1. Analyse the following time-series datasets which are available in R.
(1) Nile;
(2) treating;
(3) co2.
Write a short report in HTML from R Markdown describing the identification, estimation, and checking of the proposed models for each dataset. Provide appropriate graphs and clearly justify your choice of model in each case. Do not include any simulations. Note that there is no unique correct answer to each of these problems.
In case it is useful you can use LaTeX in the comment areas between R chunks (in the white areas), e.g.
$X_t - 0.8 X_{i-1} = Z_t - 0.2 Z_{t-1}$
becomes Xt − 0.8Xi−1 = Zt − 0.2Zt−1
2. (MATH4022 only) You work as a statistician for an environmental agency and your task is to provide a Statistical Report and an Executive Summary for an analysis of a dataset of lake levels for Mystery Lake. The aim of the project is to forecast the lake level above mean sea level (MSL) for the next three years, and provide uncertainty information. The data are available on the Moodle page in the file lakelevel.txt and consist of the MSL levels in months starting in January 1860 and ending in December 2019. The lakelevel.txt file contains a single time series of length n = 1920 presented in row order. In particular the first few values are 580.294 580.994 582.1426 584.1317
583.7293 583.0988 582.4333 ...
The Statistical Report should be produced in html from R Markdown and should be suitable for your peer statisticians to read and understand.
The Executive Summary should be maximum of one page of text that is suitable for a broad set of readers, including the CEO of the agency. Please make sure the Executive Summary contains only text and no figures.
Please ensure that you explain clearly what you are aiming to do and that you present, interpret and discuss your results in a professional manner. It is important to explain with comments how you (i) analysed the data (ii) fitted the models (iii) performed model selection (iv) checked the modelling assumptions and (v) calculated the forecasts.
Report length. The reports should not be too long. You should aim to convey the important details in a way which is easy to follow, but not excessively long. Think about someone reading it through and try to help make it easy for them. Make it clear, without too much repetition and avoid long items of numerical output.
Grading Each question will be marked out of 10:
• 5 marks for technical content, use of R and appropriate methods
• 5 marks for presentation and interpretation of results
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