Ļapunova indeksa pielietošana Markova GARCH (1,2)modeļa stacionaritātes analīzei
Loading...
Date
Authors
Advisor
Journal Title
Journal ISSN
Volume Title
Publisher
Latvijas Universitāte
Language
N/A
Abstract
Diplomdarbs veltīts procesam ar vispārināto autoregresīvo nosacīto heteroskedasticitāti – GARCH, kuriem dispersija ir nepastāvīga laikā. Tiek arī apskatītas GARCH procesa dažādas modifikācijas.
Darbā ir aprakstīts risinājuma algoritms n-dimensionālam lineāram stohastiskam diferenču vienādojumam, kura koeficienti ir atkarīgi no Markova ķēdes stāvokļiem.
Izmantojot šo algoritmu, aprēķināti piemēri, kuros ar Ļapunova indeksa palīdzību tiek atrasti ceturtā momenta stacionaritātes nosacījumi GARCH(1,2) procesam.
This Graduation work is dedicated to the process with generalized autoregressive conditional heteroskedasticity – GARCH, which variance is not permanent in time. Also examine different modifications of GARCH process. The solution’s algorithm for n-dimension linear stochastic difference equation with coefficients dependent on Markov chain states is described in this work. Using this algorithm some examples are solved, where the fourth moment stationarity conditions for GARCH(1,2) process were found with Lyapunov index help.
This Graduation work is dedicated to the process with generalized autoregressive conditional heteroskedasticity – GARCH, which variance is not permanent in time. Also examine different modifications of GARCH process. The solution’s algorithm for n-dimension linear stochastic difference equation with coefficients dependent on Markov chain states is described in this work. Using this algorithm some examples are solved, where the fourth moment stationarity conditions for GARCH(1,2) process were found with Lyapunov index help.