Reference no: EM132188120
Xt follows the AR(1): Xt = 0.64 + 0.6 xt-1 + εt, εt ~ N(0,σε)
Today, XT = 3, do you predict that X will decrease or increase over the future?
Today, XT = 1, give your best forecast and a confidence interval for XT+1, XT+2
You estimate an ARCH(1) on a daily stock returns and find: ht = 0.000288 + 0.8 rt-12, where ht is the time varying variance. For practical purpose, you assume that the daily stock return is conditionally normal N(0,ht). There are exactly 250 days in the year.
a) What is the process of the squared daily return?
Prove that the annualized standard deviation of the daily stock return is 0.6.
b) Today's return was a big 6% jump.
What is your forecast for tomorrow's standard deviation?
Give a 95% confidence interval for tomorrow's return.
Compare with an unconditional confidence interval. Assume parameters are known values.