+g2009g2869g2013g3047g2879g2869g2870+g2010g2869g2026g3047g2879g2869g2870(2) Moving one period forward: g2026g3047g2878g2869g2870=g2009g2868+g2009g2869g2013g3047g2870+g2010g2869g2026g3047g2870(3) Now consider the recursive formula for EWMA: g2026g3047g2878g2869|g3047g2870=g2019g2026g3047|g3047g2879g2869g2870+g46661−g2019g4667g4666g1844g3047−g1844g3364g4667g2870(4) Removing the conditionality: g2026g3047g2878g2869g2870=g2019g2026g3047g2870+g46661−g2019g4667g4666g1844g3047−g1844g3364g4667g2870(5) Under the GARCH(1,1) specification (Equation (3)), when g2009g2868=0, g2009g2869=1−g2019and g2010g2869=g2019; the GARCH(1,1) specification reverts to the recursive formula for the EWMA (Equation (5)). Therefore, the EWMA proves to be a special case of the GARCH(1,1) specification when g2009g2868=0, g2009g2869=1−g2019and g2010g2869=g2019.
Subscribe to view the full document.
BUSE4008 – AFRM  YS 2015 3. Estimate of the Long-Run VarianceUsing a GARCH(1,1) specification for the conditional variance, derive an estimate for the ‘true’ long-run variance. Explain clearly the steps you undertake in arriving at your estimate. Starting with the specification for the conditional variance under a GARCH(1,1) model: ℎg3047=g2009g2868+g2009g2869g2013g3047g2879g2869g2870+g2010g2869ℎg3047g2879g2869(1) Replacing ℎwith the more familiar notation for variance g4666g2026g2870g4667: g2026g3047g2870=g2009g2868+g2009g2869g2013g3047g2879g2869g2870+g2010g2869g2026g3047g2879g2869g2870(2) Moving one period forward: g2026g3047g2878g2869g2870=g2009g2868+g2009g2869g2013g3047g2870+g2010g2869g2026g3047g2870(3) As Equation (3) is set to describe the complete nature of the variance in determining a forecast for the conditional variance; it should therefore include both the short-run and long-run dynamics of the variance. It is assumed that if we can observe over an infinite horizon, the long-run dynamics of the variance it would be explained by a constant long-run variance. Under the conditional variance forecast for time g1872+1, the previous value of the error (ARCH) term and the previous value of the conditional variance (GARCH) term, are set to describe the short-run stochastic changes in the conditional variance. The contribution that these two terms make towards the overall variance forecast is dictated by their relative weightings. In this case, the relative
As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Temple University Fox School of Business ‘17, Course Hero Intern
I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
University of Pennsylvania ‘17, Course Hero Intern
The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Tulane University ‘16, Course Hero Intern
Ask Expert Tutors
You can ask 0 bonus questions
You can ask 0 questions (0 expire soon)
You can ask 0 questions
(will expire )