Search results for "correlation matrix"
showing 7 items of 7 documents
Spectral density of the correlation matrix of factor models: a random matrix theory approach.
2005
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.
Sparse model-based network inference using Gaussian graphical models
2010
We consider the problem of estimating a sparse dynamic Gaussian graphical model with L1 penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynamics, known presence or absence of links in the graphical model or equality constraints on the parameters. The model is defined on the basis of partial correlations, which results in a specific class precision matrices. A priori L1 penalized maximum likelihood estimation in this class is extremely difficult, because of the above mentioned constraints, the computational complexity of the L1 constraint on the side of the usual positive-definite constraint. The implementation is non-trivial, but we sh…
On the origin of power law tails in price fluctuations
2003
In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the response of prices to transactions. They argue that the average market impact function follows a square root law, which gives power law tails for prices with exponent roughly -3. We demonstrate that the long-memory nature of order flow invalidates their statistical analysis of market impact, and present a more careful analysis that properly takes this into account. This makes i…
Collective Behavior of Price Changes of ERC-20 Tokens
2020
We analyze a network constructed from tokens developed on Ethereum platform. We collect a large data set of ERC-20 token prices; the total market capitalization of the token set is 50.2 billion (109) US dollars. The token set includes 541 tokens; each one of them has a market capitalization of 1 million US dollars or more. We construct and analyze the networks based on cross-correlation of tokens’ returns. We find that the degree distributions of the resulting graphs do not follow the power law degree distribution. We cannot find any hierarchical structures nor groupings of ERC-20 tokens in our analysis. peerReviewed
Improving Harris corner selection strategy
2011
This study describes a corner selection strategy based on the Harris approach. Corners are usually defined as interest points for which intensity variation in the principal directions is locally maximised, as response from a filter given by the linear combination of the determinant and the trace of the autocorrelation matrix. The Harris corner detector, in its original definition, is only rotationally invariant, but scale-invariant and affine-covariant extensions have been developed. As one of the main drawbacks, corner detector performances are influenced by two user-given parameters: the linear combination coefficient and the response filter threshold. The main idea of the authors' approa…
Robustness of texture parameters for color texture analysis
2006
This article proposes to deal with noisy and variable size color textures. It also proposes to deal with quantization methods and to see how such methods change final results. The method we use to analyze the robustness of the textures consists of an auto-classification of modified textures. Texture parameters are computed for a set of original texture samples and stored into a database. Such a database is created for each quantization method. Textures from the set of original samples are then modified, eventually quantized and classified according to classes determined from a precomputed database. A classification is considered incorrect if the original texture is not retrieved. This metho…
Calculating the implied correlation matrix for a Path Analysis model
2014
To overcome the limitations of two existing methods for calculating a Path Analysis implied correlation matrix, this paper presents an alternative method for calculating this matrix. This new method is based on a recurrence principle which is easy and quick to implement. This method is also operational regardless of the number of variables. The consequences of this result with the estimation or testing stages will be illustrated on the basis of examples.