Assignment Task
Question 1
Create a “personal” cheat sheet reviewing/summarizing Topic 1 through Topic 4.
Question 2
We wish to develop a time series model for Monthly U.S. Retail Sales of Bookstores using data from 2010 through 2021.
Below you will find a time series plot of Monthly U.S. Retail Sales of Bookstores from September 2010 through April 2021.
On the basis of the time series plot,
Decide whether Monthly U.S. Retail Sales of Bookstores, Yt is a stationary time series or not. Give a reason to support your answer.
On the basis of the time series plot,
b. Decide whether the Average Monthly Temperature in the United States (in Farenheit), Yt is a stationary time series or not. Give a reason to support your answer.
Question 3
Given below are the ACFs and PACFs from 3 stationary time series. Based on your examination of the ACFs and PACFs, propose a time series model for
Situation 1
Situation 2
Situation 3
Give a reason to support your answer in each case. If an appropriate model is not evident from these plots in any of the 3 situations, explain carefully why you believe this is so.
Situation 1
Situation 2
Situation 3
Question 4
Below you will find ESACF and the SCAN statistics from a time series with a stationary mean. Propose a time series model for the time series data based on
ESACF
SCAN
Give a reason to support your answer in each case
Question 5
An autoregressive model of order 1 (i.e. a AR(1)) model has been fit to n=1000 points from a stationary time series Yt. Given in the table below are the parameter estimates from the fitted AR(1) model, a plot of the time series and the predicted values and a table of the actual values, predicted values and residuals for time, t from 990 to 1000. Calculate the predicted value at time, t=1001. (Ensure that you provide details of your calculations, since incorrect answers without any further details will receive 0 points.)
Question 6
On the following pages you will find plots and output associated with two different time series models that have been fit to data (n=998).
Examine the ACF and PACF of the data. Suggest a time series model for the data. Give reasons to support your choice.
The first model fit to the data was Model 1: ARMA(1,1). Decide if this model is a
Valid model
Parsimonious model
Give a reason to support your answers to i. and ii.
The second model fit to the data was Model 2: ARMA(1,2). Decide if this model is a
Valid model
Parsimonious model
Give a reason to support your answers to i. and ii.
Which of these two models has a lower value of AIC?
Which of these two models has a lower value of SBC? Was this finding expected and if so, why?
The value of the time series for Time 999 is -1.467966889
Model 1: ARMA(1,1) predicts the value of the time series for Time 999 to be
-1.467966889 with a 95% Confidence Interval of (-2.743303518, 1.1857755298)
Model 2: ARMA(1,2) predicts the value of the time series for Time 999 to be
-1.467966889 with a 95% Confidence Interval of (-2.744812302, 1.1862208059)
Compare and contrast the predictions from Model 1 to Model 2. Which model would you expect to be more accurate and why?
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