2

This has nothing to do with any specific model. For any event $A$, let $I_A$ be the indicator function such that $I_A(\omega)=1$ if $\omega\in A$ and $I_A(\omega)=0$ if $\omega\notin A.$ Then $\mathbb{P}(A)=\mathbb{E}[I_A],$ and here the expectation is given in terms of a density function.


2

Is there evidence for time varying second moments in annual economic data? Yes, although not that much in finance in particular but in economics in general resounding yes. For example, the highly cited Engle (2001), GARCH 101: The use of ARCH/GARCH models in applied econometrics, besides examples with daily data refers also to some examples with quarterly ...


2

The MSE is essentially a squared Euclidean distance between two vectors, say $\mathbf y$ and $\hat{\mathbf y}$, where $\mathbf y$ is the actual economic data over $T$ periods and $\hat{\mathbf{y}}$ the predicted values. A natural extension of this to matrices $\mathbf Y=(y_{it})$ and $\widehat{\mathbf Y}=(\hat y_{it})$ where $i=1,\dots,n$ and $t=1,\dots,T$ ($...


1

My question clearly is ; It is possible to use a nominal variable in a time series regression? (regardless of stationary issues) Is it possible? Yes. Should you actually do it? Probably not. Nominal variables are combination of real variables and prices. For example, nominal consumption $C_n$ will be given by: $$C_n = P C_r$$ where $C_r$ is real consumption....


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