1. Suppose that the simple return of a stock follows the model rt = 0.1 + at − 0.5at−2, where {at}T t=1 follows a white noise process with mean zero and variance σ2 a = 0.04. Please compute the following: (a). What is the mean of rt? (b). What is the variance of rt? (c). Compute the first order autocorrelation of rt. (d). Compute the second order autocorrelation of rt. (e). Assume that you are standing at period 100 and a100 = 0.01. Compute the 2-step-ahead forecast of the return.

1. Suppose that the simple return of a stock follows the modelrt = 0.1 + at − 0.5at−2,where {at}Tt=1 follows a white noise process with mean zero and variance σ2a = 0.04. Pleasecompute the following:(a). What is the mean of rt?(b). What is the variance of rt?

2. Suppose that we have an AR(2) model as follows:yt = 0.1 + ϕ1yt−1 + ϕ2yt−2 + ut,where ut follows a white noise process with mean zero and variance σ2u = 0.2. Please computethe following:(a). Assume that ϕ1 and ϕ2 take values that make the model stationary. What is the meanof yt?(b). Compute E[yt+1|Ωt].(c). Compute E[yt+2|Ωt]

EF4822 Financial Econometrics Problem Set 2 Due: Right before the class next week. Please submit hard copies in groups and write down the names and EID of all group members. If R programming is used, please show the R commands. 1. Suppose that the simple return of a stock follows the model rt = 0.1 + at − 0.5at−2, where {at}T t=1 follows a white noise process with mean zero and variance σ2 a = 0.04. Please compute the following: (a). What is the mean of rt? (b). What is the variance of rt?

Suppose that the monthly log return of a security 𝑟" follows the MA(1) model𝑟" = 𝑎" + 0.4𝑎"'& ,where {𝑎" } is a Gaussian white noise series with mean zero and variance 0.03.(a) Compute the mean and variance of the return series. (6 points)(b) Compute the lag-1 and lag-2 autocorrelations of the return series. (10 points)(c) Assume that 𝑎&$$ = 0.5. Compute the 1-step- and 2-step-ahead forecasts of the return at theforecast origin 𝑡 = 100. (8 points)(d) What are the standard deviations of the associated forecast errors? (6 points)

Consider a series that follows an MA(1) with zero mean and a moving average coefficient of 0.4. What is the value of the autocorrelation function at lag 1?Group of answer choices0.341It is not possible to determine the value of the autocovariances without knowing the disturbance variance0.4