Interpreting Boundary Estimates in a GARCH(1,1) Model

Summary

The document presents a fitting issue in a GARCH(1,1) model estimated on return data: some datasets yield an ARCH coefficient alpha of zero and a GARCH coefficient beta near 0.999. It includes a model specification with a constant mean, no autoregressive mean terms, and a Student t error distribution, but provides no answer or diagnostic analysis.

In a standard GARCH(1,1) variance equation, alpha measures how strongly recent squared shocks affect conditional variance, while beta measures persistence from the previous variance estimate. Estimates at or near parameter boundaries can arise during fitting, but the document does not establish why they occur in these cases or whether the fitted model is adequate. Interpreting the result requires checking the data, parameter constraints, estimation output, and residual diagnostics; the supplied code and question alone do not demonstrate that volatility is truly unaffected by shocks or that persistence is exactly as high as the estimate suggests.

Key ideas

• The example reports an estimated alpha of zero and beta near 0.999 for some return datasets.
• In GARCH(1,1), alpha captures the effect of recent squared shocks on conditional variance.
• The beta parameter represents persistence from the preceding conditional variance.
• The document supplies a model specification but no explanation of the estimates or diagnostic evidence.

Tags

# I am getting an $\alpha=0$ in the GARCH(1,1) model. Is this normal and how must I interpret it?


# I am getting an $\alpha=0$ in the GARCH(1,1) model. Is this normal and how must I interpret it?












I am running a GARCH(1,1) on return data. For some data sets, I am getting an $\alpha=0$ and a $\beta$ of 0.999. Is this normal? If so how should I interpret it?

Here is my code, here j are daily returns

```
spec2<-ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,1)),mean.model = list(armaOrder = c(0, 0), include.mean = TRUE, arfima = FALSE),distribution.model = "std")

mod.fit.rugarch2<-ugarchfit(spec = spec2, data = as.numeric(j))
show(mod.fit.rugarch2)
```

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