The Garch12.lng Model

Maximum Likelihood estimation of a GARCH model

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Maximum Likelihood estimation of a GARCH model.
Given a series of observations, we want to estimate the data generation process,
allowing variance to vary over time following a
first order generalized autoregressive conditional heteroscedasticity model
(i.e. GARCH(p,q), p=1 & q=1).
The y(t) are assumed to be generated by the process:
  y(t) = alpha0 + alpha1*x(t) + a(t),
  a(t) = s(t)*e(t),
  s(t)^2 = beta0 + beta1*a(t-1)^2 + beta2*s(t-1)^2.
where e(t) is white noise.

Reference: Hamilton, James D. (1994). Time Series Analysis,
Princeton University Press (see Chapter 21).
Based on a What'sBest! model by Eren Ocakverdi;


Econometrics | Forecasting | Time Series | Maximum Likelihood | GARCH | Heteroscedasticity | Volatility Modeling | ARIMA |