Econometrics

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 Price_t ) – log(Apple Stock Price_t-1 ) ? What is it commonly called?

e.What is the term in economics for the variable measured in (iii)

2.Consider the following model:

Y_t = 0.7 – 0.5 e_t-1 + 0.7 e_t-2 + e_t

where e_t 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 Y_t for h=1, 2, 3, and 4. Your information set contains information up to period t. Assume that
e_t = 0.5, e_t-1 = – 0.1, e_t-2 = – 0.2, e_t-3 = 0.7, and e_t-4 = 0.3

b.Derive the unconditional mean and variance of the Y_t 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.

Thank you

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