这是一篇来自美国的关于解决下面几个预测和风险分析问题的作业代写

1- Download monthly data for the time period 2018M1 to present, for Apple Corporation (AAPL) and S&P 500. Do the following estimates and the tests:

a.Graph the AAPL against time.  Comment on the existence of time trend, seasonal trend, cyclical trend, autocorrelation, randomness, structural breaks, and outliers.

b.Graph S&P 500 against time.  Comment on the existence of time trend, seasonal trend, cyclical trend, autocorrelation, randomness, structural breaks, and outliers.

c.Graph AAPL and S&P500 against time.  Comment on the behavior and the relationship between the two variables.

d.Repeat a to c for the monthly returns to AAPL and S&P 500.

e.Compare the risk and return of AAPL with the risk and return to S&P 500.

f.Plot histograms of returns to AAPL and returns to S&P 500. Comment on the distribution of the returns.

g.Test whether the distributions of returns to AAP and returns to S&P 500 are normal or not.

h.Fit MA(5) and MA(9) on AAPL data and compare the accuracy criterion of the fits.

i.Fit WMA(5) on AAPL data and compare its accuracy of the fit with MA(5) and MA(9).

j.Fit simple ES to AAPL data and compare its accuracy of the fit with MA(5) and MA(9).

k.Do a one-period ahead forecasting of AAPL price using simple ES model.

l.Fit Holt-Winter ES to AAPL data and compare its accuracy of the fit with MA(5) and MA(9).

m.Doe a 3-period ahead forecasting of AAPL price using Holt-Winter ES model.

1. The monthly closing prices for AAPL for the past two period and the forecast of the price is listed as:

Date Closing Price Forecast of Closing Price

Sep 2, 2014        100.75     98.80

Oct 1, 2014          97.67    101.62

a.Given that the damping effect, a= .05, do next two-periods ES forecast of the prices for Nov and Dec of 2014.

b.If SE of the forecast is 1.8, write 95% confidence interval for the forecast of November 2014.

3- Write the order of the following ARIMA models and explain whether each model is stationary or non-stationary, invertible or not.  In each case explain why.

a) yt= 2.5 +.35 yt-1

b) yt= 4.5 – 1.5 yt-1+ et -.5et-1

c) yt= 1.2 + .75 yt-1+ .3yt-2

d) yt= 2.5 + .95 yt-1+ et -.5et-1 -.2et-2

e) yt= .52 + 1.2 yt-1+ et + .2et-1

f) Dyt= 1.2Dyt-1

g) Dyt= .42Dyt-1+ et -.6et-1

h) Dyt= .62yt-1+ et -.6et-1

i) yt= 2.5 + .95Dyt-1

j) yt= 1.6 + et-.6et-1

1.  For every AR(1) model below:

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

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

a)  yt= 1.6 + .75yt-1, yo= 2, s2 = 1.21

b)  yt= 2.5 + .3y t-1, yo = 10, s2 = 6.25

c)  yt= 1.2 – .2yt-1, yo= 1.5, s2 = .49

d)  yt= 2.5 – .8yt-1, yo= 6, s2 = 3.69

e)  yt= -.5yt-1, yo= -1.6, s2 = 1.44

1. For every AR(2) model below:

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

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

a)  yt=  6 + .7yt-1+ .12yt-2, yt-1 = 5,    yt = 6, s2 = 1.21

b)  yt= 2.5 + .3y t-1 – .28yt-2, yt-1 = 1,    yt = 2, s2 = 6.25

c)  yt= 1.2 – .2yt-1– .35yt-2 , yt-1 = 1.5, yt = 2, s2 = .49

d)  yt= 2.5 – .07yt-1+ .06yt-2, yt-1 = 6,    yt = 5, s2 = 3.69

6.Correlogram and the Order of ARIMA

1. What is auto-correlation function (ACF)?
2.  What is partial auto-correlation function (PACF)?
3. Given the following correlograms write the order of the ARIMA for each model (a to d).

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