensemble model is proposed to predict short‐term wind speed. First, advanced data preprocessing technology is used to extract these feature sequences. Second, each feature sequence is predicted by bidirectional long short‐term memory. In addition, the gated recurrent unit (GRU) realizes nonlinear ensemble and integrates the prediction information. Finally, GRU with white noise test is utilized to correct the residual to retain the possible effective information in the residual. The performance of the model is evaluated using the daily and hourly wind speeds of two wind farms in the Hexi Corridor region. The experimental results show that the proposed model has the best prediction accuracy among all relevant models. Taking Zhangye wind farm as an example, in the daily wind speed dataset, mean absolute percentage error, square sum error, theil inequality coefficient and the index of agreement of the model are 0.6416, 5.4234, 0.0151, and 0.9979, respectively. In the hourly dataset, they are 0.1037, 0.0042, 0.0003, and 1.0000, respectively. In the wind speed data of the Guazhou wind farm, the hybrid model proposed in this research also performs best.

Improved Multi-Scale Deep Integration Paradigm for Point and Interval Carbon Trading Price Forecasting

The forecast of carbon trading price is crucial to both sellers and purchasers; multi-scale integration models have been used widely in this process. However, these multi-scale models ignore the feature reconstruction process as well as the residual part and also they often focus on the linear integration. Meanwhile, most of the models cannot provide prediction interval which means they neglect the uncertainty. In this paper, an improved multi-scale nonlinear integration model is proposed. The original dataset is divided into some subgroups through variational mode decomposition (VMD) and all the subgroups will go through sample entropy (SE) process to reconstruct the features. Then, random forest and long-short term memory (LSTM) integration are used to model feature sub-sequences. For the residual part, LSTM residual correction strategy based on white noise test corrects residuals to obtain point prediction results. Finally, Gaussian process (GP) is applied to get the prediction interval estimate. The result shows that compared with some other methods, the proposed method can obtain satisfying accuracy which has the minimum statistical error. So, it is safe to conclude that the proposed method is able to efficiently predict the carbon price as well as to provide the prediction interval estimate.

Experimental Data of a Hexagonal Floating Structure under Waves

Floating structures have a wide range of application and shapes. This experimental investigations observes a hexagonal floating structure under wave conditions for three different draft configurations. Regular waves as well as a range of white noise tests were conducted to quantify the response amplitude operator (RAO). Further irregular waves focused on the survivability of the floating structure. The presented dataset includes wave gauge data as well as a six degree of freedom motion measurement to quantify the response only restricted by a soft mooring system. Additional analysis include the measurement of the mass properties of the individual configuration, natural frequency of the mooring system as well as the comparison between requested and measured wave heights. This allows us to use the provided dataset as a validation experiment.

A Two-Way Transformed Factor Model for Matrix-Variate Time Series

A new framework is proposed for modeling high-dimensional matrix-variate time series via a two-way transformation, where the transformed data consist of a matrix-variate factor process, which is dynamically dependent, and three other blocks of white noises. For a given p1×p2 matrix-variate time series, nonsingular transformations are sought to project the rows and columns onto another p1 and p2 directions according to the strength of the dynamical dependence of the series on their past values. Consequently, the data are nonsingular linear row and column transformations of dynamically dependent common factors and white noise idiosyncratic components. A common orthonormal projection method is proposed to estimate the front and back loading matrices of the matrix-variate factors. Under the setting that the largest eigenvalues of the covariance of the vectorized idiosyncratic term diverge for large p1 and p2, a two-way projected Principal Component Analysis is introduced to estimate the associated loading matrices of the idiosyncratic terms to mitigate such diverging noise effects. A new white-noise testing procedure is proposed to estimate the dimension of the factor matrix. Asymptotic properties of the proposed method are established for both fixed and diverging dimensions as the sample size increases to infinity. Simulated and real examples are used to assess the performance of the proposed method. Comparisons of the proposed method with some existing ones in the literature concerning the forecastability of the factors are studied and it is found that the proposed approach not only provides interpretable results, but also performs well in out-of-sample forecasting.