Time-varying Mean Research Articles

On a quantile autoregressive conditional duration model

Autoregressive conditional duration (ACD) models are primarily used to deal with data arising from times between two successive events. These models are usually specified in terms of a time-varying conditional mean or median duration. In this work, we relax this assumption and consider a conditional quantile approach to facilitate the modeling of different percentiles. The proposed ACD quantile model is based on a skewed version of Birnbaum–Saunders distribution, which yields better fit of the tails than the traditional Birnbaum–Saunders distribution, in addition to facilitating the implementation of an expectation conditional maximization (ECM) algorithm. A Monte Carlo simulation study is performed to assess the behavior of the model as well as the parameter estimation method and the evaluation of a form of residuals. Two real financial transaction data sets are finally analyzed to illustrate the proposed approach.

Improved state augmentation method for buffeting analysis of structures subjected to non-stationary wind

Extreme winds such as hurricanes and thunderstorms often present non-stationary characteristics, having time-varying mean wind speeds and non-stationary wind fluctuations. When concerning the wind-induced vibrations under non-stationary wind, the excitation will be a non-stationary process, and the wind-structure coupled system can be represented by a linear time-varying (LTV) system. The aim of this study is to present a state augmentation method to investigate the non-stationary buffeting of a model bridge tower subjected to non-stationary wind with consideration of the aeroelastic damping. Based on the theory of stochastic differential equations and Itô’s lemma, the statistical moments of the non-stationary buffeting response are derived through solving a first-order ordinary differential equation system. The proposed method is validated by comparisons with the Monte Carlo method and the pseudo excitation method. The result shows that the state augmentation method has higher accuracy and efficiency than the well-accepted time–frequency techniques.

Optimal difference-based variance estimators in time series: A general framework

Variance estimation is important for statistical inference. It becomes nontrivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with nonconstant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many existing estimators. Necessary and sufficient conditions for consistency are investigated. The first asymptotically optimal estimator is derived. Our proposed estimator is theoretically proven to be invariant to arbitrary mean structures, which may include trends and a possibly divergent number of discontinuities.

Response statistics of monopile OWT to fully nonstationary seismic motion

At present, the vast majority of offshore wind turbines (OWTs) have been the monopile type. Although design standards recommend seismic assessments be included in their designs, there has been no guidance on how to conduct an analysis due in part to a lack of efficient methods, particularly related to the nonstationary nature of seismic motions. This article contributes to the development of an efficient pole-residue method operated in the Laplace domain to analytically compute response statistics, including the response evolutionary power spectrum (EPS) and time-varying mean square values. While the nonstationary seismic motions are treated as a uniformly modulated random process, both exponential and gamma models are considered for the modulating function. Furthermore, a fully nonstationary seismic motion with multiple independent modulated subprocesses is also studied. In the numerical studies, a 5 MW monopile OWT subjected to nonstationary stochastic seismic motion is studied; Monte Carlo simulations are employed to verify the correctness of the analytical solutions. Numerical studies confirm that the response EPS at the tower top is contributed mainly by the OWT’s first bending mode. While applying the linear superposition principle, the proposed method can also be extended to the situation that an OWT is subjected to fully nonstationary earthquake and stationary wave loadings simultaneously.

Nonstationary near-ground wind characteristics and wind-induced pressures on the roof of a low-rise building during a typhoon

Wind fields in the surface layer during typhoons usually have strong nonstationary features, which cause damage to low-rise buildings, especially their roofs. It is thus required to establish accurate models of typhoon-generated near-surface wind fields and assess typhoon effects on low-rise buildings. In this paper, a framework of extracting time-varying mean component and determining time-varying fluctuating component of nonstationary signals is established, which is applied to investigate the on-site measured near-ground nonstationary wind velocities and wind-induced pressures on the roof of a typical low-rise building during a typhoon. It is observed that near-ground wind characteristic parameters (including turbulence intensities, gust factors, peak factors and turbulence integral length scales, wind spectra) and wind pressure coefficients on the roof obtained by the nonstationary analytical approach are more reasonable than those determined by the conventional stationary analytical approach. Besides, the evolutionary power spectral density is used to examine time-frequency spectra of wind velocities and wind pressures. This comparative study based on the nonstationary and stationary analysis approaches aims to further the understanding of the nonstationary surface layer wind characteristics and wind pressures on typical low-rise buildings for reduction of windstorm damages to residential buildings in typhoon-prone regions.

Maximum dynamic response of linear elastic SDOF systems based on an evolutionary spectral model for thunderstorm outflows

The study aims to estimate the maximum dynamic response of linear elastic SDOF systems subjected to thunderstorm outflows. Starting from a recently developed Evolutionary Power Spectral Density (EPSD) model for the wind velocity, the dynamic response is decomposed into a time-varying mean and a non-stationary random fluctuation. The EPSD and the Non-Geometrical Spectral Moments (NGSMs) of the random fluctuation are derived both accounting and neglecting the transient dynamics due to the modulating function of the load. The mean value of the maximum nonstationary fluctuating component of the response is estimated based on the definition of an equivalent stationary process following an approach proposed in the literature. In order to mitigate the overestimations of the maximum dynamic response due to the Poisson approximation, analogously to the formulation developed by Der Kiureghian for withe noise excitation, an equivalent expected frequency is introduced for thunderstorm excitation. Finally, the maximum dynamic response to thunderstorms is estimated as the sum of the maximum mean and fluctuating parts and a numerical validation of the results against real recorded thunderstorms is provided, highlighting the reliability of adding up the mean and fluctuating contributions and the advantages and limits of neglecting the transient dynamics.

Human Activity Signatures Captured under Different Directions Using SISO and MIMO Radar Systems

In this paper, we highlight and resolve the shortcomings of single-input single-output (SISO) millimeter wave (mm-Wave) radar systems for human activity recognition (HAR). A 2×2 distributed multiple-input multiple-output (MIMO) radar framework is presented to capture human activity signatures under realistic conditions in indoor environments. We propose to distribute the two pairs of collocated transmitter–receiver antennas in order to illuminate the indoor environment from different perspectives. For the proposed MIMO system, we measure the time-variant (TV) radial velocity distribution and TV mean radial velocity to observe the signatures of human activities. We deploy the Ancortek SDR-KIT 2400T2R4 mm-Wave radar in a SISO as well as a 2×2 distributed MIMO configuration. We corroborate the limitations of SISO configurations by recording real human activities in different directions. It is shown that, unlike the SISO radar configuration, the proposed MIMO configuration has the ability to obtain superior human activity signatures for all directions. To signify the importance of the proposed 2×2 MIMO radar system, we compared the performance of a SISO radar-based passive step counter with a distributed MIMO radar-based passive step counter. As the proposed 2×2 MIMO radar system is able to detect human activity in all directions, it fills a research gap of radio frequency (RF)-based HAR systems.

Modeling Nonstationary Non-Gaussian Hurricane Wind Velocity and Gust Factor

This study estimated the wind gust factor and turbulence intensity for hurricane winds that are modeled as a nonstationary non-Gaussian process. The estimation considered the time-varying mean wind velocity, and the time–frequency decomposition using S-transform characterized the time-varying amplitude and frequency content of the fluctuating wind. Winds simulated by applying a newly developed algorithm were used to augment the sample size. Results indicate that the standardized power spectral density function of hurricane winds can be represented in terms of the reduced frequency but with time-varying mean wind velocity. The standardized fluctuating wind is only weakly non-Gaussian; the average skewness and kurtosis coefficients are not very sensitive to whether the 10-or 60-min time-varying mean wind speed is considered. The assessed relation between the gust factor and turbulence intensity indicates that such a relationship is influenced by whether the instantaneous aspect of the nonstationary process is considered. There is large uncertainty in the developed relationship. By removing samples associated with a low mean wind velocity, the largest value of the estimated gust factor decreases. The consideration of the non-Gaussian aspect of the fluctuating wind to estimate the gust factor could be important as turbulence intensity increases.

Thunderstorm-induced mean wind velocities and accelerations through the continuous wavelet transform

By analysing a set of thunderstorm-induced events acquired on the Italian north-west coast, the separation of the relevant wind velocity signals into a time-varying mean and a residual fluctuation is considered. It is assumed that, within a structural design process, the former is used for a quasi-steady evaluation of the aerodynamic loads and the latter to estimate the dynamic response. A procedure based on the continuous wavelet transform is proposed to obtain the time-varying mean velocity and its outcomes are compared with those of different moving average techniques. The wavelet filtering appears to provide a time-varying mean that better describes the main time variations of the original velocity signals; a decrease of the correlation between mean and residual velocities is also found. The derivative of the time-varying mean wind speed leads to a time-varying mean acceleration, whose characteristics and possible role in a design process are discussed. An estimate of the acceleration-induced contribution to the aerodynamic loads on a slender body is also carried out through the Morison equation. The force term directly related to acceleration is shown to generally have a limited influence on the total design loads, except for bodies that are considerably elongated in the flow direction.

Computer simulation of the reliability of the heat exchange surface of the steam turbine condenser

The aim of the article is to demonstrate the relationship between the adaptive regulation of the heat exchange surface to specific operating conditions of a steam turbine condenser and the reliability and availability of this surface in a specific period of time. The article exemplifies the relationship between the settings of the condenser heat exchange surface and the resulting changes in the reliability structures of this surface. The method of creating a mathematical model of reliability estimation, which is characterized by the variability of the reliability structures of the heat exchange surface in relation to specific operating conditions in a specific period of time, was indicated. Then, exemplary simulations of the adaptation of reliability structures of specific pipe systems constituting the condenser’s heat exchange surface to specific processes of operation of this condenser are presented. The simulations refer to the time-varying thermal loads of the condenser, the time-varying mean thickness of the sediments, and changes in the temperature of the cooling water at the point of its intake over time. The adaptation of certain reliability structures consists in the adaptation of specific systems of pipes through which the cooling water flows to the currently existing operating conditions of the condenser in order to maintain the desired reliability of the heat exchange surface for a specified time. This is done by enabling or disabling the flow of cooling water through a given number of pipes in specific systems under given operating conditions. On the basis of computer simulations, the reliability functions, and the availability functions of the subsystem under consideration were estimated.

A Novel Fault Detection Method Based on the Extraction of Slow Features for Dynamic Nonstationary Processes

The industrial process often shows nonstationary characteristic, such as time-varying mean and variance, due to the unmeasured disturbances, adjustments of production plans, operator interventions, etc. Because of the overlook of nonstationarity, traditional multivariate statistical methods based on the assumption of stationarity often cause low fault detection rate (FDR) and high false alarm rate (FAR). In this article, a novel fault detection framework is proposed to improve the performance of fault detection when nonstationary and stationary variables coexist. It combines slow feature analysis (SFA) and K-nearest neighbor (KNN) based on Mahalanobis distance (SFA-MDKNN). First, stationary/nonstationary variables are distinguished by the unit root test. For nonstationary variables, the stationary residuals are obtained by Johansen cointegration analysis (CA) to form a combination matrix. Second, slow features in the combination matrix are extracted to achieve feature level fusion, and KNN distance based on Mahalanobis one is introduced as the monitoring index. Finally, considering that the effect of KNN algorithm is susceptible to data distribution, the FDR and FAR are taken into account by setting dynamic control limits. Tennessee Eastman process and hot rolling process (HRP) are used to validate the proposed framework and the computational efficiency of the algorithm.

AdaptSPEC-X: Covariate-Dependent Spectral Modeling of Multiple Nonstationary Time Series

We present the AdaptSPEC-X method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components parameterized by a time-varying mean and log spectrum. The mixture components are based on AdaptSPEC, a nonparametric model which adaptively divides the time series into an unknown number of segments and estimates the local log spectra by smoothing splines. AdaptSPEC-X extends AdaptSPEC in three ways. First, through the infinite mixture, it applies to multiple time series linked by covariates. Second, it can handle missing values, a common feature of time series which can cause difficulties for nonparametric spectral methods. Third, it allows for a time-varying mean. Through these extensions, AdaptSPEC-X can estimate time-varying means and spectra at observed and unobserved covariate values, allowing for predictive inference. Estimation is performed by Markov chain Monte Carlo (MCMC) methods, combining data augmentation, reversible jump, and Riemann manifold Hamiltonian Monte Carlo techniques. We evaluate the methodology using simulated data, and describe applications to Australian rainfall data and measles incidence in the United States. Software implementing the method proposed in this article is available in the R package BayesSpec. Supplementary files for this article are available online.

Predicting short-term suicidal thoughts in adolescents using machine learning: developing decision tools to identify daily level risk after hospitalization.

Mobile technology offers unique opportunities for monitoring short-term suicide risk in daily life. In this study of suicidal adolescent inpatients, theoretically informed risk factors were assessed daily following discharge to predict near-term suicidal ideation and inform decision algorithms for identifying elevations in daily level risk, with implications for real-time suicide-focused interventions. Adolescents (N = 78; 67.9% female) completed brief surveys texted daily for 4 weeks after discharge (n = 1621 observations). Using multi-level classification and regression trees (CARTSs) with repeated 5-fold cross-validation, we tested (a) a simple prediction model incorporating previous-day scores for each of 10 risk factors, and (b) a more complex model incorporating, for each of these factors, a time-varying person-specific mean over prior days together with deviation from that mean. Models also incorporated missingness and contextual (study week, day of the week) indicators. The outcome was the presence/absence of next-day suicidal ideation. The best-performing model (cross-validated AUC = 0.86) was a complex model that included ideation duration, hopelessness, burdensomeness, and self-efficacy to refrain from suicidal action. An equivalent model that excluded ideation duration had acceptable overall performance (cross-validated AUC = 0.78). Models incorporating only previous-day scores, with and without ideation duration (cross-validated AUC of 0.82 and 0.75, respectively), showed relatively weaker performance. Results suggest that specific combinations of dynamic risk factors assessed in adolescents' daily life have promising utility in predicting next-day suicidal thoughts. Findings represent an important step in the development of decision tools identifying short-term risk as well as guiding timely interventions sensitive to proximal elevations in suicide risk in daily life.

Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors

Many financial and economic time series exhibit nonlinear patterns or relationships. However, most statistical methods for time series analysis are developed for mean-stationary processes that require transformation, such as differencing of the data. In this paper, we study a dynamic regression model with nonlinear, time-varying mean function, and autoregressive conditionally heteroscedastic errors. We propose an estimation approach based on the first two conditional moments of the response variable, which does not require specification of error distribution. Strong consistency and asymptotic normality of the proposed estimator is established under strong-mixing condition, so that the results apply to both stationary and mean-nonstationary processes. Moreover, the proposed approach is shown to be superior to the commonly used quasi-likelihood approach and the efficiency gain is significant when the (conditional) error distribution is asymmetric. We demonstrate through a real data example that the proposed method can identify a more accurate model than the quasi-likelihood method.

Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems.

Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.

Dynamic soliton–mean flow interaction with non-convex flux

The interaction of localised solitary waves with large-scale, time-varying dispersive mean flows subject to non-convex flux is studied in the framework of the modified Korteweg–de Vries (mKdV) equation, a canonical model for internal gravity wave propagation and potential vorticity fronts in stratified fluids. The effect of large amplitude, dynamically evolving mean flows on the propagation of localised waves – essentially ‘soliton steering’ by the mean flow – is considered. A recent theoretical and experimental study of this new type of dynamic soliton–mean flow interaction for convex flux has revealed two scenarios where the soliton either transmits through the varying mean flow or remains trapped inside it. In this paper, it is demonstrated that the presence of a non-convex cubic hydrodynamic flux introduces significant modifications to the scenarios for transmission and trapping. A reduced set of Whitham modulation equations is used to formulate a general mathematical framework for soliton–mean flow interaction with non-convex flux. Solitary wave trapping is stated in terms of crossing modulation characteristics. Non-convexity and positive dispersion – common for stratified fluids – imply the existence of localised, sharp transition fronts (kinks). Kinks play dual roles as a mean flow and a wave, imparting polarity reversal to solitons and dispersive mean flows, respectively. Numerical simulations of the mKdV equation agree with modulation theory predictions. The mathematical framework developed is general, not restricted to completely integrable equations like mKdV, enabling application beyond the mKdV setting to other fluid dynamic contexts subject to non-convex flux such as strongly nonlinear internal wave propagation that is prevalent in the ocean.

Time-varying mean–variance portfolio selection problem solving via LVI-PDNN

It is widely acclaimed that the Markowitz mean–variance portfolio selection is a very important investment strategy. One approach to solving the static mean–variance portfolio selection (MVPS) problem is based on the usage of quadratic programming (QP) methods. In this article, we define and study the time-varying mean–variance portfolio selection (TV-MVPS) problem both in the cases of a fixed target portfolio’s expected return and for all possible portfolio’s expected returns as a time-varying quadratic programming (TVQP) problem. The TV-MVPS also comprises the properties of a moving average. These properties make the TV-MVPS an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using an originally developed linear-variational-inequality primal–dual neural network (LVI-PDNN), we also provide an online solution to the static QP problem. To the best of our knowledge, this is an innovative approach that incorporates robust neural network techniques to provide an online, thus more realistic, solution to the TV-MVPS problem. In this way, we present an online solution to a time-varying financial problem while eliminating static method limitations. It has been shown that when applied simultaneously to TVQP problems subject to equality, inequality and boundary constraints, the LVI-PDNN approaches the theoretical solution. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to conventional MATLAB methods.

Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum-Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data.

Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum–Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum–Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.

Spatio-Temporal Encoding Improves Neuromorphic Tactile Texture Classification

With the increase in interest in the deployment of robots in unstructured environments to work alongside humans, the development of human-like sense of touch for robots becomes important. In this work, we implement a multi-channel neuromorphic tactile system that encodes contact episodes as discrete spike events that mimic the behavior of slow adapting mechanoreceptors. We study the impact of information pooling across artificial mechanoreceptors on classification performance of spatially non-uniform naturalistic textures. We encoded the spatio-temporal activation patterns of mechanoreceptors through gray-level co-occurrence matrix computed from time-varying mean spiking rate-based tactile response volume. We found that this approach greatly improved texture classification in comparison to the use of individual mechanoreceptor response alone. In addition, the performance was also more robust to changes in sliding velocity. The importance of exploiting precise spatial and temporal correlations between sensory channels is evident from the fact that on either removal of precise temporal information or altering of spatial structure of response pattern, a significant performance drop was observed. This study thus demonstrates the superiority of population coding approaches that can exploit the precise spatio-temporal information encoded in activation patterns of mechanoreceptor populations. It, therefore, makes an advance in the direction of development of bio-inspired tactile systems required for realistic touch applications in robotics and prostheses.

Active Simulation of Transient Wind Field in a Multiple-Fan Wind Tunnel via Deep Reinforcement Learning

AbstractThe transient wind field during a nonsynoptic wind event (e.g., thunderstorm downburst) presents time-varying mean and nonstationary fluctuating components, and hence is not easy to be repr...