23 Jul Copyright APPMCU BoulderSTAT/MATH 4/5540 Project
Copyright APPMCU BoulderSTAT/MATH 4/5540 Project 2 Spring 2020by: Manuel LladserINSTRUCTIONS. Failure to follow these instructions may result in points discounted.This lab is due at 10 AM on Friday, March 20, 2020. Discussing this project with anyone besidesyour group partner (if any), the Instructor, or the TA is not permitted. By submitting a report,all its participants agree to comply with the CU Honor Code Policy.Students registered for APPM 4540 may work in groups of up to 2 members, and submit one projectreport with all participant names on it. Submit a single report in CANVAS. Due to the COVID-19 (coronavirus) outbreak, avoid meeting in person and instead collaborate remotelyusing some video conferencing such as Facetime, Skype, WhatsApp, or Zoom.Students registered for APPM 5540 must work on the project on their own.Your report is limited to 5 pages with a minimum font size of 11 points and 1-inch margins; inparticular, please provide complete but brief answers. Appendices do not count toward the pagelimit!To receive full credit, you must submit a professional report addressing all the instructions andquestions in the same order as requested. Be sure to include all gures or tables and to label them(e.g., Figure 1, Table 2, etc). Also, be sure to cite any sources (textbooks, papers, websites, etc)you consult. Your write-up should include brief but complete answers to all the questions listedbelow with appropriate references to labeled gures or tables. At the end of your report, includean appendix with the R code you used to address the project. The code must include annotations.Good luck!|o|In this project you will simulate your own ARMA time series to test some of the concepts andmethods discussed in lecture. In addressing the following questions, you may cite any result coveredin lecture as of Friday, March 13, 2020.Let > 0 be nite and Zt, with t 2 Z, be i.i.d. random variables with Zt Normal(0; 2).Consider the time series de ned as:Xt :=1Xj=02j + 12j Ztj ; for each t 2 Z: (?)1. Determine the mean function of fXtg.2. Show that 4Xt 4Xt1 + Xt2 = 4Zt + 2Zt1, for all t 2 Z.3. What type of ARMA process is fXtg? Justify!4. Is fXtg causal? Explain!5. Is fXtg invertible? Explain! In the armative case, represent each Zt as in nite linearcombination of Xj , with j t.6. Determine a homogeneous linear recursion with constant coecients satis ed by the auto-covariance function (h) of fXtg.1Copyright APPMCU Boulder7. Compute (0); : : : ; (3).8. Show that if Z Normal(0; 2) then EjZj = 2 q2 .9. Markov’s inequality states that for all random variable S and > 0: P(jSj ) EjSj=.Using this, determine k such that the probability that jPj Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline. Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax. We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers. To make an Order you only need to click on “Order Now” and we will
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