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Measure Theory and Probability Theory

Krishna B. Athreya Soumendra N. Lahiri

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2006 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-32903-1

ISBN electrónico

978-0-387-35434-7

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, LLC 2006

Cobertura temática

Tabla de contenidos

Measures and Integration: An Informal Introduction

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 1-7

Measures

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 9-38

Integration

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 39-82

-Spaces

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 83-111

Differentiation

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 113-145

Product Measures, Convolutions, and Transforms

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 147-188

Probability Spaces

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 189-218

Independence

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 219-235

Laws of Large Numbers

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 237-285

Convergence in Distribution

Krishna B. Athreya; Soumendra N. Lahiri

In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.

Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.

We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.

Pp. 287-315