What is the conditional mean:

For every AR(1) model below:

a. Do a three-period ahead forecasting using the given initial values and statistics.  Write a 95% confidence interval for each forecast.

b. Do a long-run (unconditional) forecasting and write a 95% confidence interval.

a)  y_t = 1.6 + .75y_t-1 + e_t,                     y_t = 2,                          s² = 1.21        

b)  y _t = 2.5 + .3y _t-1 + e_t,                      y_t = 10,                                    s² = 6.25        

c)  y_t = 1.2 - .2y_t-1 + e_t,                        y_t = 1.5,                       s² = .49          

d)  Dy_t = 2.5 - .8Dy_t-1 + e_t,                  y_t = 6,  y_t-1 = 5,            s² = 3.69        

For every AR(2) model below:

a. Do a three-period ahead forecasting using the given initial values and statistics.  Write a 95% confidence interval for each forecast.

b. Do a long-run (unconditional) forecasting and write a 95% confidence interval.

a)  y_t =  6 + .7y_t-1 + .12y_t-2+ e_t,                        y_o = 5, y₁ = 6,              s² = 1.21        

b)  y _t = 2.5 + .3y _t-1 - .28y_t-2 + e_t,                     y_o = 1, y₁ = 2,              s² = 6.25        

c)  y_t = 1.2 - .2y_t-1 - .35y_t-2 + e_t,                        y_o = 1.5, y₁ = 2,           s² = .49          

d)  y_t = 2.5 - .07y_t-1 + .06y_t-2 + e_t,                    y_o = 6,    y₁ = 5,            s² = 3.69        

 

 

For the ARCH model, Y_t = 8.5 + .6Y_t-1 ,     Y_t = 10,     e_t = .5

                                               (3.2)  (2.8)

                                                e²_t = 1.2 + .2e²_t-1

 

1. What is the conditional mean of Y at times t+1, t+2, t+3?
2. What is the conditional variance of Y at times t+1, t+2, t+3?
3. What is the unconditional (long-run) mean of Y?
4. What is the unconditional (long-run) variance of Y?
5. Write 95% confidence interval for the long-run forecast of Y.
6. Write 95% confidence interval for forecasts of Y at time t+1, t+2, and t+3.

 

For the following ARCH model, Y_t = 4.5  + 0.4Y_t-1, Y_t = 5,     e_t = .3

                                                                   (3.2)  (2.8)

                                                                     e²_t = 2.6 + .8e²_t-1

1. What is the conditional mean of Y at times t+1, t+2, t+3?
2. What is the conditional variance of Y at times t+1, t+2, t+3?
3. What is the unconditional (long-run) mean of Y?
4. What is the unconditional (long-run) variance of Y?
5. Write 95% confidence interval for the long-run forecast of Y.
6. Write 95% confidence interval for forecasts of Y at time t+1, t+2, and t+3.

1.  Use The ARIMA file in the course site in BB. For each variables in the ARIMA file: 

a) Test for the stationarity of the variable.

b)  Do the correlogram of the variable and decide the order of the ARIMA(p, d, q).

c)  Run the best ARIMA model.

d) Do three period ex-ante dynamic forecasting and write 95% confidence intervals.

e) Do three period ex-post static forecasting and write 95% confidence intervals.

f) Do long-run forecasting of each variable and write 95% confidence interval.

Posted Date: 2/13/2013 12:24:19 AM | Location : United States

Ask an Expert

Related Discussions:- What is the conditional mean - initial values and statistics, Assignment Help, Ask Question on What is the conditional mean - initial values and statistics, Get Answer, Expert's Help, What is the conditional mean - initial values and statistics Discussions

Write discussion on What is the conditional mean - initial values and statistics
Your posts are moderated

Write your message here..

Related Questions

PRINCIPLE OF TRANSPORT ECONOMICS, IN YOUR OWN WORDS,HOW DO YOU DIFINE TRANS... IN YOUR OWN WORDS,HOW DO YOU DIFINE TRANSPORT ECONOMICS?GIVE RELAVANT EXAMPLES OF THIS AREA OF ECONOMICS.

Economic profit in a monopoly 2006 ap exam, is it just assumed that a monop... is it just assumed that a monopoly graph is showing economic profit instead of accounting profit

The demand for big macs, illustrate and explain the changing demand gor big... illustrate and explain the changing demand gor big Mac using the indifference curves and budget line

Why a high level of labor force growth is correlated, Why a high level of l... Why a high level of labor force growth is correlated A high level of labor force growth is correlated--even though less powerfully--with a low level of output per worker. The a

Uncertainty and risk, friedman and savage hypothesis friedman and savage hypothesis

Factors of production, The process of production needs several inputs. Thes... The process of production needs several inputs. These inputs are known as the factors of production. In most cases, firms own some of the factors of production while some have to b

Find the monopsony first mover competitive fringe buyer, Draw the suitable ... Draw the suitable graph for each situation and describe a real world situation in health care in which the market structure utilized in the question may exist. Demand: P=6,000-0

Determinants of social demand for education - excellence, Determinants of S... Determinants of Social Demand for Education - Excellence Apart from the three considerations identified by Prof. Musgrave for public investments in education and discussed abo

Lonief production function, f(x1 x2,x3,x4) =min(x1/4x22/3,x3+2x4) f(x1 x2,x3,x4) =min(x1/4x22/3,x3+2x4)

Modern Economics approach, what does General Equilibrium in consumption mea... what does General Equilibrium in consumption means?