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. (6 Marks) (b) Write down the full set of equations for a time series (Xt)tZ following an AR(1) model with non-zero mean and ARCH(1) errors (3 Marks) (c) Discuss any three implications of the univariate and multivariate stylized facts of financial returns to risk modeling ( 6 Marks)