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PSTAT 174/274: Homework # 2

发布时间：2023-02-06

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PSTAT 174/274: Homework # 2 (week 2 & 3).

1. (both 174 & 274 attempt)

Review the lecture material in Module III (Home Work Reading: Preliminary Concepts). Discuss this with your tutors if you have any questions about this preliminary background mathematics and notation that will be used throughout the course.

In particular remind yourself of the following core concepts:

• Dirac notation (selection function)

• Geometric series

• Simple partial fractions

• Complex numbers and complex random variable

• Matrix inverse

2. (both 174 & 274 attempt)

Review the following two articles and their associate time series data sets produce by Our World in Data

https://ourworldindata.org/ by going to the following case study they provide:

• Artificial Intelligence https://ourworldindata.org/artificial-intelligence

Charlie Giattino, Edouard Mathieu, Julia Broden and Max Roser (2022) - ”Artificial Intelligence”. Published online at OurWorldInData.org. Retrieved from: ’https://ourworldindata.org/artificial- intelligence’ [Online Resource]

• Technology Adoption https://ourworldindata.org/technology-adoption

Hannah Ritchie and Max Roser (2017) - ”Technology Adoption”. Published online at OurWorldIn- Data.org. Retrieved from: ’https://ourworldindata.org/technology-adoption’[Online Resource]

summarise the key ideas from these time series case studies and write a 1 page executive summary explaining what the core arguments each case study is making and key take away messages. Download the data sets used and explore them further with some basic time series plotting or analysis of your choosing.

3. (both 174 & 274 attempt)

Start to plan your data case study (perhaps references like OurWorldinData can be useful starting guides).

Start to collect your sets of data (3-5 time series) for your term long assignment. Write a 1-2 page description of the data you have collected in an Rmarkdown, explaining:

• Why are these 3-5 time series data sets interesting to study - what practical problem or questions are they associated with or allow you to study or explore?

• Describe the properties of the time series with regard to the 5V’s of data. In particular explain your choices when selecting the data sets for the Volume, Velocity, Value, Variability, Veracity, Variety.

• Use the package naniar https://cran.r-project.org/web/packages/naniar/vignettes/naniar-visualisation.htmlto plot your data and determine if there is any missingness in your data records. explore various as- pects of this package visualisation to determine the veracity of your data selected for your term long project.

• create a sequence of R time series plots for each data set and explain the basic properties of the data empirically observed and what this may mean for structure in your time series.

• Summarise your findings with a short 1 page executive summary.

4. (both 174 & 274 attempt)

Rewrite the following expressions using Backshift operator notation or Difference Operator notation in time series:

• Yt−k + 4

• Yt − Yt−1 − 5

• Yt + 2Yt−1 − 3Yt−10

• 对 Yt−j

• 对i(j)=0 ( − 1)i ( )i(j) Yt−i

5. (both 174 & 274 attempt)

Find the partial fraction representation for the following expression:

(1 − 8x)(3 − 2x)