Final Questions

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School

University of Houston, Downtown *

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4307

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Statistics

Date

Feb 20, 2024

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docx

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1

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WARNINGS: You are to work alone. Asking (..'.?.iffi‘:? for clarification are not allowed during the exam. Receiving or giving unauthorizec ance, or attempting to give or receive such assistance, in connection with exam will constitute a violation of the UHD Honor Code. INSTRUCTIONS: Show and properly label all of your work to receive full credit. You must use only RMarkdown for your work. Non-compliance to the solution/answer rules/instructions/guidelines will be penalized. Label your solutions/answers clearly in Rmarkdown or PDF/Word to ensure that due credits are given acccurately. Use code chunks whenever possible to avoid one big chunk of codes. Nonsubmission of an RMarkdown/R file or submission of an empty RMarkdown/R file will result to an automatic 70% penalty. There will be a 10% penalty for late submission for every five minutes after the due date and time. Upload only two files (RMarkdown and PDF/Word files only) in Blackboard. Show R codes in the PDF/Word file. Zip file submission will not be marked for credit Problem 1. (5 pts each) Explain or describe in layman’s terms (in only one sentence) what it means for a s to be i) invertible; ii) stationary. Problem 2. (5 pts each) Give an example of a process {z;} that satisfies the following (you can describe an example or cite a "named” example in class or write down an algebraic model.) Treat each criterion separately. Be very specific with your answers (i) A nor ry process or data with a constant mean. (ii) A stationary process or data that has nonzero autocorrelation at lag 4 only. ation (iii) A stationary process that has a lag 1 autocorrelation of -0.8 (iv) A nonstationary process whose first ordinary difference is weakly stationary Problem 3. (10 pts each) Let (i) 20 = 0.82¢-1 + wy 2we1; (i) 20 = Zem1 + wr 1.2we—1 + 0.3wy—2 For each model above, (a) Determine whether the model for {z;} is stationary and/or invertible. (b) Identify the model as an ARIMA (p,d,q) pr Problem 4. Let z; be the number of home runs hits allowed (denoted as HR) by the New York Yankees each year during 1903-2017. Download the csv file from Blackboard and use read.csv("yankees.csv"). (i) (10 pts)Using Box-Jenkins method (with appropriate transformation if needed to improve the model fit), find an appropriate model for the data. Write down the algebraic form of the fitted model. (i) (5 pts) Using auto.arima(), write your model in this format SARIM A(approriate data, p,d.q, P, D,Q,s). (i) (5 pts) Which of the two models do you prefer? Why? Name an advantage of Box-Jenkins over auto.arima (iv) (5 pts) The HR’s for the year 2018, 2019, and 2020 are 267,306, and 94, respectively. Compare your forecasts using your final model in one sentence. Problem 5. Consider the birth data from astsa package. Show the steps or details on how you arrive to your final model. . (i) (15 pts) Find a reasonable model (with ‘good’ fit) and write the model in this format SARIM Aapproriate data, p,d,q, P, D, Q, (i) (5 pts) Print and plot your predictions for the next six time periods. Problem 6. (5 pts) Using RMarkdown, produce a PDF or MS Word (where R codes are displayed in the PDF/Word file) of your work and upload both RMarkdown and PDF/Word files in Blackboard. Zip files will not be marked for cre
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