Questions tagged [covariance-estimation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2 votes
1 answer
77 views

Sample Variance of Portfolio

Let $w$ denote a vector of portfolio weights, $r_i$ denote the $i$th return vector, $\Sigma$ denote the Covariance matrix of $r_i$ and let $\hat{\Sigma}$ denote the sample covariance matrix of $r_i$. ...
user avatar
  • 137
1 vote
1 answer
124 views

Shrinkage of the Sample Covariance matrix, theory

is there any theory behind the covariance matrix shrinkage paper, why it works? I am talking about this stats exchange thread
user avatar
0 votes
2 answers
127 views

Number of Observations for Non-Singular Covariance Matrix Estimation

Marcos López de Prado writes the following in his book Advances in Financial Machine Learning: In general, we need at least \frac{1}{2} N (N+1) independent and ...
user avatar
  • 46
4 votes
0 answers
69 views

Implementing Hierarchical PCA for financial time series in R

I would like to implement the method "Hierarchical PCA", as described in the following paper and compare it to a "standard" PCA. I like to do this in R AVELLANEDA, Marco. ...
user avatar
  • 61
0 votes
1 answer
66 views

Odd Result from Computing Correlation Matrix from Kalman Filter Posteriori Covariance Estimate

I am using a Kalman Filter to estimate the return dynamics of a forwards curve on a particular commodity. My state space is the initial forwards values, and an initial guess of the drift functions for ...
user avatar
1 vote
0 answers
37 views

Can the covariance matrix be represented as a scalar or something similarly small, instead of a large pair-wise grid?

The covariance matrix tabulates pair-wise interactions between variables (assets) one-at-a-time into a grid, which can quickly become large as the number of assets included in a portfolio, for example,...
user avatar
  • 2,815
0 votes
1 answer
80 views

Update sample covariance matrix

I would like to update a covariance matrix $\mathbf{R}_T$ with a new incoming sample at time $T+1$, i.e. I would like a rank-1 update of the form $\frac{1}{T+1} [T \mathbf{R}_T + \mathbf{x}_{T+1}\...
user avatar
  • 101
1 vote
2 answers
244 views

Meaning of an identity matrix for the covariance in portfolio optimization

Instead of using a sample covariance matrix for portfolio optimization, Ledoit and Wolf use an estimator that is the weighted average of the sample covariance matrix and the identity matrix, $I$. This ...
user avatar
  • 2,815
0 votes
1 answer
214 views

Covariance Shrinkage in Black-Litterman Framework

Good evening guys I am looking into the effects of covariance shrinkage on the diversification of asset weights for different portfolio optimisations. Initially, I was interested to see how it affects ...
user avatar
  • 95
4 votes
1 answer
449 views

Ledoit/Wolf covariance shrinkage in risk-parity optimisation

This is more of a theoretical question. I have been working on some mean-variance / Black-Litterman models and played around with Ledoit/Wolf's covariance shrinkage method (sklearn function in Python)....
user avatar
  • 95
0 votes
1 answer
122 views

Effective Time Length of Exponentially Weighted Covariance Matrix Estimate

In [1] Pafka, Potters and Kondor mention the following in section 2: In contrast, if this covariance matrix estimate is used for portfolio optimization (i.e. for selecting the portfolio in a ...
user avatar
  • 442
1 vote
0 answers
69 views

Risk-Neutral covariance matrix of arbitrage-free Nelson Siegel

For my thesis on a Bayesian sampling routine for a modification on arbitrage-free Nelson-Siegel I came across an equation that involves a matrix exponential within an integral, i.e. $\int_{0}^{\Delta ...
user avatar
2 votes
2 answers
1k views

Creating a Covariance Matrix

Lets say that you have the correlation of x,y and you have the standard deviations of x and y , how would you then find the covariance of x,y using the correlation of x,y and and the standard ...
user avatar
  • 199
4 votes
6 answers
409 views

Is a more robust Covariance estimation possible?

I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...
user avatar
  • 169
1 vote
0 answers
44 views

Correlation coefficient without cash flows?

I'm an intern at a company and one of our tasks is to calculate the the probability of default of both participants of a Swap(a Client and a Bank), for which we first need the correlation coefficient ...
user avatar
  • 21
1 vote
1 answer
73 views

Misunderstanding of time series autocovariance

I'm reading the "Time Series: Theory and Methods (2nd ed.)" by P.J.Brockwell and R.A.Davis. I've stopped at the one moment at pp.218-219 (Chapter 7 "Estimation of the mean and the Autocovariance ...
user avatar
  • 221
1 vote
0 answers
162 views

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 ...
user avatar
4 votes
0 answers
142 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 ...
user avatar
  • 1,541
4 votes
1 answer
436 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 ...
user avatar
  • 478
1 vote
0 answers
144 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/...
user avatar
  • 11
0 votes
1 answer
569 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 ...
user avatar
  • 1,132
3 votes
0 answers
94 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 ...
user avatar
1 vote
0 answers
172 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 ...
user avatar
  • 191
2 votes
0 answers
245 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 ...
user avatar
  • 21
5 votes
2 answers
2k 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:...
user avatar
  • 1,626
4 votes
4 answers
10k 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 ...
user avatar
  • 1,541
1 vote
0 answers
169 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 ...
user avatar
2 votes
1 answer
131 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
user avatar
3 votes
2 answers
793 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 ...
user avatar
  • 31
8 votes
2 answers
4k 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 ...
user avatar
8 votes
0 answers
3k 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 ...
user avatar
  • 385
0 votes
1 answer
2k 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 ...
user avatar
  • 385
6 votes
0 answers
891 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 ...
user avatar
  • 13.2k
15 votes
1 answer
847 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 ...
user avatar
  • 1,543