Time-varying Variance Research Articles

Diversifying crude oil price risk with crude oil volatility index: The role of volatility-of-volatility

To understand the diversification benefit of crude oil volatility, we examine the return-volatility relation in the crude oil market, given the interaction of the volatility (VOL) and the volatility-of-volatility (VOV). We develop a novel empirical model of the crude oil price and crude oil volatility index (OVX) returns incorporating both time-varying and state-dependent variances and correlations, thus allowing us to identify distinct market regimes of VOL and VOV. We find that the behavior of the return-volatility relation is contingent on the prevailing VOV regimes. Specifically, in a low (high) VOV regime, the relation becomes less (more) negative as VOL increases. These empirical results therefore imply that the diversification benefit of crude oil volatility is far from uniform across the different market states. Finally, using our proposed empirical model, we demonstrate the economic significance of recognizing both the time-varying and state-dependent variances/correlations in portfolio risk forecasting and construction.

Time-frequency analysis of nonlinear structures under nonstationary excitation by directly solving structural dynamic equation through absolute displacement

The time-frequency evolution of seismic ground motion energy under strong earthquakes, which can be described by the evolutionary power spectral density (EPSD) matrix, will amplify the most unfavorable responses of members in nonlinear structural systems. However, the existing general finite element software fails to reduce the dimension of the EPSD matrix and then decouple time from frequency in frequency domain analysis. This failure greatly limits the simulation and calculation of multi-dimensional nonlinear structures with multiple degrees of freedom by the stochastic vibration theory. In this study, the pseudo excitation method (PEM), which can direct solve structural dynamic equations using absolute displacement, is used to derive the self-spectral and cross-spectral densities of seismic ground motions in one-dimensional and multi-dimensional cases. In MATLAB, the EPSD matrix is transformed into a four-dimensional uniform modulation excitation matrix independent of the time variable. Nonlinear iteration is conducted and the precise integration method (PIM) is employed through a transient analysis module. Furthermore, a simple one-dimensional example is presented to verify the correctness of the proposed algorithm herein. Finally, as an example, we select important parameters of the coherence model at different supports of a half-through three-span concrete-filled steel tubular (CFST) tied-arch bridge in view of real engineering conditions, and calculate the time-varying power spectrum and variance of the responses of arch ribs, arch feet and the bridge deck system. The results show that the theoretical derivation and the algorithm constructed in this paper can simulate the time-delay effect of the nonlinear structural system. This proves the feasibility of general finite element software in solving and analyzing random responses to multi-dimensional and multi-support non-stationary excitation of nonlinear structures.

SCARNet: using convolution neural network to predict time series with time-varying variance

SCARNet: using convolution neural network to predict time series with time-varying variance

Frame-wise speech extraction with recursive expectation maximization for partially deformable microphone arrays

Large-apertured wearable and deformable microphone arrays have shown their better performance than conventional small wearable and rigid microphone arrays for speech extraction tasks, especially when the desired speech is far away from the arrays or there exist a great number of directional noises in practical applications. Most existing beamforming methods that require the information of the desired sound direction often cannot be used directly on deformable arrays because their shape might continuously change over time. To tackle the problem of utilizing partially deformable microphone arrays for target speech extraction, this paper derives a frame-wise speech extraction method, which is referred to as the recursive multichannel Wiener filter with generalized Gamma priors. In this method, the complex spectrum of the desired speech is assumed to follow a zero-mean complex Gaussian distribution with time-varying variance, and the reciprocal of this time-varying variance known as the precision is further assumed to follow a Gamma distribution, while the complex spectrum of the noise is assumed to follow a zero-mean complex Gaussian distribution. Under these two assumptions, we derive the recursive expectation maximization algorithm to extract the desired speech in a frame-by-frame manner. Experimental results show the promising performance of the proposed method in terms of multiple objective metrics.

Jump-diffusion option pricing with non-IID jumps

This paper investigates how violations of the assumption that jumps are identically and independently distributed (IID) affect option prices. We characterize several types of IID jumps violations including jumps with time-varying means, time-varying variances, and time-varying autocorrelations, and analyze the combined effect of these violations on option prices. These IID violations affect option prices in different ways. Different effects of IID violations can either offset each other to eliminate the effect of isolated IID violations or can act as leverages increasing the magnitude of mispricing created by a single violation of the IID assumption. Our investigation is performed inside a new framework for the pricing of options that relaxes the assumption that jumps are IID. We derive three families of jump-diffusion option pricing formulae with non-IID jumps. Numerically and empirically, we show that the non-IID models can improve the BSM on the S&P 500 options for both in-samples and out-of-the-samples data in terms of SSE, AE and ARE.

A Nonparametric Test for Instantaneous Causality with Time-varying Variances

A Nonparametric Test for Instantaneous Causality with Time-varying Variances

Predictors of time-varying and time-invariant components of psychological distress during COVID-19 in the U.K. Household Longitudinal Study (understanding society).

To understand psychological distress during COVID-19, we need to ensure that the same construct is measured over time and investigate how much of the variance in distress is attributable to chronic time-invariant variance compared to transient time-varying variance. We conducted secondary data analyses of Understanding Society, a U.K. probability-based longitudinal study of adults, using prepandemic (2015-2020) and pandemic data (N = 17,761, April 2020-March 2021). Using the General Health Questionnaire-12 (GHQ-12), analyses encompassed (a) five annual waves before COVID-19 plus the first survey wave during COVID-19 and (b) eight (bi)monthly waves during COVID-19. We investigated (a) longitudinal measurement invariance of distress, (b) time-invariant and time-varying variance components of distress using latent trait-occasion modeling, and (c) predictors of these different variance components. In all analyses, unique measurement invariance in distress was established, indicating the same unidimensional construct was measured using the GHQ before and during COVID-19. Time-varying variance was higher at the first COVID-19 lockdown (April 2020, 61.2%) compared to before COVID-19 (∼50%), suggesting increased fluctuations in distress at the start of the pandemic. Sensitivity analyses with equal time lags pre- and during COVID-19 confirmed this interpretation. During the pandemic, the highest distress time-varying variance (40.7%) was detected in April 2020, decreasing to 29.0% (July 2020) after restrictions eased. Despite mean-level fluctuations, time-varying variance remained stable during subsequent lockdowns, indicating more rank-order stability after this first major disruption. Loneliness most strongly predicted time-varying variance during the first lockdown. Life dissatisfaction and financial difficulties were associated with both variance components throughout the pandemic. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Unifying Estimation and Inference for Linear Regression with Stationary and Integrated or Near-Integrated Variables

Abstract There is a discrepancy in the limiting distributions of least-squares estimators for stationary and integrated variables. For statistical inference, it must be decided which distribution should be used in advance. This motivates us to develop a unifying inference procedure based on weighted estimation. The asymptotic distributions of the proposed estimators are developed and a random weighting bootstrap method is proposed for constructing confidence regions. The proposed method outperforms existing methods (with time constant or time-varying error variance) in simulations. We further study the predictability of asset returns in a setting where some of our state variables are endogenous.

Global impacts of US monetary policy uncertainty shocks

We build a new empirical model, which admits time-varying variances of local structural shocks, to estimate the global impact of an increase in the volatility of US monetary policy shocks. By allowing for rich dynamic interaction between the endogenous variables and time-varying volatility in the global setting, we find that US interest rate uncertainty not only drives local output and inflation volatility, but also causes declines in output, inflation, and the interest rate. Moreover, we document strong global impacts, making the world move in a very synchronous way. Crucially, spillback effects are found to be significant even for the US economy.

Fast estimation of a large TVP-VAR model with score-driven volatilities

This paper proposes a fast approach to estimating a large time-varying parameter vector autoregressive (TVP-VAR) model. Based on a score-driven modeling framework, we first assume that the time-varying variances of random errors in each equation of the TVP-VAR are score-driven, and then propose filtering and smoothing procedures to estimate time-varying parameters and time-varying volatilities. We show that under the forgetting factors, the filtering estimation of time-varying parameters is equivalent to an equation-by-equation estimator, significantly reducing the dimension of state space and thus delivering fast estimation. Moreover, a fast smoothing estimation can be derived, avoiding the inverse of the super-high dimensional state equation covariance matrix. We provide dynamic model averaging (selection) and maximum likelihood estimates for forecasting and inference. Our simulation study shows that the proposed method is more accurate than the popular methods and enjoys tremendous computational gain from the equation-by-equation estimator. Finally, we conduct an empirical study on the dynamic connectedness of global stock markets, demonstrating the merits of our methods in real-time and ex-post analysis.

Heuristic method of adaptive filtering for noisy GARCH processes

In this paper, the filtering problems of the discrete systems with noisy GARCH(1,1) processes are discussed by the heuristic method. Based on the intuition that the density function of the noisy GARCH(1,1) process can be well approximated by its driving noise density function with time-varying variance, three different approximating methods are proposed, respectively. The first is to approximate the density function of the system measurement noise by its driving noise density function with time-varying variance, then calculate the iterative state vector and measurement vector. The second is only to use its driving noise density function to approximate the density function of the state noisy GARCH(1,1) process, and then calculate the iterative state and measurement vector. The third is to use its driving noise density functions with time-varying variances to directly approximate the density functions of the noisy GARCH(1,1) processes for the state and measurement vectors. The numerical simulation results demonstrate the effectiveness of our algorithms in the noisy GARCH(1,1) environment.

Thunderstorm gust response factor: A closed-form solution

The Davenport gust factor technique is an efficient approach for the estimate of the wind loading on structures due to synoptic winds and the availability of closed-form solutions favoured its implementation in codes and standards. The gust response factor was generalized for thunderstorm outflows based on the definition of suitable equivalent parameters to account for the nonstationary characteristics of the wind velocity. Its sensitivity to the shape of the slowly-varying mean wind velocity was investigated, showing that it has a significant impact on the gust response factor, especially when the structure is lowly-damped. In order to simplify the derivation of the gust response factor the present paper outlines the derivation of a closed-form solution for the equivalent parameters, starting from the approximation of the time-varying variance of the response. The gust response factor derived through the closed-form solution proposed is compared with numerical solution and the existing formulation from literature. Results show that the proposed solution is very accurate and accounts for the transient dynamic effects neglected by the existing formulation, providing an efficient and handy tool for the structural design.

Research on non-smooth signal identification algorithm for electronic communication in a two-way relay network

Abstract To better allow accurate identification of non-smooth signals in two-way relay networks. In this paper, an algorithm based on the two-way relay network system model, the RLS algorithm, is proposed. The algorithm introduces the recursive least squares principle algorithm to the basic cost function of nonsmooth signal identification, optimizes the signal identification model by exponential weighting, and uses the time-varying variance matrix and the optimal identification data separation matrix to make real-time estimates of the new cost function for obtaining nonsmooth signals. And a new index, the PI index, is introduced to define whether the non-stationary signal is stable and reliable. Through two sets of comparison tests, we can learn that the RLS algorithm based on the two-way relay network system is better than other algorithms in the identification of non-stationary signals. It shows that the RLS algorithm can better identify and manage the information flow in a two-way relay network, make the non-stationary signal more stable, and further improve the convergence and convergence speed of the non-stationary signal to provide a better information interaction experience for both sides of electronic communication.

Stochastic properties of nonlinear locally-nonstationary filters

This article delivers conditions for the existence of a unique stationary, ergodic and φ-mixing invertible solution for nonlinear time-varying parameter models that are locally non-stationary or explosive. The assumptions are different from existing conditions as they do not impose Lipschitz, bounded growth or drift restrictions. Instead we require that the time series contains resetting dynamics. These dynamics are present in time series with sudden changes, such as stock prices with financial bubbles. We explain how our results can be applied to multiple models with time-varying conditional mean and time-varying conditional variance. Additionally, we show the empirical relevance of locally non-stationary models by developing a robust score-driven locally-nonstationary location model that allows us to identify price bubbles. In particular, we revisit the early warning system for Alert of Price Spikes (ALPS) developed by the World Food Programme (WFP, 2014). Our model is able to correctly identify price bubbles both in-sample and out-of-sample. We show that this information can be crucially relevant for the Global Information Early Warning System of the Food and Agriculture Organization (GIEWS) of the United Nations which identifies market bubbles in prices of grains and cereals in order to manage and prevent impending food crises in developing countries.

Sub-band attention CNN with feature evaluation for chatter detection

In chatter detection, feature evaluation is an important task to identify mechanical systems and achieve higher classification accuracy. The importance of frequency bands is useful under various operating conditions. In this study, we propose a new methodology to identify the importance of frequency bands based on sub-band attention CNN. The sub-band attention CNN is a structure that combines the sub-band CNN and the attention layer. Unlike conventional CNNs that treat all frequency components with the same filter, the sub-band CNN processes different filters for each band. The attention layer is used to evaluate the importance of each band. The time-varying variance in frequency domain is used to extract chatter characteristics that vary greatly with time and it is used as an input for chatter detection. The useful frequency bands for chatter detection are obtained from the sub-band attention CNN. The importance of the frequency band is analyzed with the frequency response of the mechanical system.

An Optimized FIR Predictor for Incomplete Measurement Data of Hydrogen Masers Relative to an Optical Clock

By considering the observation samples of a hydrogen maser relative to an optical clock with time-varying variances, this paper proposes an optimized predictor based on the finite impulse response (FIR) to improve the predictability of hydrogen masers. The design idea and rationality of the predictor were characterized from a theoretical viewpoint, showing its potential predictability for missing partial measurement data or unequal interval measurement data. The prediction results for simulated hydrogen masers reveal its comparable predictability with least squares method (LS). As proof of concept, it was applied to the actual data of typical hydrogen maser relative to a <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">87</sup> Sr optical lattice clock developed by the National Institute of Metrology (NIM). Compared with the LS, the prediction error after 7 days obtained by the proposed method is ~40 ps smaller than LS.

Improving time-varying minimum variance portfolio through penalized likelihood estimation

Improving time-varying minimum variance portfolio through penalized likelihood estimation

Robust Adaptive Heading Tracking Fusion for Polarization Compass With Uncertain Dynamics and External Disturbances

For the polarization compass (PC), maintaining high-precision and high-robustness autonomous measurement of the heading information under conditions where the atmospheric polarized light is being blocked or disturbed represents a challenging problem. In this paper, the E-vector orientation algorithm, which provides high orientation accuracy and real-time performance in sunny weather, and the symmetric axis orientation algorithm, which offers a strong anti-interference ability in occluded environments, are integrated to solve this problem. Furthermore, an improved state error model is established to increase the accuracy of the heading estimation. To track the system state rapidly and circumvent the uncertainties caused by measurement noise variance, an improved variational Bayesian strong tracking cubature Kalman filter (VBSTCKF) is proposed to estimate both the state and the time-varying measurement noise variance accurately. In addition, a multi-frequency data fusion algorithm based on residual compensation is proposed to overcome the inconsistent sampling operation frequency problems of the two orientation algorithms. The outstanding feature is that the proposed multi-frequency VBSTCKF (MF-VBSTCKF) can improve the orientation precision and robustness while also ensuring the high-frequency output performance. Finally, experimental results acquired in occluded environments verify the superiority of the proposed method.

COVID-19 and risk spillovers of China's major financial markets: Evidence from time-varying variance decomposition and wavelet coherence analysis

COVID-19 has influenced financial markets drastically; however, this influence has received little attention, particularly in China. This study investigates risk spillovers across China's financial and shipping markets through dynamic spillover measures based on time-varying parameter vector autoregression and generalized forecast error variance decompositions. Stock, fund, and futures markets are identified as major risk senders, whereas other markets are identified as major risk receivers. Surprisingly, bonds, gold, and shipping are safe havens that facilitate portfolio optimization. Furthermore, using wavelet coherence analysis, we find that the coherence between dynamic total spillover and COVID-19 varies across time and frequency domains.

Forward detrending for heteroskedasticity-robust panel unit root testing

The variances of most economic time series display marked fluctuations over time. Panel unit root tests of the so-called first and second generation are not robust in such cases. In response to this problem, a few heteroskedasticity-robust panel unit root tests have been proposed. An important limitation of these tests is, however, that they become invalid if the data are trending. As a prominent means of drift adjustment under the panel unit root hypothesis, the (unweighted) forward detrending scheme of Breitung suffers from nuisance parameters if the data feature time-varying variances. In this article, we propose a weighted forward-detrending scheme. Unlike its unweighted counterpart, the new detrending scheme restores the pivotalness of the heteroskedasticity-robust panel unit root tests suggested by Demetrescu and Hanck and Herwartz et al. when applied to trending panels with heteroskedastic variances. As an empirical illustration, we provide evidence in favor of non-stationarity of health care expenditures as shares of GDP in a panel of OECD economies.