scholarly journals A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2083
Author(s):  
Won-Tak Hong ◽  
Jiwon Lee ◽  
Eunju Hwang
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Average Length ◽  
Real Data ◽  
Spot Price ◽  
Correlated Errors ◽  
Sample Mean ◽  
Q Model ◽  
Multiple Assets ◽  
Least Squares Estimates

In this work, multivariate heterogeneous autoregressive-realized volatility (HAR-RV) models are discussed with their least squares estimations. We consider multivariate HAR models of order p with q multiple assets to explore the relationships between two or more assets’ volatility. The strictly stationary solution of the HAR(p,q) model is investigated as well as the asymptotic normality theories of the least squares estimates are established in the cases of i.i.d. and correlated errors. In addition, an exponentially weighted multivariate HAR model with a common decay rate on the coefficients is discussed together with the common rate estimation. A Monte Carlo simulation is conducted to validate the estimations: sample mean and standard error of the estimates as well as empirical coverage and average length of confidence intervals are calculated. Lastly, real data of volatility of Gold spot price and S&P index are applied to the model and it is shown that the bivariate HAR model fitted by selected optimal lags and estimated coefficients is well matched with the volatility of the financial data.

Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications

1993 ◽  
Vol 9 (2) ◽  
pp. 263-282 ◽  
Author(s):  
In Choi
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Confidence Intervals ◽  
Unit Roots ◽  
Small Sample ◽  
Asymptotic Distributions ◽  
Standard Normal Distribution ◽  
Finite Sample ◽  
Standard Normal ◽  
Least Squares Estimates

Using the asymptotic normality of the least-squares estimates for the autoregressive (AR) process with real, positive unit roots and at least one stable root, we consider the asymptotic distributions of the Wald and t ratio tests on AR coefficients. In addition, we propose a method of constructing confidence intervals for the sum of AR coefficients possibly in the presence of a unit root. Using simulation methods, we compare the finite-sample cumulative distributions of the t ratios for individual autoregressive coefficients with those of standard normal distributions, and investigate the finite-sample performance of our confidence intervals and t ratios. Our simulation results show that the t ratios for nonstationary processes converge to a standard normal distribution more slowly than those for stationary processes. Further, the confidence intervals are shown to work reasonably well in moderately large samples, but they display unsatisfactory performance at small sample sizes.

Least-squares reverse time migration of multiples in viscoacoustic media

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. S285-S297
Author(s):  
Zhina Li ◽  
Zhenchun Li ◽  
Qingqing Li ◽  
Qingyang Li ◽  
Miaomiao Sun ◽  
...  
Keyword(s):  
Least Squares ◽  
Signal To Noise Ratio ◽  
Real Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Q Model ◽  
Standard Linear Solid ◽  
Standard Linear

The migration of multiples can provide complementary information about the subsurface, but crosstalk artifacts caused by the interference between different-order multiples reduce its reliability. To mitigate the crosstalk artifacts, least-squares reverse time migration (LSRTM) of multiples is suggested by some researchers. Multiples are more affected by attenuation than primaries because of the longer travel path. To avoid incorrect waveform matching during the inversion, we propose to include viscosity in the LSRTM implementation. A method of LSRTM of multiples is introduced based on a viscoacoustic wave equation, which is derived from the generalized standard linear solid model. The merit of the proposed method is that it not only compensates for the amplitude loss and phase change, which cannot be achieved by traditional RTM and LSRTM of multiples, but it also provides more information about the subsurface with fewer crosstalk artifacts by using multiples compared with the viscoacoustic LSRTM of primaries. Tests on sensitivity to the errors in the velocity model, the Q model, and the separated multiples reveal that accurate models and input multiples are vital to the image quality. Numerical tests on synthetic models and real data demonstrate the advantages of our approach in improving the quality of the image in terms of amplitude balancing and signal-to-noise ratio.

scholarly journals Integral Least-Squares Inferences for Semiparametric Models with Functional Data

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Limian Zhao ◽  
Peixin Zhao
Keyword(s):  
Data Analysis ◽  
Asymptotic Normality ◽  
Least Squares ◽  
Confidence Intervals ◽  
Functional Data ◽  
Estimation Method ◽  
Real Data ◽  
Semiparametric Models ◽  
Simulation Studies ◽  
Finite Sample

The inferences for semiparametric models with functional data are investigated. We propose an integral least-squares technique for estimating the parametric components, and the asymptotic normality of the resulting integral least-squares estimator is studied. For the nonparametric components, a local integral least-squares estimation method is proposed, and the asymptotic normality of the resulting estimator is also established. Based on these results, the confidence intervals for the parametric component and the nonparametric component are constructed. At last, some simulation studies and a real data analysis are undertaken to assess the finite sample performance of the proposed estimation method.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling

2021 ◽  
Vol 5 (1) ◽  
pp. 59
Author(s):  
Gaël Kermarrec ◽  
Niklas Schild ◽  
Jan Hartmann
Keyword(s):  
Least Squares ◽  
Laser Scanner ◽  
Real Data ◽  
Point Clouds ◽  
Statistical Testing ◽  
Normal Vector ◽  
Engineering Structures ◽  
3D Point Clouds ◽  
Least Squares Adjustment ◽  
Correlation Parameters

Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds.

scholarly journals Penalized partial least squares for pleiotropy

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Camilo Broc ◽  
Therese Truong ◽  
Benoit Liquet
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Association Studies ◽  
A Priori ◽  
Simulated Data ◽  
Real Data ◽  
Genome Wide Association Studies ◽  
Genetic Associations ◽  
Multiple Traits ◽  
Application Fields

Abstract Background The increasing number of genome-wide association studies (GWAS) has revealed several loci that are associated to multiple distinct phenotypes, suggesting the existence of pleiotropic effects. Highlighting these cross-phenotype genetic associations could help to identify and understand common biological mechanisms underlying some diseases. Common approaches test the association between genetic variants and multiple traits at the SNP level. In this paper, we propose a novel gene- and a pathway-level approach in the case where several independent GWAS on independent traits are available. The method is based on a generalization of the sparse group Partial Least Squares (sgPLS) to take into account groups of variables, and a Lasso penalization that links all independent data sets. This method, called joint-sgPLS, is able to convincingly detect signal at the variable level and at the group level. Results Our method has the advantage to propose a global readable model while coping with the architecture of data. It can outperform traditional methods and provides a wider insight in terms of a priori information. We compared the performance of the proposed method to other benchmark methods on simulated data and gave an example of application on real data with the aim to highlight common susceptibility variants to breast and thyroid cancers. Conclusion The joint-sgPLS shows interesting properties for detecting a signal. As an extension of the PLS, the method is suited for data with a large number of variables. The choice of Lasso penalization copes with architectures of groups of variables and observations sets. Furthermore, although the method has been applied to a genetic study, its formulation is adapted to any data with high number of variables and an exposed a priori architecture in other application fields.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

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