White Noise Test Research Articles

A Simple Test for White Noise in Functional Time Series

We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the L2‐distance between the spectral density operator and its best (L2‐)approximation by a spectral density operator corresponding to a white noise process. The estimation of this distance can be easily accomplished by sums of periodogram kernels, and it is shown that an appropriately standardized version of the estimator is asymptotically normal distributed under the null hypothesis (of functional white noise) and under the alternative. As a consequence, we obtain a very simple test (using the quantiles of the normal distribution) for the hypothesis of a white noise functional process. In particular, the test does not require either the estimation of a long‐run variance (including a fourth order cumulant) or resampling procedures to calculate critical values. Moreover, in contrast to all other methods proposed in the literature, our approach also allows testing for ‘relevant’ deviations from white noise and constructing confidence intervals for a measure that measures the discrepancy of the underlying process from a functional white noise process.

The effect of technology innovation on mobile communication and mobile products

PurposeIn order to understand the influence of technology innovation on market demand diffusion in the ICT service market, the purpose of this paper is to examine technology innovation in the mobile product market, which keeps a complementary relationship with the mobile communication market.Design/methodology/approachThis study collected mobile communication user information of four leading countries in the ICT market – the USA, the UK, Korea, and Japan from 1981 to 2014. This study applies the Bass diffusion model to analyze the form of market demand diffusion and conducts white noise test to verify the hypotheses.FindingsTechnology innovation of mobile communication leads to an increase in innovation effect and a decrease in imitation effect. Thus, technology innovation of mobile communication needs to be promoted continuously for the purpose of increasing adopters in the early stage. Besides, mobile product’s technology innovation leads to an increase in imitation effect and a decrease in innovation effect, because individuals were aware of the usefulness of the products and services. Hence, the increase in the number of imitators caused a higher increase in imitation effect than in the mobile communication’s innovation effect.Originality/valueBased on the results of this study, the role that product and service technology innovation plays in renewing the form of market demand diffusion in the ICT service market was defined. Also, since the strategies and plans to acquire competitive advantage of business were understood, it may help both companies and policy decision makers.

Inference for the autocovariance of a functional time series under conditional heteroscedasticity

Most methods for analyzing functional time series rely on the estimation of lagged autocovariance operators or surfaces. As in univariate time series analysis, testing whether or not such operators are zero is an important diagnostic step that is well understood when the data, or model residuals, form a strong white noise. When functional data are constructed from dense records of, for example, asset prices or returns, a weak white noise model allowing for conditional heteroscedasticity is often more realistic. Applying inferential procedures for the autocovariance based on a strong white noise to such data often leads to the erroneous conclusion that the data exhibit significant autocorrelation. We develop methods for performing inference for the lagged autocovariance operators of stationary functional time series that are valid under general conditional heteroscedasticity conditions. These include a portmanteau test to assess the cumulative significance of empirical autocovariance operators up to a user selected maximum lag, as well as methods for obtaining confidence bands for a functional version of the autocorrelation that are useful in model selection/validation. We analyze the efficacy of these methods through a simulation study, and apply them to functional time series derived from asset price data of several representative assets. In this application, we found that strong white noise tests often suggest that such series exhibit significant autocorrelation, whereas our tests, which account for functional conditional heteroscedasticity, show that these data are in fact uncorrelated in a function space.

Testing for White Noise Hypothesis of Stock Returns

Weak form efficiency of stock markets implies unpredictability of stock returns in a time series sense, and the latter is tested predominantly under a serial independence or martingale difference assumption. Since these properties rule out weak dependence that may exist in stock returns, it is of interest to test whether returns are white noise. We perform white noise tests assisted by Shao's (2011) blockwise wild bootstrap. We reveal that, in rolling windows, the block structure inscribes an artificial periodicity in bootstrapped confidence bands. We eliminate the periodicity by randomizing a block size. The white noise hypothesis is accepted for Chinese and Japanese markets, suggesting that those markets are weak form efficient. The white noise hypothesis is rejected for U.K. and U.S. markets during the Iraq War and the subprime mortgage crisis due to significantly negative autocorrelations, suggesting that those markets are inefficient in crisis periods.

Erratum: Testing for high-dimensional white noise using maximum cross-correlations

Erratum: Testing for high-dimensional white noise using maximum cross-correlations

Testing for high-dimensional white noise using maximum cross-correlations

We propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross-correlations of the component series. Based on an approximation by the |$L_\infty$|-norm of a normal random vector, the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution. In contrast to the conventional white noise test, the new method is proved to be valid for testing departure from white noise that is not independent and identically distributed. We illustrate the accuracy and the power of the proposed test by simulation, which also shows that the new test outperforms several commonly used methods, including the Lagrange multiplier test and the multivariate Box–Pierce portmanteau tests, especially when the dimension of the time series is high in relation to the sample size. The numerical results also indicate that the performance of the new test can be further enhanced when it is applied to pre-transformed data obtained via the time series principal component analysis proposed by J. Chang, B. Guo and Q. Yao (arXiv:1410.2323). The proposed procedures have been implemented in an R package.

Identification of equivalent mechanical properties for unreinforced masonry walls

Transverse vibrations of beams are an interesting topic for numerous engineering fields. The equations of motion develop under various assumptions and associate a frequency equation. This paper expresses the frequency equation for two specific models, using the Timoshenko beam theory. The first model is a typical cantilever beam with an additional mass attached to the free end. The second model considers a beam partially clamped at the base and with an elastic connection of the additional mass to the free end. The relevance of the used theory is discussed and the importance of each term of the equation is studied. These models find applications in unreinforced masonry. They are indeed fitted to identify, from white noise tests, equivalent mechanical properties of unreinforced load-bearing clay masonry walls including soundproofing devices in the perspective of modelling these elements with a macro-scale approach. Discrepancies with respect to current standards are underscored.

Identification of equivalent mechanical properties for unreinforced masonry walls

Transverse vibrations of beams are an interesting topic for numerous engineering fields. The equations of motion develop under various assumptions and associate a frequency equation. This paper expresses the frequency equation for two specific models, using the Timoshenko beam theory. The first model is a typical cantilever beam with an additional mass attached to the free end. The second model considers a beam partially clamped at the base and with an elastic connection of the additional mass to the free end. The relevance of the used theory is discussed and the importance of each term of the equation is studied. These models find applications in unreinforced masonry. They are indeed fitted to identify, from white noise tests, equivalent mechanical properties of unreinforced load-bearing clay masonry walls including soundproofing devices in the perspective of modelling these elements with a macro-scale approach. Discrepancies with respect to current standards are underscored.

White noise testing and model diagnostic checking for functional time series

This paper is concerned with white noise testing and model diagnostic checking for stationary functional time series. To test for the functional white noise null hypothesis, we propose a Cramér–von Mises type test based on the functional periodogram introduced by Panaretos and Tavakoli (2013a). Using the Hilbert space approach, we derive the asymptotic distribution of the test statistic under suitable assumptions. A new block bootstrap procedure is introduced to obtain the critical values from the non-pivotal limiting distribution. Compared to existing methods, our approach is robust to the dependence within white noise and it does not involve the choices of functional principal components and lag truncation number. We employ the proposed method to check the adequacy of functional linear models and functional autoregressive models of order one by testing the uncorrelatedness of the residuals. Monte Carlo simulations are provided to demonstrate the empirical advantages of the proposed method over existing alternatives. Our method is illustrated via an application to cumulative intradaily returns.

The Sound of Many Funds Rebalancing

This paper proposes that portfolio-rebalancing cascades generate noise in financial markets. In particular, we study the rebalancing decisions of exchange-traded funds (ETFs). Stocks are often held by many different ETFs that track a wide variety of benchmarks. We show theoretically that, when many ETFs are involved, small price changes can trigger large rebalancing cascades that wind up affecting unrelated stocks on the opposite side of the market. We then show empirically that, when many ETFs hold a stock, aggregate ETF demand for that stock passes statistical tests for white noise and that aggregate ETF volume predicts total trading volume, liquidity, and insider-trading activity. These results persist when we instrument for aggregate ETF volume with the number of unrelated ETFs in the market — that is, with the number of ETFs that hold neither the target stock nor any stocks held by ETFs that hold the target stock. The number of unrelated ETFs is correlated with the potential for rebalancing cascades but not with characteristics of the target stock, so our results are unlikely to be driven by unobserved stock-level differences.

Large sample behaviour of high dimensional autocovariance matrices

The existence of limiting spectral distribution (LSD) of $\hat{\Gamma}_u+\hat{\Gamma}_u^*$, the symmetric sum of the sample autocovariance matrix $\hat{\Gamma}_u$ of order $u$, is known when the observations are from an infinite dimensional vector linear process with appropriate (strong) assumptions on the coefficient matrices. Under significantly weaker conditions, we prove, in a unified way, that the LSD of any symmetric polynomial in these matrices such as $\hat{\Gamma}_u+\hat{\Gamma}_u^*$, $\hat{\Gamma}_u\hat{\Gamma}_u^*$, $\hat{\Gamma}_u\hat{\Gamma}_u^*+\hat{\Gamma}_k\hat{\Gamma}_k^*$ exist. Our approach is through the more intuitive algebraic method of free probability in conjunction with the method of moments. Thus, we are able to provide a general description for the limits in terms of some freely independent variables. All the previous results follow as special cases. We suggest statistical uses of these LSD and related results in order determination and white noise testing.

A Max-Correlation White Noise Test for Weakly Dependent Time Series

This paper presents bootstrapped p-value white noise tests based on the max-correlation, for a time series that may be weakly dependent under the null hypothesis. The time series may be prefiltered residuals. Our test statistic is a scaled maximum sample correlation coefficient where the maximum lag increases at a rate slower than the sample size. We only require uncorrelatedness under the null hypothesis, along with a moment contraction dependence property that includes mixing and non-mixing sequences, and exploit two wild bootstrap methods for p-value computation. We operate either on a first order expansion of the sample correlation, or Delgado and Velasco's (2011) orthogonalized correlation for fixed lag length, both to control for the impact of residual estimation. A numerical study shows the first order expansion is superior, especially for large lag length. When the filter involves a GARCH model then the orthogonalization breaks down, while the first order expansion works quite well. We show Shao's (2011) dependent wild bootstrap is valid for a much larger class of processes than originally considered. Since only the most relevant sample serial correlation is exploited amongst a set of sample correlations that are consistent asymptotically, empirical size tends to be sharp and power is comparatively large for many time series processes. The test has non-trivial local power against local alternatives, and can detect very weak and distant serial dependence better than a variety of other tests. Finally, we prove that our bootstrapped p-value leads to a valid test without exploiting extreme value theoretic arguments, the standard in the literature.

A posteriori model validation for the temporal order of directed functional connectivity maps.

A posteriori model validation for the temporal order of neural directed functional connectivity maps is rare. This is striking because models that require sequential independence among residuals are regularly implemented. The aim of the current study was (a) to apply to directed functional connectivity maps of functional magnetic resonance imaging data an a posteriori model validation procedure (i.e., white noise tests of one-step-ahead prediction errors combined with decision criteria for revising the maps based upon Lagrange Multiplier tests), and (b) to demonstrate how the procedure applies to single-subject simulated, single-subject task-related, and multi-subject resting state data. Directed functional connectivity was determined by the unified structural equation model family of approaches in order to map contemporaneous and first order lagged connections among brain regions at the group- and individual-levels while incorporating external input, then white noise tests were run. Findings revealed that the validation procedure successfully detected unmodeled sequential dependencies among residuals and recovered higher order (greater than one) simulated connections, and that the procedure can accommodate task-related input. Findings also revealed that lags greater than one were present in resting state data: With a group-level network that contained only contemporaneous and first order connections, 44% of subjects required second order, individual-level connections in order to obtain maps with white noise residuals. Results have broad methodological relevance (e.g., temporal validation is necessary after directed functional connectivity analyses because the presence of unmodeled higher order sequential dependencies may bias parameter estimates) and substantive implications (e.g., higher order lags may be common in resting state data).

Regular transformation groups based on Fourier-Gauss transforms

We discuss different representations of the white noise test functions (E)β , 0 ≤ β < 1 by introducing generalized Wick tensors. As an application we state the following generalization of the Mehler formula for the Ornstein-Uhlenbeck semigroup, see [7, p. 237]: Let a, b ∈ C, 0 ≤ β < 1. Then a · ∆G + b · N is the infinitesimal generator of the following regular differentiable one parameter transformation group { Pa,b,t } t∈R ⊂ GL((E)β): (i) if b = 0 then for all φ ∈ (E)β , t ∈ R :

1-g Experimental investigation of bi-layer soil response and kinematic pile bending

The effect of soil inhomogeneity and material nonlinearity on kinematic soil–pile interaction and ensuing bending under the passage of vertically propagating seismic shear waves in layered soil, is investigated by means of 1-g shaking table tests and nonlinear numerical simulations. To this end, a suite of scale model tests on a group of five piles embedded in two-layers of sand in a laminar container at the shaking table facility in BLADE Laboratory at University of Bristol, are reported. Results from white noise and sine dwell tests were obtained and interpreted by means of one-dimensional lumped parameter models, suitable for inhomogeneous soil, encompassing material nonlinearity. A frequency range from 0.1Hz to 100Hz and 5Hz to 35Hz for white noise and sine dwell tests, respectively, and an input acceleration range from 0.015g to 0.1g, were employed. The paper elucidates that soil nonlinearity and inhomogeneity strongly affect both site response and kinematic pile bending, so that accurate nonlinear analyses are often necessary to predict the dynamic response of pile foundations.

Experimental identification of the six DOF C.G.S., Algeria, shaking table system

Servohydraulic shaking tables are being increasingly used in the field of earthquake engineering. They play a critical role in the advancement of the research state and remain one of the valuable tools for seismic testing. Recently, the National Earthquake Engineering Research Center, CGS, has acquired a 6.1m x 6.1 m shaking table system which has a six degree-of-freedom testing capability. The maximum specimen mass that can be tested on the shaking table is 60 t. This facility is designed specially for testing a complete civil engineering structures, substructures and structural elements up to collapse or ultimate limit states. It can also be used for qualification testing of industrial equipments. The current paper presents the main findings of the experimental shake-down characterization testing of the CGS shaking table. The test program carried out in this study included random white noise and harmonic tests. These tests were performed along each of the six degrees of freedom, three translations and three rotations. This investigation provides fundamental parameters that are required and essential while elaborating a realistic model of the CGS shaking table. Also presented in this paper, is the numerical model of the shaking table that was established and validated.

A New Approach for Optimal Decomposition Level Selection in Wavelet De-Noising

The paper introduces a novel algorithm to determine the optimal decomposition level in wavelet de-noising. The algorithm selects the optimal decomposition level by comparing the sparsity of wavelet coefficients at adjacent levels. The level whose wavelet coefficient has the maximum sparsity can be confirmed as the optimal decomposition level. We demonstrate experimentally that wavelet de-noising performs better using optimal decomposition level determined by our proposed algorithm than White Noise Test (WNT) method and Maximum Energy (ME) method.

ADAPTIVE K-S TESTS FOR WHITE NOISE IN THE FREQUENCY DOMAIN

Since the classical Kolmogorov-Smirnov (K-S) tests for white noise are completely insensitive to both tails it is difficult in a particular application to detect departure from whiteness. A modified version of the widely used (K- S) test of null hypothesis is constructed, that a given time series is Gaussian white noise, against the alternative hypothesis that the time series contains an added or multiplicative deterministic periodic component of unspecified fre- quency. The usual K-S test is treated as a special case. The proposed test is more powerful than the ordinary K-S test in detecting extreme (low or high) hidden periodicities. Computational procedures necessary for implementation are given.

Experimental study on the hydrodynamic performance of FDPSO and SRV

FDPSO (floating, drilling, production, storage and offloading unit) is a multifunction floating platform which has the combined functions of offshore drilling, production, storage and offloading oil. SRV (sheltered riser vessel), which is situated in the moonpool of the FDPSO hull, serves as an independent buoyant can to provide riser tension and compensate the heave motion of the hull. In order to study the hydrodynamic performance of FDPSO and SRV, a series of model tests have been carried out in the Deepwater Offshore Basin at the State Key Laboratory of Ocean Engineering at Shanghai Jiao Tong University. The model tests are composed of decay tests, white noise tests and irregular wave tests. The operating sea state of the South China Sea is simulated in the irregular wave tests. The motion characteristics of the FDPSO hull and SRV are analysed and the feasibility of the SRV concept is examined. Experimental results revealed that the heave motion of SRV is less than that of the FDPSO hull, demonstrating the effectiveness of SRV in compensating the heave response of the hull. Apart from the heave, the motion responses of SRV are quite similar to those of the hull.

Evaluating Foamed Asphalt Stability Using Acoustic Emission Techniques

AbstractThis paper focuses on the feasibility of using acoustic emission (AE) techniques to evaluate stability of foams produced from paving-grade asphalt binders. The study compared asphalt foamability index [expansion ratio (ER) and half-life (H-L)] measurements with AE measurements for the same foamed asphalt produced using a Wirtgen Model WLB 10 S Laboratory Asphalt Foaming Device. Both ER and H-L are used to characterize the suitability of asphalt binders to produce good-quality foamed asphalt binders for pavement construction. However, current methods for determining foamability are considered as empirical, operator-dependent, and cannot be used for continuous monitoring of the foaming process. Two performance-graded asphalt binders, four foaming water contents, and two foaming temperatures were used. Spectral analyses using a test for white noise suggest AE signals resulting from asphalt foaming are not white noise (p-value<0.0001) and therefore could be useful for evaluating foamed asphalt stabili...