Interpreting a Return and Variance ARMA-GARCH Specification

Summary

The document presents a proposed model for the change in a return-like series, with the conditional mean depending on the current level and variance. The innovation is specified as normally distributed with that variance. The variance equation depends on a constant, the current series level, lagged variance, and the previous squared innovation. The author asks what kind of ARMA-GARCH model this represents and how to specify it in the R package rugarch.

The equations expose a modeling question rather than provide a worked answer. In particular, the variance recursion includes a linear term in the series level, alongside the usual lagged variance and squared-shock components, so a standard GARCH label or direct package specification cannot be confirmed from the document alone. No estimation results, data context, constraints, or implementation details are supplied. The material is useful as an example for identifying and checking a conditional mean and variance specification, but it does not resolve whether the proposed variance process is supported by the package or statistically well behaved.

Key ideas

• The conditional mean includes the current series level and current variance.
• The innovation is assumed normal with conditional variance given by the model.
• The variance recursion combines a series-level term, lagged variance, and a lagged squared shock.
• The document asks for model classification and rugarch implementation but supplies no answer or empirical results.

Tags

# What kind of ARMA-GARCH model is that?


# What kind of ARMA-GARCH model is that?












My question is what kind of ARMA-GARCH model is the following equation and how to specify it in rugarch `R` module:

$$r_{t+1}- r_t = \alpha_0 + \alpha_1r_t+\alpha_2V_t+\epsilon_{t+1},$$ $$\epsilon_{t+1} \sim N(0,V_t), \text{and}$$ $$V_t = \beta_0 + \beta_1r_t + \beta_2V_{t-1}+\beta_3 \epsilon_t^2.$$

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.