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Questions tagged [covariance-estimation]

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Estimating an GARCH(1,1) model? Long hand method

I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so ...
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38 views

Is Ledoit-Wolf Shrinkage with a Constant Correlation Prior Reasonable for a Stock/Bond Mix?

I've been looking into Ledoit-Wolf shrinkage but I've found the papers concentrate on large numbers of assets that tend to all be highly correlated. Often a universe of large cap stocks. I'm ...
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94 views

Shrink covariance or correlation matrix

Is it preferable to shrink the covariance matrix vs the correlation matrix? Technically this amounts to either shrinking the sample correlation matrix and then transforming the shrunk correlation ...
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0answers
78 views

Black Litterman - numerical instability

I am trying to work out the formula for the posterior mean in Black Litterman's model assuming 100% confidence : Ref: https://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/...
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Applicability of econometric models in forecating one-month ahead covariance matrices

For example, in the paper A Test of Covariance-Matrix Forecasting Methods, Zakamulin (2015) forecasts monthly covariance matrices by multivariate GARCH models from daily data. He does this by making ...
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1answer
227 views

Portfolio Optimisation/Covariance Estimation on a large scale

When using Markowitz Portfolio Theory, e.g. for finding an optimal portfolio composition, one needs to have estimates of the returns, but most importantly of the covariance matrix. If our universe of ...
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54 views

What is special about covariance estimation from statistical factor models?

If you were to compare the usual sample covariance estimate to a robust covariance estimate (such as MCD), you can say that the robust estimate is more tolerant to outliers in the data and will not be ...
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135 views

Fourier transform covariance estimator

I am estimating realized variance and covariance by the estimator described in this paper, and relying on Fourier Transform. Now, as my data is one day of data in ultra high frequency, so that the ...
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0answers
143 views

OHLC Covarianc Estimation

Is there an R package which can estimate a covariance matrix using OHLC (Open/High/Low/Close) share prices for upwards of 40 shares using the Yang & Zhang method using daily data? I google ...
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2answers
935 views

Implementation of Ledoit Wolf shrinkage estimator within R package tawny

I want to implement the shrinkage intensity given by Ledoit and Wolf, see here page 13. They define $y_{it}$ with $1\le i\le N$ and $1\le t\le t$ be the return on stock $i$ at time $t$. Moreover, $z_i:...
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2answers
3k views

Multivariate GARCH in Python

Is there a package to run simplified multivariate GARCH models in Python? I found the Arch package but that seems to work on only univariate models. I'd like to test out some of the more simple ...
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0answers
109 views

MLE estimate of normal distribution

Probably a naive question. I am quoting this from Greene's econometrics book: "The occasional statement that the properties of the MLE are only optimal in large samples is not true, however. It can ...
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1answer
101 views

Bayes Stein Porfolio Implementation

From this paper from Jorion. Has anyone implemented this? How is the Covariance matrix estimated? It needs to estimate also the conditional distribution of the returns? Best
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2answers
493 views

How to get Multivariate Betas from an Estimated EWMA co variance Matrix?

I have a portfolio of 4 assets. I also have returns for 3 indices. I want to get the multivariate betas for these 4 assets-based on these assets. I only have the 7 x 7 covariance matrix estimated by a ...
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2answers
3k views

Portfolio Optimization : Shrinkage of Covariance Matrix when data is available

It seems that shrinking the covariance matrix is especially useful if the number of individual stocks is greater than the number of data points. However is there any special gain if you're not ...
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0answers
966 views

Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
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1answer
1k views

Step-by-Step PCA algorithm (checking correctness without math packages)

I would appreciate if someone could correct me if i am wrong in my suggestion. I am using PCA to : find measure of cointegration between selected assets find the eigenvector and its portfolio with ...
6
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0answers
709 views

Shrinkage Estimator for Newey-West Covariance Matrix

I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$ \Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right), $$ where $\Sigma(i)$ is the lag ...
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1answer
524 views

Covariance estimation: shrinkage, random matrix theory, what else?

Shrinkage was much en-vogue before random matrix theory (RMT) took everybody's attention in covariance matrix estimation, however the latter also showed its limits. A plethora of other estimators has ...