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In this paper we present a new autoregressive (AR) method for bispectrum estimation defined in terms of its third‐moment sequence. The method is based on the segmentation of data into coupled records, and can be considered to be a modification of the “third order recursion method”(TOR). Its foundation resides in considering the data of the process at the left and the right of each record (needed for the calculation of third moment sequence) as not null and taking them as the data corresponding to the preceding and succeeding record respectively. Several simulated examples show that this method allows model parameters to be obtained with greater precision, most of all when only few data are available per record. The influence of factors such as number of data and records, model order, and added white and coloured Gaussian noise on the parameters’ estimation is also considered.

This paper deals with bispectrum estimation via autoregressive (AR) modelling of a process contaminated by additive Gaussian noise (white and coloured). Two main contributions are provided in this work. First, a comparison between the existing third order recursion (TOR) and the constrained third order mean (CTOM) methods is presented. Basically, the second method is shown to be a smoothing windowed version (i.e. a covariance‐type estimator) of the first one, achieved at the expense of the loss of the recursivity in the AR‐model order. This prior analysis has induced us to develop an alternative scheme to tackle this type of problem, which, while maintaining the main feature of the CTOM method as a covariance type estimator, is a recursive‐in‐order algorithm. This recursivity is obtained carrying out an appropriate minimization procedure of some prediction squared errors also defined here. The paper also compares, by means of simulations, this proposed method and the two existing ones.

The authors proposed a new method of fast time delay measurement for integrated pulsar pulse profiles in X-ray pulsar-based navigation (XNAV). As a basic observation of exact orientation in XNAV, time of arrival (TOA) can be obtained by time delay measurement of integrated pulsar pulse profiles. Therefore, the main purpose of the paper is to establish a method with fast time delay measurement on the condition of limited spacecraft’s computing resources.

Given that the third-order cumulants can suppress the Gaussian noise and reduce calculation to achieve precise and fast positioning in XNAV, the proposed method sets the third-order auto-cumulants of standard pulse profile, the third-order cross-cumulants of the standard and the observed pulse profile as basic variables and uses the cross-correlation function of these two variables to estimate the time delay of integrated pulsar pulse profiles.

The proposed method is simple, fast and has high accuracy in time delay measurement for integrated pulsar pulse profiles. The result shows that compared to the bispectrum algorithm, the method improves the precision of the time delay measurement and reduced the computation time significantly as well.

To improve the performance of time delay estimation in XNAV systems, the authors proposed a novel method for XNAV to achieve precise and fast positioning.

Compared to the bispectrum algorithm, the proposed method can improve the speed and precision of the TOA’s calculation effectively by using the cross-correlation function of integrated pulsar pulse profile’s third-order cumulants instead of Fourier transform in bispectrum algorithm.

The purpose of this paper is to investigate the monitoring of the friction condition of mechanical seals.

Acoustic emission signals from the friction of the seal end face were obtained, and their bispectral characteristics were extracted. The variation of non-Gaussian information with the degree of friction was investigated, and by combining bispectral characteristics with information entropy, a bispectral entropy index was established to represent the friction level of the seal end face.

In the start-up stage, the characteristic frequency amplitude of the micro-convex body contact is obvious, the friction of the end face is abnormal, the complexity of the system increases in a short time and the bispectral entropy rises continuously in a short time. In the stable operation stage, the characteristic frequency amplitude of the micro-convex body contact varies with the intensity of the seal face friction, the seal face friction is stable and the bispectral entropy fluctuates up and down for a period of time.

The bispectral analysis method is applied to the seal friction monitoring, the seal frequency domain characteristics are extracted, the micro-convex body contact characteristic frequency is defined and the bispectral entropy characteristic index is proposed, which provides a certain theoretical basis for the mechanical seal friction monitoring.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2023-0242/

The purpose of this paper is to first, test for nonlinearity in Local Indian Exchange Traded Funds (ETFs) listed at NSE, India – NIFTYBEES, JUNIORBEES, BANKBEES, PSUBANKBEES, and INFRABEES – using a battery of nonlinearity tests; second, to ascertain, using both metric and topological approaches, the adequacy of appropriate AR-GARCH models when it comes to capturing all of the nonlinearity in Indian ETFs; and third, to test for chaos in Indian ETFs.

To start with, a battery of tests such as and limited to McLeod Li test, Engle's LM test, Tsay F-test, Hinich Bispectrum Test and Hinich Bicorrelation test were employed to test for nonlinearity in Indian ETFs. Subsequently, the nature of nonlinearity in all the ETFs was systematically investigated by subjecting the ETF data sets to a metric (BDS test) and a topological test (close returns tests) at different stages of the model-building process. Finally, Lyapunov Exponent test was employed to test for chaos in Indian ETFs.

Test outcomes pertaining to a battery of nonlinearity tests indicate prevalence of nonlinearity amidst all ETFs except for INFRABEES. BDS test outcomes at the different stages of the model-building process indicated high sensitivity of the test outcomes to choice of embedding dimension, threshold value and residual transformations. Close returns test outcomes indicated that, but for BANKBEES, all of the nonlinearity in Indian ETFs could be captured by appropriate GARCH models. Finally, chaos was found to be absent in any of the ETFs considered for this study.

The collective take-way from this study is threefold in nature. First, in light of the many limitations of the BDS test, topological approaches such as close-returns test offer a better avenue to test for adequacy of AR-GARCH models in explaining the nature of nonlinearity in asset price movements. Second, adequacy of AR-GARCH models in capturing all of the nonlinearity in NIFTYBEES, JUNIORBEES, PSUBANKBEES, and INFRABEES, as indicated by close-returns test findings, is a reflection of multiplicative nature of nonlinearity in these five ETFs. Third, persistence of nonlinearity in AR-GARCH filtered standardized residuals of BANKBEES, coupled with the absence of chaos in any of the ETFs considered for this study, brings to light the possibility of existence of additive nonlinearity in conjunction with multiplicative nonlinearity.

This is possibly the first study that systematically investigates the nature of nonlinearity in Indian ETFs and ascertains the adequacy of AR-GARCH models when it comes to capturing all of the nonlinearity in Indian ETFs using a topological approach.

In marine structures, the long‐term non‐stationary response of flexible lines, due to random environmental loads, may be regarded as successive short‐term stationary processes in which current, wind and ocean wave conditions remain constant. The power spectrum of each stationary process can be characterized by its linear and non‐linear energy components: the linear energy defines a Gaussian process, and the additional nonlinear energy characterizes a non‐Gaussian process. Within this scope, digital bispectral analysis has enabled one to describe non‐linear stationary response of flexible lines in the frequency domain, so that the complex coefficients of a quadratic model, in the frequency domain, can be estimated. The real and symmetrical matrix constructed from these coefficients has eigenvalues and eigenvectors useful to describe the characteristic function of the response from where the probability density function can be obtained by using a fast Fourier transform algorithm. The bases of the method presented here have already been treated, in a similar but pure algebraic method, to obtain the asymptotic probability function applicable to the response of non‐linear systems in closed form.