RiskARCH1
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Description |
RiskARCH1
ARCH processes are used when there is reason to believe that the variance of the process varies through time.
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Examples |
RiskARCH1(50, 10, 0.5, 49) generates an ARCH1 process with mean 50, volatility parameter 10, error coefficient 0.5, and value 49 at time 0. RiskARCH1(C10, C11, C12, C13) specifies an ARCH1 process with parameters taken from cells C10 to C13.
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Guidelines |
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Technical Details |
Define Then
where
The idea is that
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generates a first-order autoregressive conditional heteroskedasticity (ARCH1) process with mean 
, volatility parameter 
, error coefficient 
, and value 
at time 0. 
a sample from a Normal(0,1) distribution
is modeled as
is normally distributed with mean 
and variance 
, but this variance, conditional on the previous value of the process, is a weighted combination of the volatility parameter 
and the previous squared deviation from the mean.