(a) State Sklar's Theorem, giving both the main statement and its converse. Explain the relevance of the result from the point of view of studying dependencies between random variables and constructing multivariate models for applications. (b) Write down the full set of equations for a time series (X₂)tez following an AR(1) model with non-zero mean and ARCH(1) errors (c) Discuss any three implications of the univariate and multivariate stylized facts of financial returns to risk modeling S

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
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4. (a) State Sklar's Theorem, giving both the main statement and its converse. Explain
the relevance of the result from the point of view of studying dependencies
between random variables and constructing multivariate models for applications.
(b) Write down the full set of equations for a time series (X+) tez following an AR(1)
model with non-zero mean and ARCH(1) errors
(c) Discuss any three implications of the univariate and multivariate stylized facts
of financial returns to risk modeling S
5
4-
Transcribed Image Text:4. (a) State Sklar's Theorem, giving both the main statement and its converse. Explain the relevance of the result from the point of view of studying dependencies between random variables and constructing multivariate models for applications. (b) Write down the full set of equations for a time series (X+) tez following an AR(1) model with non-zero mean and ARCH(1) errors (c) Discuss any three implications of the univariate and multivariate stylized facts of financial returns to risk modeling S 5 4-
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