Plagiarism free pls

What is the stationarity condition for an AR(1) model ?

Please explain what is the defination of the autocorrelation function (ACF) and how to test it?

Q1 In the following linear AR(1) model, rt is the log price of a security at time t.

,

here at is a random process obeying normal distribution N( µ, σ2) with mean µ and variance σ2, such as the following

∼ iid N(0, 0.36),

Assume further that r100 = 3.865. Compute the 95% interval forecast for r101 at the forecast origin t = 100.

Q2 Consider the following first 12 lags of sample PACF and some Information Criteria for a series of monthly stock returns from 01/1926 to 12/2008. Using the 5% significant level, please identify the order p of AR time series. How about the answer for 1% significance?