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 Target Matrix Estimators in Risk-Based Portfolios

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 125 ◽  
Author(s):  
Marco Neffelli
Keyword(s):  
Covariance Matrix ◽  
Moving Average ◽  
Minimum Variance ◽  
Sample Covariance Matrix ◽  
Estimation Errors ◽  
Sample Mean ◽  
Index Model ◽  
Single Index Model ◽  
Sample Covariance ◽  
Risk Contribution

Portfolio weights solely based on risk avoid estimation errors 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. Using 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 (MV), Inverse Volatility (IV), Equal-Risk-Contribution (ERC), and Maximum Diversification (MD) portfolios. We find out that the Identity and Variance Identity have very good statistical properties, also being well conditioned in high-dimensional datasets. In addition, these two models are the best target towards which 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 to reduce weight 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 and so benefit less from shrinkage.

Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by VARMA

2020 ◽  
pp. 2150022
Author(s):  
Boping Tian ◽  
Yangchun Zhang ◽  
Wang Zhou
Keyword(s):  
Covariance Matrix ◽  
Moving Average ◽  
Sample Covariance Matrix ◽  
Autoregressive Moving Average ◽  
Average Model ◽  
Largest Eigenvalue ◽  
Vector Autoregressive ◽  
Autoregressive Moving Average Model ◽  
Sample Covariance ◽  
Moving Average Model

In this paper, we derive the Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by the vector autoregressive moving average model when the dimension is comparable to the sample size. This result is applied to make inference on the vector autoregressive moving average model. Simulations are conducted to demonstrate the finite sample performance of our inference.

scholarly journals A Sparse-Based Off-Grid DOA Estimation Method for Coprime Arrays

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 3025 ◽  
Author(s):  
Weijian Si ◽  
Fuhong Zeng ◽  
Changbo Hou ◽  
Zhanli Peng
Keyword(s):  
Covariance Matrix ◽  
Estimation Error ◽  
Estimation Method ◽  
Doa Estimation ◽  
Sample Covariance Matrix ◽  
Estimation Methods ◽  
Matrix Estimation ◽  
Estimation Process ◽  
Sample Covariance ◽  
Coprime Arrays

Recently, many sparse-based direction-of-arrival (DOA) estimation methods for coprime arrays have become popular for their excellent detection performance. However, these methods often suffer from grid mismatch problem due to the discretization of the potential angle space, which will cause DOA estimation performance degradation when the target is off-grid. To this end, we proposed a sparse-based off-grid DOA estimation method for coprime arrays in this paper, which includes two parts: coarse estimation process and fine estimation process. In the coarse estimation process, the grid points closest to the true DOAs, named coarse DOAs, are derived by solving an optimization problem, which is constructed according to the statistical property of the vectorized covariance matrix estimation error. Meanwhile, we eliminate the unknown noise variance effectively through a linear transformation. Due to finite snapshots effect, some undesirable correlation terms between signal and noise vectors exist in the sample covariance matrix. In the fine estimation process, we therefore remove the undesirable correlation terms from the sample covariance matrix first, and then utilize a two-step iterative method to update the grid biases. Combining the coarse DOAs with the grid biases, the final DOAs can be obtained. In the end, simulation results verify the effectiveness of the proposed method.

SHRINKAGE ESTIMATION OF MEAN-VARIANCE PORTFOLIO

2016 ◽  
Vol 19 (01) ◽  
pp. 1650003 ◽  
Author(s):  
YAN LIU ◽  
NGAI HANG CHAN ◽  
CHI TIM NG ◽  
SAMUEL PO SHING WONG
Keyword(s):  
Covariance Matrix ◽  
Sample Covariance Matrix ◽  
Risk Level ◽  
Sample Mean ◽  
Expected Gain ◽  
Sample Covariance ◽  
Shrinkage Method ◽  
Gain Loss ◽  
Mean Variance Portfolio ◽  
Mean Vector

This paper studies the optimal expected gain/loss of a portfolio at a given risk level when the initial investment is zero and the number of stocks [Formula: see text] grows with the sample size [Formula: see text]. A new estimator of the optimal expected gain/loss of such a portfolio is proposed after examining the behavior of the sample mean vector and the sample covariance matrix based on conditional expectations. It is found that the effect of the sample mean vector is additive and the effect of the sample covariance matrix is multiplicative, both of which over-predict the optimal expected gain/loss. By virtue of a shrinkage method, a new estimate is proposed when the sample covariance matrix is not invertible. The superiority of the proposed estimator is demonstrated by matrix inequalities and simulation studies.

Analysis of grid operation state based on improved maximum eigenvalue sample covariance matrix algorithm

2021 ◽  
pp. 095965182110012
Author(s):  
Dinghui Wu ◽  
Juan Zhang ◽  
Bo Wang ◽  
Tinglong Pan
Keyword(s):  
Covariance Matrix ◽  
Signal To Noise Ratio ◽  
Poor Performance ◽  
Sample Covariance Matrix ◽  
Maximum Eigenvalue ◽  
Signal To Noise ◽  
Matrix Algorithm ◽  
Sample Covariance ◽  
Noise Ratio ◽  
Application Fields

Traditional static threshold–based state analysis methods can be applied to specific signal-to-noise ratio situations but may present poor performance in the presence of large sizes and complexity of power system. In this article, an improved maximum eigenvalue sample covariance matrix algorithm is proposed, where a Marchenko–Pastur law–based dynamic threshold is introduced by taking all the eigenvalues exceeding the supremum into account for different signal-to-noise ratio situations, to improve the calculation efficiency and widen the application fields of existing methods. The comparison analysis based on IEEE 39-Bus system shows that the proposed algorithm outperforms the existing solutions in terms of calculation speed, anti-interference ability, and universality to different signal-to-noise ratio situations.

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