| Title |
Quadratic ARCH models with long memory and QML estimation / |
| Translation of Title |
Kvadratiniai ilgosios atminties ARCH modeliai ir parametrų vertinimas kvazididžiausio tikėtinumo metodu. |
| Authors |
Škarnulis, Andrius |
| Full Text |
|
| Pages |
162 |
| Keywords [eng] |
ARCH ; long memory ; parametric estimation ; FIGARCH ; quasi-maximum likelihood |
| Abstract [eng] |
This dissertation focuses on quadratic ARCH models with long memory. The class of ARCH models was introduced in 1982 by Nobel prize winner Robert Engle. The main purpose of the introduction of these models was to mathematically describe empirical features (stylized facts) of financial time series. One of these stylized facts – the long memory, which is often characterized by a slow decay of autocorrelations. There is much discussion on controversies surrounding the existence of stationary long memory ARCH(∞) and its particular cases (especially FIGARCH equation) processes. For a long time it was thought that the ARCH(∞) models do not have a long memory stationary solution with the finite variance. We solved this controversy by showing that FIGARCH and integrated ARCH(∞) equations with zero intercept may have a nontrivial covariance stationary solution with a long memory. We provided a complete answer to the long standing conjecture of Ding and Granger (1996) about the existence of the Long Memory ARCH model. We also study the five-parametric QML estimation for a quadratic ARCH process with long memory and strictly positive conditional variance. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Doctoral thesis |
| Language |
English |
| Publication date |
2017 |
