代做STATS 4A03 Homework 5调试数据库编程

Homework 5

STATS 4A03

Due on Crowdmark by Friday, April 5 at 11:59pm

Guidelines: Unless otherwise specified, you are required to justify and prove all your answers.

You are welcome and encouraged to collaborate with other students on homework assignments, and you should feel free to discuss the problems and talk about how to come up with solutions with each other. However, you are expected to write all your solutions independently of any collaborators and you should not share written solutions with other students before the deadline. If you collaborate with other students, you must cite any collaborators that you had on any given problem.

You may use the textbook and lecture slides. You are discouraged from using outside resources (online, Math stack, etc.), but if you decide to do so, you must cite all your sources. If your solution is too similar to the cited one, you may lose credit on the problem.

Your homework grade will be based on completeness plus the correctness of a random subset of four (4) problems.

Exercise 1. Suppose the annual sales (in millions of dollars) of some company follows an AR(2) model given by

Yt = 4 + Yt−1 − 0.4Yt−2 + et,

where σe 2 = 1 and the unit of time is in years.

a) Suppose the sales for 2015, 2016, and 2017 are $9 million, $10.9 million, and $10 million, respectively. Find the forecasts of the sales for 2018 and 2019.

b) Find the 0.95 prediction limits for the forecast of 2018.

c) Suppose the actual sales for 2018 is $11 million. Find the updated forecast for 2019.

Exercise 2. Using the estimated cosine trend on pg. 192 of the textbook,

a) Forecast the average monthly temperature in Dubuque, Iowa, for April 1976.

b) Find a 95% prediction interval for your forecast (the estimate of √γ0 for this model is 3.719◦ F).

c) What is the forecast for April 1977? For April 2009?

Exercise 3. Identify the following as certain multiplicative seasonal ARIMA models:

a) Yt = 0.5Yt−1 + Yt−4 − 0.5Yt−5 + et − 0.3et−1.

b) Yt = Yt−1 + Yt−12 − Yt−13 + et − 0.5et−1 − 0.5et−12 + 0.25et−13.

Exercise 4. Suppose that the process {Yt} develops according to Yt = Yt−4+et with Yt = et for t = 1, 2, 3, 4.

a) Find the variance function for {Yt}.

b) Find the autocorrelation function for {Yt}.

c) Identify the model for {Yt} as a certain seasonal ARIMA model.