Return Models and Covariance Matrices
(2014) FYSM60 20141Department of Physics
Mathematical Physics
- Abstract
- Return models and covariance matrices of return series have been studied. In particular, GARCH and SV models are compared with respect to their forecasting accuracy when applied to intraday return series. SV models are found to be considerably more accurate and more consistent in accuracy in forecasting.
Covariance matrices formed from Gaussian and GARCH return series, and in particular, return series auto-correlated as an AR(1) process, have been studied. In the case of Gaussian returns, the largest eigenvalue is found to approximately follow a gamma distribution also when the returns are auto-correlated. Expressions relating the mean and the variance of the asymptotic Gaussian distribution of the matrix elements are derived. In the... (More) - Return models and covariance matrices of return series have been studied. In particular, GARCH and SV models are compared with respect to their forecasting accuracy when applied to intraday return series. SV models are found to be considerably more accurate and more consistent in accuracy in forecasting.
Covariance matrices formed from Gaussian and GARCH return series, and in particular, return series auto-correlated as an AR(1) process, have been studied. In the case of Gaussian returns, the largest eigenvalue is found to approximately follow a gamma distribution also when the returns are auto-correlated. Expressions relating the mean and the variance of the asymptotic Gaussian distribution of the matrix elements are derived. In the case of GARCH returns, both the largest and the smallest eigenvalues of the covariance matrix are seen to increase with increasing auto-correlation. The matrix elements are found to follow Levy distributions with different Levy indexes for the diagonal and the non-diagonal elements.
Localization of eigenvectors of covariance matrices of returns from GARCH processes has been investigated. It is found that the localization is reduced as the auto-correlation is increased. Quantitatively, the number of localized eigenvectors
decreases approximately as a quadratic function with the auto-correlation strength, i.e. the autoregressive coefficient of the AR(1) process. (Less) - Popular Abstract
- Can we predict the movements of the financial market? The direct answer is "no", but there is more to be said. One cannot predict the price movement in an efficient market, but one can indeed predict how "volatile" the prices are (volatility). This does not lead to profits, but is useful for risk management --- if one pursues a profit, one must take a risk. Knowing and quantitatively managing the risks associated with investments, one often makes wiser decisions.
This report entails, first of all, a comparison of return models in the context of intraday returns. 6 return series are studied: Nordea, Volvo and Ericsson in the time scales of 15 and 30 minutes. Stochastic Volatility (SV) models and GARCH models are fitted to these series... (More) - Can we predict the movements of the financial market? The direct answer is "no", but there is more to be said. One cannot predict the price movement in an efficient market, but one can indeed predict how "volatile" the prices are (volatility). This does not lead to profits, but is useful for risk management --- if one pursues a profit, one must take a risk. Knowing and quantitatively managing the risks associated with investments, one often makes wiser decisions.
This report entails, first of all, a comparison of return models in the context of intraday returns. 6 return series are studied: Nordea, Volvo and Ericsson in the time scales of 15 and 30 minutes. Stochastic Volatility (SV) models and GARCH models are fitted to these series and the resulting volatility forecasts are compared. SV models are found to be more accurate in most cases.
Covariance matrices, which give the correlation between different companies, are also studied. In particular, the eigenvectors and eigenvalues of a covariance matrix, which respectively represent a set of driving factors of the companies' shares and the variances of these factors, are studied. It is found that when the return series are auto-correlated, i.e. when observations at different times are correlated, the eigenvectors are delocalized --- their expansion as a linear combination of the basis vectors involve more appreciable coefficients. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/4519670
- author
- Xie, Xiaolei LU
- supervisor
-
- Sven Åberg LU
- organization
- course
- FYSM60 20141
- year
- 2014
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- returns, stochastic volatility, GARCH, covariance matrix, random matrix, spectral distribution
- language
- English
- id
- 4519670
- date added to LUP
- 2014-06-27 10:30:57
- date last changed
- 2015-12-14 13:32:33
@misc{4519670,
abstract = {{Return models and covariance matrices of return series have been studied. In particular, GARCH and SV models are compared with respect to their forecasting accuracy when applied to intraday return series. SV models are found to be considerably more accurate and more consistent in accuracy in forecasting.
Covariance matrices formed from Gaussian and GARCH return series, and in particular, return series auto-correlated as an AR(1) process, have been studied. In the case of Gaussian returns, the largest eigenvalue is found to approximately follow a gamma distribution also when the returns are auto-correlated. Expressions relating the mean and the variance of the asymptotic Gaussian distribution of the matrix elements are derived. In the case of GARCH returns, both the largest and the smallest eigenvalues of the covariance matrix are seen to increase with increasing auto-correlation. The matrix elements are found to follow Levy distributions with different Levy indexes for the diagonal and the non-diagonal elements.
Localization of eigenvectors of covariance matrices of returns from GARCH processes has been investigated. It is found that the localization is reduced as the auto-correlation is increased. Quantitatively, the number of localized eigenvectors
decreases approximately as a quadratic function with the auto-correlation strength, i.e. the autoregressive coefficient of the AR(1) process.}},
author = {{Xie, Xiaolei}},
language = {{eng}},
note = {{Student Paper}},
title = {{Return Models and Covariance Matrices}},
year = {{2014}},
}