On the Invertibility of EGARCH(p,q)
Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH(p,q) model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH(p,q) parameters.
|Keywords||Leverage, asymmetry, existence, stochastic process, asymptotic properties, invertibility.|
|JEL||Time-Series Models; Dynamic Quantile Regressions (jel C22), Model Evaluation and Testing (jel C52), Financial Econometrics (jel C58), Financing Policy; Capital and Ownership Structure (jel G32)|
|Publisher||Erasmus University Rotterdam|
|Series||Econometric Institute Research Papers|
Martinet, G.G, & McAleer, M.J. (2015). On the Invertibility of EGARCH(p,q) (No. EI 2015-12). Econometric Institute Research Papers. Erasmus University Rotterdam. Retrieved from http://hdl.handle.net/1765/78126