By Mariachiara Fortuna | May 17, 2020
Affiliations:
John K. Dagsvik, Statistics Norway, Research Department;
Mariachiara Fortuna, freelance statistician, Turin;
Sigmund Hov Moen, Westerdals Oslo School of Arts, Communication and Technology.
Corresponding author:
John K. Dagsvik, E-mail: john.dagsvik@ssb.no
Mariachiara Fortuna, E-mail: mariachiara.fortuna@vanlog.it (reference for code and analysis)
TABLES
Table 1. Parameter estimation for the selected time series
Estimation results for selected cities based on characteristic function regression and Whittle MLE method. Monthly data.
| City | H_c | SE(H_c) | H_w | SE(H_w) | Ann. H_c | Ann. H_w | Ann. SE(H_w) |
|---|---|---|---|---|---|---|---|
| Germany, Berlin | 0.664 | 0.009 | 0.662 | 0.012 | 0.726 | 0.712 | 0.041 |
| Switzerland, Geneva | 0.693 | 0.001 | 0.667 | 0.012 | 0.845 | 0.818 | 0.042 |
| Switzerland, Basel | 0.625 | 0.011 | 0.622 | 0.012 | 0.664 | 0.720 | 0.042 |
| France, Paris | 0.733 | 0.010 | 0.672 | 0.012 | 0.873 | 0.802 | 0.042 |
| Sweden, Stockholm | 0.681 | 0.015 | 0.721 | 0.012 | 0.614 | 0.632 | 0.041 |
| Italy, Milan | 0.724 | 0.019 | 0.709 | 0.012 | 0.851 | 0.826 | 0.043 |
| Czech Republic, Prague | 0.684 | 0.015 | 0.670 | 0.012 | 0.745 | 0.716 | 0.043 |
| Hungary, Budapest | 0.627 | 0.011 | 0.645 | 0.012 | 0.682 | 0.663 | 0.043 |
| Denmark, Copenhagen | 0.755 | 0.051 | 0.758 | 0.013 | 0.817 | 0.753 | 0.045 |
Table 2. Selected time series and Chi-square test
Chi-square statistics of the FGN hypothesis for selected cities
| City | \(Q(H_c)\) | \(Q(H_w)\) |
|---|---|---|
| Germany, Berlin | -0.518 | -0.626 |
| Switzerland, Geneva | -0.222 | -1.622 |
| Switzerland, Basel | -0.409 | -0.484 |
| France, Paris | 1.286 | -2.791 |
| Sweden, Stockholm | -1.209 | 1.098 |
| Italy, Milan | -1.339 | -2.335 |
| Czech Republic, Prague | -0.198 | -0.855 |
| Hungary, Budapest | -0.819 | -0.255 |
| Denmark, Copenhagen | -1.006 | -0.693 |
FIGURES
Figure 1. Illustration of statistical self-similarity. Annual temperature for Paris
Figure 2. Graphical tests of self-similarity and normality
Figure 3. Simulated FGN process with zero mean and unit variance
Figure 4. Reconstructed temperature data by Moberg et al. (2005a)
Figure 5. Test of self-similarity and normality
Reconstructed temperature data by Moberg et al. (2005a)
Figure 6. Empirical vs FGN autocorrelations
Reconstructed temperature data by Moberg et al. (2005a)
Empirical vs FGN autocorrelation with confidence bands. H=0.95