1. a What is the main difference between time series observations and cross sectional observations?
b.What is covariance stationarity of a time series?
c.What is mean stationarity? Do the following time series seem to be mean stationary? Justify your answer?
d.What is the economic meaning of the series: log(Apple Stock Pricet ) – log(Apple Stock Pricet-1 ) ? What is it commonly called?
e.What is the term in economics for the variable measured in (iii)
2.Consider the following model:
Yt = 0.7 – 0.5 et-1 + 0.7 et-2 + et
where et is normally distributed white noise with zero mean and variance 0.04.
a.Derive h-period ahead optimal forecasts and corresponding forecast intervals (90%) of Yt for h=1, 2, 3, and 4. Your information set contains information up to period t. Assume that
et = 0.5, et-1 = – 0.1, et-2 = – 0.2, et-3 = 0.7, and et-4 = 0.3
b.Derive the unconditional mean and variance of the Yt process. How do your point forecasts and forecast variances in a. above compare with these unconditional mean and variance?
The full version is attached below.
Clear and step-by-step process is needed. Please answer with the important concepts and formulas.