Temperature fluctuation paper - Main Results

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:

Mariachiara Fortuna, E-mail: (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