regression with ARMA_GARCH errors
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I want to estimate a regression model with ARMA(3,3) - GARCH(1,1) errors:
y_t = bX_t + e_t
e_t = a_1e_{t-1}+...+a_3e_{t-3} + u_t + r_1u_{t-1}+...+r_3u_{t-3}
u_t = h_tε_t
h_t = ω + αu^2_{t-1} + βh_{t-1}
I know I can do it in two steps. Estimate the regression first and then fit an ARMA model with GARCH variance to the residuals of the regression, however I was wondering If I could do it in one step. The obvious choice would be a regARIMA model but regARIMA model doesn't support garch(1,1) value in 'Variance'.
Thank in advance
2 个评论
Giovambattista Perciaccante
2017-12-20
suppose your observed variable is called:
yt
specify the model for the conditional variance as GARCH(1,1)
varmdl = garch('GARCHLags', 1, 'ARCHLags', 1)
You haven't estimated anithing yet.
Then specify the model for the mean as ARMA(3,3). Inside the function ARIMA you call the model for the variance specifying the option 'Variance'
mdl = arima('ARLags',3, 'MALags',3,'Variance', varmdl)
Again you haven't estimated anything yet.
Finally using the function ESTIMATE you estimate all the coefficients in one go:
es = estimate(mdl, yt)
Manthos Vogiatzoglou
2017-12-24
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