Wavelet Estimation Research Articles

Integration and volatility spillover amongst banks: a cross-correlation analysis

PurposeThe rising interconnectedness between international banks, at one end, allow participants to share risk and diversification which leads to stable local lending and increase in competitiveness, however, at the other end poses potential for volatility spillover and thereby contagion phenomena. Therefore, investigating the presence of co-integration amongst international banks can provide useful information about risk spillover in times of financial turbulenceDesign/methodology/approachThe authors employ wavelet correlation and wavelet multiple cross-correlation strategies, following an initial decomposition of returns series through maximal overlap discrete wavelet transformation (MODWT).FindingsThe results indicate high integration level between Citibank and Deutsche Bank whereas potential of diversification exists between pairs of Citibank–Hong Kong and Shanghai Banking Corporation and Bank of America–Deutsche Bank, with former more evident in short- and medium-term relationship and later in long-run investment horizon. This paper carries implications for investors, fund managers and policymakers in foreseeing the prospects of contagion attributable to high level integration levels.Practical implicationsImplications for cross-border banking integration includes the presence of common lender effect which appears as a dominant factor for cross-border contagion. Therefore, banks based in different countries should focus more on funds diversification rather than borrowing much from any single creditor. Furthermore, foreign operations based on subsidiaries instead of relying on direct cross-border lending can help in reducing volatility of the foreign financial resources. Nevertheless, based on the results and significant strand of existing literature, the presence of contagion is inevitable, and therefore, a careful consideration of cross-border banking supervision and co-operation by the financial authorities can help in mitigating the volatility of global capital flows.Originality/valueFirst, this study fills gap in the existing literature regarding the discussion on portfolio diversification opportunities in the banking sector. The banking sector is usually perceived as a main source of fixed income securities or financing; however, on the contrary, investors may also be interested for investments in publicly listed bank's stock. Most of the work regarding portfolio diversification revolves around capital market instruments; however, publicly listed shares of largest bank also present an avenue for diversification. Second, major fundamentals and the associated factor for banks performance are reflected in the its profits, either these profits result from large customer base or proper allocation of bank's assets, etc. Therefore, returns of these banks serve as a barometer for their performance and co-movement between any two banks can highlight the presence and extent of their underlying association. Third, the authors apply the latest extensions in wavelet techniques after decomposing returns series through the MODWT framework. This decomposition followed by wavelet estimations allow us to investigate banks integration level across different time and frequency space thereby carrying implications for both short- and long-run investors. Fourth, by analysing the presence of returns co-movements, the authors can predict the extent of plausible contagion since the recent global financial crisis of 2008–2009 used banks as the main medium of propagation of shocks. Fifth, the work presents many implications for the investment community, major trading partners associated with banks through different instruments and for policymakers so that the effect of contagion can be anticipated or at least mitigated in case of future financial turbulence.HighlightsWe investigate portfolio diversification opportunities in the banking sector.Time-frequency returns co-movements is measures by applying wavelet multiple correlation and cross-correlation techniques on decomposed return series.Deutsche Bank and Bank of America act as highest transmitter and recipient of volatility, respectively using the spillover approach of Diebold and Yilmaz (2012).Citibank and Deutsche Bank exhibit high pairwise correlation indicating no diversification benefits.Citibank exhibits high level of integration with other banks in the short- and medium-run whereas Deutsche Bank exercises high integration levels in the long-run investment period.

Multivariate wavelet density estimation for strong mixing stratified size-biased sample

This paper considers wavelet estimations of a multivariate density function based on stratified size-biased and strong mixing data. We provide upper bounds of the mean integrated squared error for linear and nonlinear wavelet estimators in Besov space It is shown that the linear estimator achieves the optimal convergence rate in the case of Moreover, the convergence rate of nonlinear estimator coincides with the optimal convergence rate up to a factor for In addition, the nonlinear wavelet estimator is adaptive.

The optimal wavelet estimation for biased density

In this paper, the optimal estimation at a given point is considered for biased density in theory. A lower bound is first provided for all possible estimators over the local Hölder space. Using wavelet method, a linear wavelet estimator is constructed and turned out to be optimal by investigating its upper bound of pointwise convergence rate. To get the adaptivity, a nonlinear wavelet estimator is obtained and proved to be near-optimal within a logarithmic factor.

Chebyshev wavelet approximation of functions having first derivative of H$$\ddot{\text {o}}$$lder’s class

In this paper, the Chebyshev wavelet approximations of a uniformly continuous function f and a functions f whose first derivative $$f'$$ of class $$H^\alpha [0,1), 0 < \alpha \le 1$$ , have been determined. These wavelet estimators are sharper, better and best possible in Wavelet analysis. A new method for solving differential equations by the Chebyshev wavelet method has been proposed. Lane-Emden and third-order pantograph non-linear differential equations have been solved by this method. The solutions of these equations have been compared by their exact solution. It is found that the exact solutions and solutions by the Chebyshev Wavelet method are nearly same. This is a significant achievement in wavelet analysis.

Practical considerations in the implementation of time-domain acoustic full waveform inversion

Full waveform inversion (FWI) plays a major role in the oil and gas industry as a state-of-the-art technique that produces quantitative subsurface structures with high-fidelity images. Various FWI studies have been conducted, and these suggest that FWI is a promising inversion method. Recently, many attempts have been made toward three-dimensional (3D) and four-dimensional FWI applications (which were difficult to perform in the past) because of the progress made in computer science and the growth of computer resources. To manage the very large data requirement of 3D problems, a time-domain FWI that is relatively efficient in terms of memory demands must be implemented. However, it could encounter practical issues, leading to failure in its convergence. In this paper, we introduce these practical issues and several alternative methods for mitigating them. The first issue is the bandpass filtering of the observed seismograms. We suggest that the frequency-domain filter based on a reference wavelet would be optimal in terms of both bandpass filtering and source wavelet estimation. The second issue is related to acoustic approximation. We show that a simple density model comprising only water and solid layers is a reasonable option to address seafloor reflectivity properly. The last issue is the accumulation of round-off errors due to the massive computation of the objective function. We demonstrate that a simple modification of the error calculation can resolve this round-off error problem.

Adaptive and optimal pointwise deconvolution density estimations by wavelets

This paper considers multivariate deconvolution density estimations under the local Holder condition by wavelet methods. A pointwise lower bound of the deconvolution model is first investigated; then we provide a linear wavelet estimate to obtain the optimal convergence rate. The nonlinear wavelet estimator is introduced for adaptivity, which attains a nearly optimal rate (optimal up to a logarithmic factor). Because the nonlinear wavelet estimator depends on an upper bound of the smoothness index of unknown functions, we finally discuss a data-driven version without any assumption on the estimated functions.

Single Image De-Hazing via Multiscale Wavelet Decomposition and Estimation with Fractional Gradient-Anisotropic Diffusion Fusion

This paper presents algorithms based on fractional multiscale gradient fusion and multilevel wavelet decomposition for underwater and hazy image enhancement. The algorithms utilize partial differential equation (PDE)-generated low- and high-frequency images fused via gradient domain and anisotropic diffusion. Furthermore, wavelet multi-level decomposition, estimation and adjustment of detail and approximation coefficients are employed in improving local and global enhancement. Solutions to halo effect are also developed using compressive bilateral filters or other nonlinear/nonlocal means filter. Ultimately, experimental comparisons indicate that the proposed methods surpass or are comparable to several algorithms from the literature.

Legendre wavelet approximation of functions having derivatives of Lipschitz class

In this paper, Legendre Wavelet approximation of functions f having first derivative f' and second derivative f'' of Lip? class, 0 &lt; ? ? 1, have been determined. These wavelet estimators are sharper, better and best possible in Wavelet Analysis. It is observed that the LegendreWavelet estimator of f whose f'' ? Lip? is sharper than the estimator of f having f ' ?Lip? class.

Wavelet estimation in heteroscedastic regression models with α-mixing random errors∗

We investigate the heteroscedastic regression model Yni = g(xni) + σnieni, i = 1, . . . , n, where $$ {\sigma}_{ni}^2 $$ = f(uni), (xni, uni) are known fixed design points, g and f are unknown functions, and the errors eni are assumed to form a stationary α-mixing random variables. Under some mild conditions, we obtain the asymptotic normality for wavelet estimators of f, prove their the asymptotic normality, and establish the Berry–Esseen-type bound for wavelet estimators of g. Also, by the given conditions we study the Berry–Esseen-type bound for estimators of g; for any δ > 0, it is of order O(n−(1/30)+δ). Finally, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.

Variational Bayesian Learning for Decentralized Blind Deconvolution of Seismic Signals Over Sensor Networks

This work discusses a variational Bayesian learning approach towards decentralized blind deconvolution of seismic signals within a sensor network. Blind seismic deconvolution is cast into a probabilistic framework based on Sparse Bayesian learning developed for blind image deconvolution. The posterior distribution of the signals of interest is then approximated using a variational Bayesian method. Depending on a particular form of selected variational factors, the scheme is shown to generalize the state-of-the-art distributed seismic blind deconvolution algorithm. The algorithm operates by repeatedly alternating between two stages: (i) estimation of seismic source wavelet and (ii) reflectivity estimation. The wavelet is estimated in a distributed fashion using Alternating Direction Method of Multipliers. Based on this estimate, each sensor then locally obtains a sparse reflectivity estimate. Numerical evaluation with synthetic seismic data shows that the proposed method outperforms existing deconvolution algorithms in a high signal-to-noise ratio (SNR) region. In low SNR regime a higher sensitivity of sparse Bayesian learning regarding model mismatches in the estimated source wavelet is observed. Also, processing of seismic data generated with an acoustic wave equation showed that the proposed method is able recover the original reflectivities more accurately, with more distinct support of the reflectivities, as compared to existing methods despite present model mismatches. The algorithm is also applied to the estimation of real seismic data, and shows improved performance as compared to state-of-the-art estimation method.

Estimating the distribution density function using a DOG wavelet

It is often necessary to obtain information on the distribution form of a random variable within the framework of statistical data analysis. There are several ways of estimating probability density distributions. Wavelet density estimators distribution of a random variable, built with DOG wavelet, would be considered. Three methods are proposed for determining the normalizing parameter, which provides a correction for the non-orthogonality of the DOG wavelet. In addition, studies have been carried out on the impact on quality wavelet estimates of parameters such as sample size, a number of coefficients of expansion, a function by series in the expression for wavelet density estimates. In the course of this process, it was noted that the quality of estimates on the smoothing parameter is substantial. Moreover, there is its best meaning. The conclusion is made that the estimate is based on DOG wavelet, provides quality recovery density functions.

A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods

The purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation method. We obtain rates of almost sure convergence over compact subsets of Rd. A general estimator beyond the wavelet methodology is also proposed, discussing adaptivity within this statistical framework.

Point-Wise Wavelet Estimation in the Convolution Structure Density Model

By using a kernel method, Lepski and Willer establish adaptive and optimal $$L^p$$ risk estimations in the convolution structure density model in 2017 and 2019. They assume their density functions to be in a Nikol’skii space. Motivated by their work, we first use a linear wavelet estimator to obtain a point-wise optimal estimation in the same model. We allow our densities to be in a local and anisotropic Holder space. Then a data driven method is used to obtain an adaptive and near-optimal estimation. Finally, we show the logarithmic factor necessary to get the adaptivity.

Time-varying wavelet estimation and deconvolution for nonstationary data based on a FWE function

• We present a nonstationary convolution model constituted of the reflectivity series and a time-varying wavelet matrix. • We propose a novel wavelet estimation method toextract time-varying wavelet at every instant for nonstationary seismic data . • We achieve blind deconvolution without assumptions about factor Q value and the source wavelet.

Statistical estimation for heteroscedastic semiparametric regression model with random errors

This paper is concerned with the estimating problem of heteroscedastic semiparametric regression model. We investigate the asymptotic normality for wavelet estimators of the slope parameter and the nonparametric component in the case of known error variance with ϕ-mixing random errors. Also, when the error variance is unknown, the asymptotic normality for the estimators of the slope parameter and the nonparametric component as well as variance function is considered under independent assumptions. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.

Consistency and asymptotic normality of wavelet estimator in a nonparametric regression model

In this paper, the nonparametric regression model with repeated measurements based on ϕ-mixing errors is considered. The rth mean consistency, strong consistency, strong convergence rate, complete consistency and the asymptotic normality of the wavelet estimator are established under some mild conditions on moments and mixing coefficients.

Pointwise Wavelet Estimation of Density Function with Change-Points Based on NA and Biased Sample

This paper is concerned with the density estimation problem of negatively associated biased sample with the presence of multiple change-points. We use the peaks-over-threshold approach to estimate the number and locations of change-points and give an equispaced design estimation to evaluate the jump sizes for the underlying density function. Subsequently, we propose a nonlinear wavelet change-point estimation of the underlying density and show the convergence rate under poinwise risk over Besov space. It should be pointed out that the convergence rate of wavelet change-point estimation is near optimal (up to a logarithmic term) and remains the same as that of the usual wavelet density estimation without change-points.

Anisotropic functional deconvolution for the irregular design: A minimax study

Anisotropic functional deconvolution model is investigated in the bivariate case when the design points ti , and xl , are irregular and follow known densities h 1, h 2, respectively. In particular, we focus on the case when the densities h 1 and h 2 have singularities, but and are still integrable on [0, 1]. We construct an adaptive wavelet estimator that attains asymptotically near-optimal convergence rates in a wide range of Besov balls. The convergence rates are completely new and depend on a balance between the smoothness and the spatial homogeneity of the unknown function f, the degree of ill-posed-ness of the convolution operator and the degrees of spatial irregularity associated with h 1 and h 2. Nevertheless, the spatial irregularity affects convergence rates only when f is spatially inhomogeneous in either direction.

Asymptotics for L_{1}-wavelet method for nonparametric regression

Wavelets are particularly useful because of their natural adaptive ability to characterize data with intrinsically local properties. When the data contain outliers or come from a population with a heavy-tailed distribution, L_{1}-estimation should obtain a better fit. In this paper, we propose a L_{1}-wavelet method for nonparametric regression, and derive the asymptotic properties of the L_{1}-wavelet estimator, including the Bahadur representation, the rate of convergence and asymptotic normality. The rate of convergence of it is comparable with the optimal convergence rate of the nonparametric estimation in nonparametric models, and it does not require the continuously differentiable conditions of a nonparametric function.

On the seismic wavelet estimative and reflectivity recovering based on linear inversion: Well-to-seismic tie on a real data set from Viking Graben, North Sea

Tying seismic data to well data is critical in reservoir characterization. In general, the main factors controlling a successful seismic well tie are an accurate time-depth relationship and a coherent wavelet estimate. Wavelet estimation methods are divided into two major groups: statistical and deterministic. Deterministic methods are based on using the seismic trace and the well data to estimate the wavelet. Statistical methods use only the seismic trace and generally require assumptions about the wavelet’s phase or a random process reflectivity series. We have compared the estimation of the wavelet for seismic well tie purposes through least-squares minimization and zero-order quadratic regularization with the results obtained from homomorphic deconvolution. Both methods make no assumption regarding the wavelet’s phase or the reflectivity. The best-estimated wavelet is used as the input to sparse-spike deconvolution to recover the reflectivity near the well location. The results show that the wavelets estimated from both deconvolutions are similar, which builds our confidence in their accuracy. The reflectivity of the seismic section is recovered according to known stratigraphic markers (from gamma-ray logs) present in the real data set from the Viking Graben field, Norway.