Statistical methods for scale-invariant and multifractal stochastic processes.
This thesis focuses on stochastic modeling, and statistical methods, in finance and in climate science. Two financial markets, short-term interest rates and electricity prices, are analyzed. We find that the evidence of mean reversion in short-term interest rates is week, while the “log-returns” of electricity prices have significant anti-correlations. More importantly, empirical analyses confirm the multifractal nature of these financial markets, and we propose multifractal models that incorporate the specific conditional mean reversion and level dependence. A second topic in the thesis is the analysis of regional (5◦ × 5◦ and 2◦ × 2◦ latitude- longitude) globally gridded surface temperature series for the time period 1900-2014, with respect to a linear trend and long-range dependence. We find statistically significant trends in most regions. However, we also demonstrate that the existence of a second scaling regime on decadal time scales will have an impact on trend detection. The last main result is an approximative maximum likelihood (ML) method for the log- normal multifractal random walk. It is shown that the ML method has applications beyond parameter estimation, and can for instance be used to compute various risk measures in financial markets.
ForlagUiT Norges arktiske universitet
UiT The Arctic University of Norway
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