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SPRING SEMESTER 2021-2022

MATH 4022 - TIME SERIES AND FORECASTING

1. The dataset cet_temp .csv (available from the ‘ MATH4022 Assessed Coursework’ section of the MATH4022 moodle page) contains the annual mean temperature in degrees celsius for the years 1900 to 2021 (inclusive) for the Midlands region of England, recorded by the UK Meteorological Office Hadley Climate Centre and sourced from www .metoffice .gov .uk/hadobs/hadcet.

Once the dataset has been read into R (using the command read .csv), the annual mean temperature may be set as time series data using the command:

ts(cet_temp$avg_annual_temp_C,start=1900,frequency=1).

Your task is to analyse this dataset by fitting a suitable time series model to describe these data. You should write a short report to describe how you have identified and checked the fit of your chosen model. The equation of your final fitted model should be included in your report.

Please note, there is no unique, correct, solution to this task. Credit will awarded for appropriate justification and explanation of your model choice and communication of your results.

The R code used to produce your report should be suitably commented and included at the end of your report as a separate appendix for marking. Your report should be no longer than SIX A4 pages in length,

including all plots and/or tables but not including the appendix that contains your R code. This task will marked out of 10 with marks allocated as follows:

Technical content, appropriate methods and justification of your modelling: 4 Marks Overall presentation, writing and interpretation: 4 Marks Correct and appropriately commented R code: 2 Marks

2. At the beginning of 2020, suppose that you work as a statistician for a local government agency. The agency would like you to analyse a dataset of monthly average house prices in the East Midlands region and forecast some future average house prices.

The dataset em_house_prices .csv (available from the MATH4022 moodle page) contains mean house sale prices in East Midlands (in £GBP), calculated monthly, from January 2010 to December 2019.

Once the dataset has been read into R (using the command read .csv), the monthly average price may be set as time series data using the command:

ts(em_house_prices$average_price_gbp,start=2010,frequency=12).

Using this dataset, your task is to produce a time series model to forecast the monthly house prices for the first six months of 2020.

You should produce a short report that would be suitable for your peer statisticians/data scientists to understand. Your report should contain:

(i) The main aim(s) of your work.

(ii) A clear and succinct description of how you analysed the data and arrived at your final model. (iii) Information on how you checked model fit.

(iv) Information on the forecasted house prices for January–June 2020, together with associated uncertainty.

The first page of your report should be an ‘ Executive Summary’ in which you convey the main findings of your work. The executive summary must be no longer than one page, consisting of text and at most one

plot (with font size no smaller than 11 points). The executive summary must be concise and suitable for a broad set of non-statistician readers to understand, including the head of the local government agency.

The R code that you used for your work should be suitably commented and included as an appendix to your report for marking.

Your report should be no longer than 12 A4 pages in length, including all figures and tables but not including the R code appendix or one-page executive summary. When typing your work, a font size no smaller than 11 points should be used. Please note: this does not mean that a completely correct solution would need to be a 12 page report.

Throughout your report you should aim to convey important details of your work in a way which is easy to follow but not excessively long and credit will be given for this. When producing your report, think about someone reading it through and try to make it easy for them to understand your work. Try to be clear in your writing, without too much repetition, and avoid long items of numerical output.

This task will be marked out of 30, with marks allocated as follows:

Technical content, appropriate methods and justification of your modelling: 10 Marks Overall presentation, writing and interpretation of results: 10 Marks Executive summary: 5 Marks Correct and appropriately commented R code: 5 Marks