Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNoise Dressing of Financial Correlation Matrices
167
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the present study is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). In particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.
rate research
Read More
Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed. We develop a new and alternative method to estimate this noise. To this end, we simulate certain time series and random matrices which can model financial correlations. With our approach, different correlation structures buried under this noise can be detected. Moreover, we introduce a measure for the relation between noise and correlations. Our method is based on a power mapping which efficiently suppresses the noise. Neither further data processing nor additional input is needed.
In this paper, we provide a negative answer to a long-standing open problem on the compatibility of Spearmans rho matrices. Following an equivalence of Spearmans rho matrices and linear correlation matrices for dimensions up to 9 in the literature, we show non-equivalence for dimensions 12 or higher. In particular, we connect this problem with the existence of a random vector under some linear projection restrictions in two characterization results.
I show analytically that the average of $k$ bootstrapped correlation matrices rapidly becomes positive-definite as $k$ increases, which provides a simple approach to regularize singular Pearson correlation matrices. If $n$ is the number of objects and $t$ the number of features, the averaged correlation matrix is almost surely positive-definite if $k> frac{e}{e-1}frac{n}{t}simeq 1.58frac{n}{t}$ in the limit of large $t$ and $n$. The probability of obtaining a positive-definite correlation matrix with $k$ bootstraps is also derived for finite $n$ and $t$. Finally, I demonstrate that the number of required bootstraps is always smaller than $n$. This method is particularly relevant in fields where $n$ is orders of magnitude larger than the size of data points $t$, e.g., in finance, genetics, social science, or image processing.
We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.
We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results for some colored noise signals.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
