Report

There are 9 graded tasks in this assignment, each one is worth 1 point; a score of 9 yields a grade of 10 for this group assignment. For scoring a 0.25 point resolution is used.

These solutions are given for the De Bilt file (the other stations give much similar results).

Task 0.1 (not graded)

Task 1.2

How can we use the find_frequency function to find the frequencies of all periodic pattern in the data? In other words, how can we iteratively detect the frequencies in the data? ‘Removing’ periodic patterns is done by actually accounting for them in the functional model, through the A-matrix.

Write your answer, detailing the procedure, in a bulleted list that describes the procedure in your report. [1 point; 0.25 per item]

Task 1.3

Include the resulting periodogram plot in your report. [1 point; deduct 0.25 per mistake]

Task 1.4 (not graded)

Task 1.6

Describe the steps taken in the previous task and the outcomes, and explain in your own words how the dominant frequencies were determined (list them in your report). [0.25]

How did you decide when to stop? Which frequencies do you consider to be dominant? [0.25] Include in your report the periodogram plot resulting from running find_frequency for the second time. [0.25]

Is the final (detrended) time series (i.e. the final least-squares residuals) stationary? [0.25] Explain. Include your answers in the report.

Task 2.2

• Include the numerical parameter estimates in your report. [0.25]

• What can you say about the parameters, do the parameter estimates make sense? [0.50]

• What time of the year is the temperature highest (on average)? [0.25]

Task 3.2

Include the ACF plot in your report. [0.5] What can you conclude from this ACF? [0.25] Do the residuals originate from a white noise process? [0.25]

Task 3.5

Include in your report the ACF plot of the residuals after fitting the AR(1) model. [0.25] What can you observe from this ACF? [0.25] Is the AR(1) model a good fit to the residuals? [0.25] What would you do if the AR(1) model is not a good fit to the residuals? [0.25]

Task 4.1

Include the numerical predicted temperature values in your report. [2x 0.5]

Task 5.1

Compute and make a plot of the daily temperature averaged over the 30 years time frame from 1991 to 2020. Include the resulting plot in your report. [1 point; deduct 0.25 per mistake]

Task 5.2

Compute the residuals of the daily mean temperature time series (the input with Part 0) with respect to the ‘daily temperature averaged over the 30 years time frame from 1991 to 2020’ just computed in Task 5.1.

Finally compute and plot the normalized autocovariance function (ACF) of these residuals (include the ACF plot of the residuals in your report [0.5]), and comment on this plot, e.g. comparing it with the ACF from Task 3.1. [0.5]

By Caspar Jungbacker, Delft University of Technology. CC BY 4.0, more info on the Credits page of Workbook.