Explain the following concepts related to the analysis of _nancial time series, (a) Return, (b) Volatility, (c) Heteroskedasticity, and (d) Risk. Let Pk(t) be a k order polynomial de_ned by Pk(t) =...

Explain the following concepts related to the analysis of _nancial time

series, (a) Return, (b) Volatility, (c) Heteroskedasticity, and (d) Risk.

Let Pk(t) be a k order polynomial de_ned by

Pk(t) = a0 + a1t + a2t2 + aktk:

Show that (1 􀀀 B)kPk(t) = c, where c is a constant

Let yt = "t+X "t􀀀1 be a sequence of independent identically distributed

(i.i.d.) random variables, where X is a random variable with mean _ and

variance _2X

, f"tg is a sequence of i.i.d. random variables with zero-mean and

variance _2

" . Furthermore, X and f"tg are independent. Is fytg a weakly

stationary process? If this is true, calculate the autocovariance function of

fytg.