Coursework1

Deadline:

Friday,14March2025,at12:00.

StudentDetails:Full Name:Student Number:

SubmissionInstructions:

• PleasesubmityourworkelectronicallyasasinglePDFfile(includingRcode,graphs,explana- tions, anddescriptions) via Blackboard.No more than 10 pages.
• PleasedoNotsubmitRscripts,youcancopythecodeintothePDF
• Itisyourresponsibilitytodouble-checkwhetheryousubmitthecorrect
• Emailsubmissionswillnotbe

MarkingCriteria:

• Courseworkismarkedoutof100 Thenumberofmarksofeachmainquestionisindicated at the beginning of each.
• TheworkshouldbeyourCopyingfromotherstudentsorresourceswillresultinaZEROmark.
• LateSubmission:Incaseswheretherearenoacceptedmitigatingcircumstances,latesubmission of coursework will lead automatically to the imposition of a penalty.Your mark will be reduced inlinewiththeUniversityspenaltiesschemeforlatesubmissionof TheUniversitys regulationsaboutthelatesubmissionofcourseworkarefoundinSenateRegulation7: governingtheAssessmentofTaughtProgrammes.Referspecificallyto7.94fordetailsonpenaltiesforlate submission.

Question[100marks]

ElectricityDemandPatternsinAdelaide

Adelaide is the capital and most populous city of South Australia, where electricity demand during summerishighlyvolatileandstronglyinfluencedbytemperature. Summerscanbeextremelyhot,anda significantportionofAdelaideselectricityconsumptionisdrivenbyairconditioning.Thisstudyaims to analyse whether sufficient capacity would be available to meet demand under different temperature scenarios.

Tocapturevariationsthroughouttheday,theanalysiswasconductedusinghalf-hourlydata,withapar- ticular focus on key periods when peak demand typically occurs (e.g., afternoon).The dataset includes half-hourly electricity demand records for Mondays in Adelaide from January 1, 2002, to March 31, 2007.It comprises 273 Mondays, with measurements taken every 30 minutes from 00:00 to 23:59. However,ouranalysiswillfocusonAdelaideselectricityconsumptionfromMarch31,2002,toMarch 31, 2007, covering 261 Mondays.

Asaresult,thisdatasetcanbeconsiderednon-periodicfunctionaldata(i.e.,apopulationof261curves). Please download the fda-MondayDemand.dat file to complete the following tasks.

Task1[40marks]

1. [10marks]Downloadthefda-MondayDemand.datdatafileandfollowtheinstructionstostruc- ture the Monday Electricity Demand dataset as a functional dataset.
2. [15 marks]Plot the entire time series from March 31, 2002, to March 31, 2007, covering 261 Mondays.In other words, visualize the dataset as a time series to observe its overall patterns and
3. 15 marks]Plot the electricity demand curves for the 1st, 2nd, and 99th Mondays on the same

Task2[60marks]

1. [20marks]Usethefunctionalsmoothingtechniquestoprocessthisdataset,andprovideadetailed description of your steps.
2. [20marks]Determinethesmoothingparameter?byGeneralizedCross-Validation,andprovidean explanation for your choice.
3. [20 marks]Using the selected value of?, smooth the dataset and generate a plot of the smoothed functional data. Describe the resulting curves from the smoothing process.