An approach to a low dimensional covariance matrix for minimum variance beamforming

2014 ◽  
Author(s):  
Seyede Elham Shamsian ◽  
Sayed Mahmoud Sakhaei
Keyword(s):  
Covariance Matrix ◽  
Minimum Variance ◽  
Low Dimensional

scholarly journals Shrinking the Variance-Covariance Matrix: Simpler is Better

2016 ◽  
Vol 21 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Muhammad Husnain ◽  
Arshad Hassan ◽  
Eric Lamarque
Keyword(s):  
Root Mean Square Error ◽  
Covariance Matrix ◽  
Mean Square Error ◽  
Minimum Variance ◽  
Factor Models ◽  
The Philippines ◽  
Risk Profile ◽  
Additional Benefit ◽  
Mean Square ◽  
Weighted Portfolio

This study focuses on the estimation of the covariance matrix as an input to portfolio optimization. We compare 12 covariance estimators across four categories – conventional methods, factor models, portfolios of estimators and the shrinkage approach – applied to five emerging Asian economies (India, Indonesia, Pakistan, the Philippines and Thailand). We find that, in terms of the root mean square error and risk profile of minimum variance portfolios, investors gain no additional benefit from using the more complex shrinkage covariance estimators over the simpler, equally weighted portfolio of estimators in the sample countries.

scholarly journals MVDR Algorithm Based on Estimated Diagonal Loading for Beamforming

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yuteng Xiao ◽  
Jihang Yin ◽  
Honggang Qi ◽  
Hongsheng Yin ◽  
Gang Hua
Keyword(s):  
Signal Processing ◽  
Covariance Matrix ◽  
Optimization Model ◽  
Matrix Theory ◽  
Minimum Variance ◽  
Signal Model ◽  
Diagonal Loading ◽  
Minimum Variance Distortionless Response ◽  
The Matrix ◽  
Beamforming Algorithm

Beamforming algorithm is widely used in many signal processing fields. At present, the typical beamforming algorithm is MVDR (Minimum Variance Distortionless Response). However, the performance of MVDR algorithm relies on the accurate covariance matrix. The MVDR algorithm declines dramatically with the inaccurate covariance matrix. To solve the problem, studying the beamforming array signal model and beamforming MVDR algorithm, we improve MVDR algorithm based on estimated diagonal loading for beamforming. MVDR optimization model based on diagonal loading compensation is established and the interval of the diagonal loading compensation value is deduced on the basis of the matrix theory. The optimal diagonal loading value in the interval is also determined through the experimental method. The experimental results show that the algorithm compared with existing algorithms is practical and effective.

scholarly journals The GARCH (1, 1) Model As A Risk Predictor For International Portfolios

2011 ◽  
Vol 7 (11) ◽  
Author(s):  
Jean-François Laplante ◽  
Jean Desrochers ◽  
Jacques Préfontaine,
Keyword(s):  
Standard Deviation ◽  
Stock Returns ◽  
Covariance Matrix ◽  
Minimum Variance ◽  
Stock Index ◽  
Forecasting Model ◽  
Portfolio Risk ◽  
Volatility Forecasting ◽  
Forecasting Models ◽  
Minimum Variance Portfolio

This study pertains to forecasting portfolio risk using a GARCH (Generalized Autoregressive Conditional Heteroscedasticity) approach. Three models are compared to the GARCH model (1,1) i.e., random walk (RW), historical mean (HMM) and J.P. Morgans exponentially weighted moving average (EWMA). In recent years, many volatility forecasting models have been presented in the financial literature. Using the historical average of stock returns to determine the optimal portfolio is current practice in academic circles. However, we doubt the ability of this method to provide the best estimated portfolio variance. Moreover, an error in the estimated covariance matrix could result in a completely different portfolio mix. Consequently, we believe it would be relevant to examine the volatility forecasting model proposed in different studies to estimate the standard deviation of an efficient portfolio. With a view to building an efficient portfolio in an international context, we will analyze the forecasting models mentioned above. The purpose of this research is to determine whether a GARCH approach to forecasting the covariance matrix makes it possible to obtain a risk that most resembles the actual observed risk for a given return than the model traditionally used by practitioners and academic researchers. To this end, we selected six international stock indices. The study was conducted in a Canadian context and consequently, each stock index is converted into Canadian dollars. Initially, we estimate the covariance matrix for each forecasting model mentioned above. Then, we determine the proportions to invest in the portfolio and calculate the standard deviation of a minimum variance portfolio. Finally, the best model is selected based on the variances between estimated and actual risk by minimizing the root mean squared error (RMSE) for each forecasting model. Our results show that the GARCH (1,1) model is good for estimating risk in a minimum variance portfolio. As well, we find that it is statistically impossible to make a distinction between the accuracy of this model and the RW model. Lastly, our results show that based on the four statistical error measures used, the HMM is the least accurate for estimating portfolio risk. We therefore decided not to use this model and to rely instead on the GARCH approach or the RW, the simplest of all the models.

scholarly journals Seleção de carteiras ótimas sob restrições nas normas dos vetores de alocação: uma avaliação empírica com dados da BM&FBOVESPA

2015 ◽  
Vol 13 (3) ◽  
pp. 504
Author(s):  
Paulo Ferreira Naibert ◽  
João Caldeira
Keyword(s):  
Stock Market ◽  
Covariance Matrix ◽  
Portfolio Selection ◽  
Stock Exchange ◽  
Minimum Variance ◽  
Average Risk ◽  
Short Sale ◽  
Performance Indexes ◽  
Out Of Sample ◽  
Minimum Variance Portfolio

In this paper, we study the problem of minimum variance portfolio selection based on a recent methodology for portfolio optimization restricting the allocation vector proposed by Fan et al. (2012). To achieve this, we consider different conditional and unconditional covariance matrix estimators. The main contribution of this paper is one of empirical nature for the brazilian stock market. We evaluate out of sample performance indexes of the portfolios constructed for a set of 61 different stocks traded in the São Paulo stock exchange (BM&FBovespa). The results show that the restrictions on the norms of the allocation vector generate substantial gains in relation to the no short-sale portfolio, increasing the average risk-adjusted return (larger Sharpe Ratio) and lowering the portfolio turnover.

scholarly journals Evaluating Various Portfolio Optimization Strategies using High-Dimensional Covariance Matrix Estimators

2020 ◽  
Vol 9 (6) ◽  
pp. 64-67
Keyword(s):  
Portfolio Optimization ◽  
Covariance Matrix ◽  
Global Minimum ◽  
Evaluation Studies ◽  
Minimum Variance ◽  
Portfolio Allocation ◽  
New Strategy ◽  
Rotationally Invariant ◽  
Diversified Portfolio ◽  
Allocation Strategies

We compare the performance of multiple covariance matrix estimators for the purpose of portfolio optimization. This evaluation studies the ability of estimators like Sample Based Estimator (SCE), Ledoit-Wolf Estimator (LWE), and Rotationally Invariant Estimators (RIE) to estimate covariance matrix and their competency in fulfilling the objectives of various portfolio allocation strategies. In this paper, we have captured the effectiveness of strategies such as Global Minimum Variance (GMVP) and Most-Diversified Portfolio (MDP) to produce optimal portfolios. Additionally, we also propose a new strategy inspired from MDP: Most-Diversified Portfolio (MMDP), that enables diversification upon minimizing risk. Empirical evaluations show that by and large, MMDP furnishes the maximum returns. LWE are relatively more robust than SCE and RIE but RIE performs better under certain conditions.

Diagonal rejection-based minimum variance distortionless response for fiber underwater acoustic array

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740065
Author(s):  
Yang Chen ◽  
Ling Zou ◽  
Bin Zhou
Keyword(s):  
Covariance Matrix ◽  
Array Signal Processing ◽  
Spatial Filter ◽  
Minimum Variance ◽  
Observation Time ◽  
Small Aperture ◽  
Underwater Acoustic ◽  
Low Snr ◽  
Minimum Variance Distortionless Response ◽  
Acoustic Array

The high mounting precision of the fiber underwater acoustic array leads to an array manifold without perturbation. Besides, the targets are either static or slowly moving in azimuth in underwater acoustic array signal processing. Therefore, the covariance matrix can be estimated accurately by prolonging the observation time. However, this processing is limited to poor bearing resolution due to small aperture, low SNR and strong interferences. In this paper, diagonal rejection (DR) technology for Minimum Variance Distortionless Response (MVDR) was developed to enhance the resolution performance. The core idea of DR is rejecting the main diagonal elements of the covariance matrix to improve the output signal to interference and noise ratio (SINR). The definition of SINR here implicitly assumes independence between the spatial filter and the received observations at which the SINR is measured. The power of noise converges on the diagonal line in the covariance matrix and then it is integrated into the output beams. With the diagonal noise rejected by a factor smaller than 1, the array weights of MVDR will concentrate on interference suppression, leading to a better resolution capability. The algorithm was theoretically proved with optimal rejecting coefficient derived under both infinite and finite snapshots scenarios. Numerical simulations were conducted with an example of a linear array with eight elements half-wavelength spaced. Both resolution and Direction-of-Arrival (DOA) performances of MVDR and DR-based MVDR (DR–MVDR) were compared under different SNR and snapshot numbers. A conclusion can be drawn that with the covariance matrix accurately estimated, DR–MVDR can provide a lower sidelobe output level and a better bearing resolution capacity than MVDR without harming the DOA performance.

A Low-complexity Minimum-variance Beamformer Based on Orthogonal Decomposition of the Compounded Subspace

2020 ◽  
Vol 43 (1) ◽  
pp. 3-18
Author(s):  
Yinmeng Wang ◽  
Yanxing Qi ◽  
Yuanyuan Wang
Keyword(s):  
Computational Complexity ◽  
Covariance Matrix ◽  
Spatial Resolution ◽  
Low Complexity ◽  
Minimum Variance ◽  
Adaptive Beamforming ◽  
Orthogonal Decomposition ◽  
In Vivo Studies ◽  
Total Output ◽  
Accurate Estimation

Minimum-variance (MV) beamforming, as a typical adaptive beamforming method, has been widely studied in medical ultrasound imaging. This method achieves higher spatial resolution than traditional delay-and-sum (DAS) beamforming by minimizing the total output power while maintaining the desired signals. However, it suffers from high computational complexity due to the heavy calculation load when determining the inverse of the high-dimensional matrix. Low-complexity MV algorithms have been studied recently. In this study, we propose a novel MV beamformer based on orthogonal decomposition of the compounded subspace (CS) of the covariance matrix in synthetic aperture (SA) imaging, which aims to reduce the dimensions of the covariance matrix and therefore reduce the computational complexity. Multiwave spatial smoothing is applied to the echo signals for the accurate estimation of the covariance matrix, and adaptive weight vectors are calculated from the low-dimensional subspace of the original covariance matrix. We conducted simulation, experimental and in vivo studies to verify the performance of the proposed method. The results indicate that the proposed method performs well in maintaining the advantage of high spatial resolution and effectively reduces the computational complexity compared with the standard MV beamformer. In addition, the proposed method shows good robustness against sound velocity errors.

scholarly journals Target Matrix Estimators in Risk-Based Portfolios

2018 ◽  
Author(s):  
Marco Neffelli
Keyword(s):  
Covariance Matrix ◽  
Moving Average ◽  
Estimation Error ◽  
Minimum Variance ◽  
Sample Covariance Matrix ◽  
Sample Mean ◽  
Index Model ◽  
Single Index Model ◽  
Sample Covariance ◽  
Risk Contribution

Portfolio weights solely based on risk avoid estimation error from the sample mean, but they are still affected from the misspecification in the sample covariance matrix. To solve this problem, we shrink the covariance matrix towards the Identity, the Variance Identity, the Single-index model, the Common Covariance, the Constant Correlation and the Exponential Weighted Moving Average target matrices. By an extensive Monte Carlo simulation, we offer a comparative study of these target estimators, testing their ability in reproducing the true portfolio weights. We control for the dataset dimensionality and the shrinkage intensity in the Minimum Variance, Inverse Volatility, Equal-risk-contribution and Maximum Diversification portfolios. We find out that the Identity and Variance Identity have very good statistical properties, being well-conditioned also in high-dimensional dataset. In addition, the these two models are the best target towards to shrink: they minimise the misspecification in risk-based portfolio weights, generating estimates very close to the population values. Overall, shrinking the sample covariance matrix helps reducing weights misspecification, especially in the Minimum Variance and the Maximum Diversification portfolios. The Inverse Volatility and the Equal-Risk-Contribution portfolios are less sensitive to covariance misspecification, hence they benefit less from shrinkage.

scholarly journals Técnicas Quantitativas de Otimização de Carteiras Aplicadas ao Mercado de Ações Brasileiro

2012 ◽  
Vol 10 (3) ◽  
pp. 369
Author(s):  
André Alves Portela Santos ◽  
Cristina Tessari
Keyword(s):  
Covariance Matrix ◽  
Minimum Variance ◽  
Short Selling ◽  
Optimization Techniques ◽  
Market Portfolio ◽  
Sample Covariance ◽  
Out Of Sample ◽  
Weighted Portfolio ◽  
Performance Statistics ◽  
Mean Variance

In this paper we assess the out-of-sample performance of two alternative quantitative portfolio optimization techniques - mean-variance and minimum variance optimization – and compare their performance with respect to a naive 1/N (or equally-weighted) portfolio and also to the market portfolio given by the Ibovespa. We focus on short selling-constrained portfolios and consider alternative estimators for the covariance matrices: sample covariance matrix, RiskMetrics, and three covariance estimators proposed by Ledoit and Wolf (2003), Ledoit and Wolf (2004a) and Ledoit and Wolf (2004b). Taking into account alternative portfolio re-balancing frequencies, we compute out-of-sample performance statistics which indicate that the quantitative approaches delivered improved results in terms of lower portfolio volatility and better risk-adjusted returns. Moreover, the use of more sophisticated estimators for the covariance matrix generated optimal portfolios with lower turnover over time.

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