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

Mid-life alcohol consumption and survival to age 90 in men: The Tromsø Study 1979–1980 with follow-up to 2019

Aims: The Tromsø Study 1979–1980 collected information on alcohol (beer, wine and spirits) consumption frequency and inebriation frequency, and the oldest male participants (aged 50–54 years) were followed for all-cause mortality. This study aimed to identify the impact of habitual alcohol consumption in mid-life on reaching up to 90 years of age. Results: Among the study sample of 778, a total of 120 (15.4%) men reached the age of 90. The most common reported alcohol consumption frequency was ‘never or a few times a year’, and 18.9% of those in this group reached 90 compared with 11.9% of those who reported a more frequent beer consumption. Fifty per cent survival in these groups was 80.5 and 76.9 years, respectively. The pattern was similar for spirits consumption and for inebriation but not for wine consumption. Number of deaths increased gradually with increasing beer and spirits consumption frequency and with inebriation frequency. We observed no J-shape or pattern that revealed a beneficial influence of light alcohol consumption. Daily smoking, physical inactivity, marital status, blood pressure and total cholesterol reduced the contribution of alcohol consumption to a small degree. Conclusions: This study shows that all beer and spirits consumption frequencies in mid-life affect later life and total lifespan. Refraining from alcohol consumption or drinking only a few times a year increases one’s chances of living longer, and the chance of reaching 90 years of age is 1.6-fold higher than in those with more frequent alcohol consumption

Estimation of Excess Mortality and Years of Life Lost to COVID-19 in Norway and Sweden between March and November 2020

We estimate the weekly excess all-cause mortality in Norway and Sweden, the years of life lost (YLL) attributed to COVID-19 in Sweden, and the significance of mortality displacement. We computed the expected mortality by taking into account the declining trend and the seasonality in mortality in the two countries over the past 20 years. From the excess mortality in Sweden in 2019/20, we estimated the YLL attributed to COVID-19 using the life expectancy in different age groups. We adjusted this estimate for possible displacement using an auto-regressive model for the year-to-year variations in excess mortality. We found that excess all-cause mortality over the epidemic year, July 2019 to July 2020, was 517 (95%CI = (12, 1074)) in Norway and 4329 [3331, 5325] in Sweden. There were 255 COVID-19 related deaths reported in Norway, and 5741 in Sweden, that year. During the epidemic period of 11 March–11 November, there were 6247 reported COVID-19 deaths and 5517 (4701, 6330) excess deaths in Sweden. We estimated that the number of YLL attributed to COVID-19 in Sweden was 45,850 [13,915, 80,276] without adjusting for mortality displacement and 43,073 (12,160, 85,451) after adjusting for the displacement accounted for by the auto-regressive model. In conclusion, we find good agreement between officially recorded COVID-19 related deaths and all-cause excess deaths in both countries during the first epidemic wave and no significant mortality displacement that can explain those deaths

Modeling electricity spot prices using mean-reverting multifractal processes

We discuss stochastic modeling of volatility persistence and anti-correlations in electricity spot prices, and for this purpose we present two mean-reverting versions of the multifractal random walk (MRW). In the first model the anti-correlations are modeled in the same way as in an Ornstein-Uhlenbeck process, i.e. via a drift (damping) term, and in the second model the anti-correlations are included by letting the innovations in the MRW model be fractional Gaussian noise with H < 1/2. For both models we present approximate maximum likelihood methods, and we apply these methods to estimate the parameters for the spot prices in the Nordic electricity market. The maximum likelihood estimates show that electricity spot prices are characterized by scaling exponents that are significantly different from the corresponding exponents in stock markets, confirming the exceptional nature of the electricity market. In order to compare the damped MRW model with the fractional MRW model we use ensemble simulations and wavelet-based variograms, and we observe that certain features of the spot prices are better described by the damped MRW model. The characteristic correlation time is estimated to approximately half a year.Comment: 13 pages, 4 figures, 2 table

The bidirectional associations between leisure time physical activity change and body mass index gain. The Tromsø Study 1974–2016

Objectives: To examine whether leisure time physical activity changes predict subsequent body mass index (BMI) changes, and conversely, whether BMI changes predict subsequent leisure time physical activity changes. Methods: This prospective cohort study included adults attending ≥3 consecutive Tromsø Study surveys (time: T1, T2, T3) during 1974–2016 (n = 10779). If participants attended >3 surveys, we used the three most recent surveys. We computed physical activity change (assessed by the Saltin-Grimby Physical Activity Level Scale) from T1 to T2, categorized as Persistently Inactive (n = 992), Persistently Active (n = 7314), Active to Inactive (n = 1167) and Inactive to Active (n = 1306). We computed BMI change from T2 to T3, which regressed on preceding physical activity changes using analyses of covariance. The reverse association (BMI change from T1 to T2 and physical activity change from T2 to T3; n = 4385) was assessed using multinomial regression. Results: Average BMI increase was 0.86 kg/m2 (95% CI: 0.82–0.90) from T2 to T3. With adjustment for sex, birth year, education, smoking and BMI at T2, there was no association between physical activity change from T1 to T2 and BMI change from T2 to T3 (Persistently Inactive: 0.89 kg/m2 (95% CI: 0.77–1.00), Persistently Active: 0.85 kg/m2 (95% CI: 0.81–0.89), Active to Inactive: 0.90 kg/m2 (95% CI: 0.79–1.00), Inactive to Active 0.85 kg/m2 (95% CI: 0.75–0.95), p = 0.84). Conversely, increasing BMI was associated with Persistently Inactive (odds ratio (OR): 1.17, 95% CI: 1.08–1.27, p  Conclusions: We found no association between leisure time physical activity changes and subsequent BMI changes, whereas BMI change predicted subsequent physical activity change. These findings indicate that BMI change predicts subsequent physical activity change at population level and not vice versa

Is the ongoing obesity epidemic partly explained by concurrent decline in cigarette smoking? Insights from a longitudinal population study. The Tromsø Study 1994–2016

The increase of obesity coincides with a substantial decrease in cigarette smoking. We assessed post-cessation weight change and its contribution to the obesity epidemic in a general population in Norway. A total of 14,453 participants (52.6% women), aged 25–54 years in 1994, who attended at least two of four surveys in the Tromsø Study between 1994 and 2016, were included in the analysis. Hereof 77% participated in both the first and the last survey. Temporal trends in mean body mass index (BMI), prevalence of obesity (BMI ≥ 30 kg/m2) and daily smoking were estimated with generalized estimation equations. We assessed BMI change by smoking status (ex-smoker, quitter, never smoker, daily smoker), and also under a scenario where none quit smoking. In total, the prevalence of daily smoking was reduced over the 21 years between Tromsø 4 (1994–1995) and Tromsø 7 (2015–2016) by 22 percentage points. Prevalence of obesity increased from 5 – 12% in 1994–1995 to 21–26% in 2015–2016, where obesity in the youngest (age 25–44 in 1994) increased more than in the oldest (p < 0.0001). Those who quit smoking had a larger BMI gain compared to the other three smoking subgroups over the 21 years (p < 0.0001). The scenario where none quit smoking would imply a 13% reduction in BMI gain in the population, though substantial age-related differences were noted. We conclude that smoking cessation contributed to the increase in obesity in the population, but was probably not the most important factor. Public health interventions should continue to target smoking cessation, and also target obesity prevention

Lifestyle factors as mediators of area-level socioeconomic differentials in mental health and cognitive function: the Tromsø Study

Introduction - Low socioeconomic status (SES) is associated with poor mental health and cognitive function. Individual-level SES and area-level SES (ASES) may affect mental health and cognitive function through lifestyle. We aimed to quantify the associations of ASES with mental health and cognitive function and examine the mediating role of lifestyle behaviours independent of individual-level SES in a Norwegian population. Methods - In this cross-sectional study, we included 7211 participants (54% women) from the seventh survey of the Tromsø Study (2015–2016) (Tromsø7). The exposure variable ASES was created by aggregating individual-level SES variables (education, income, housing ownership) from Statistics Norway at the geographical subdivision level. Tromsø7 data were used as mediators (smoking, snuff, alcohol, physical activity, diet) and outcomes (cognitive function, anxiety, depression, insomnia). Mediation and mediated moderation analysis were performed with age as a moderator, stratified by sex. Results - Higher ASES was associated with better cognitive function and fewer depression and insomnia symptoms, independent of individual-level SES. These associations were mediated by smoking and physical activity. Alcohol was a mediator for depression and cognitive function in women. Age was a significant moderator of the association between ASES and global cognitive function in women. The largest total indirect effect of ASES was found for depression, with the joint effect of the mediators accounting for 36% of the total effect. Conclusions - People living in areas with lower ASES are at higher risk of poor mental health, such as depression and insomnia, and have lower cognitive function possibly due to unhealthy lifestyle (smoking, alcohol and physical inactivity)

Lifestyle factors as mediators of area-level socio-economic differentials in cardiovascular disease risk factors. The Tromsø Study

Introduction: Cardiovascular disease (CVD) is a leading cause of death and disability and living in areas with low socio-economic status (SES) is associated with increased risk of CVD. Lifestyle factors such as smoking, physical inactivity, an unhealthy diet and harmful alcohol use are main risk factors that contribute to other modifiable risk factors, such as hypertension, raised blood cholesterol, obesity, and diabetes. The potential impact of arealevel socio-economic status (ASES) on metabolic CVD risk factors via lifestyle behaviors independent of individual SES has not been investigated previously. Aims: To estimate associations of ASES with CVD risk factors and the mediating role of lifestyle behaviors independent of individual-level SES. Methods: In this cross-sectional study, we included 19,415 participants (52% women) from the seventh survey of the Tromsø Study (2015–2016) (Tromsø7). The exposure variable ASES was created by aggregating individuallevel SES variables (education, income, housing ownership) at the geographical subdivision level. Individuallevel SES data and geographical subdivision of Tromsø municipality (36 areas) were obtained from Statistics Norway. Variables from questionnaires and clinical examinations obtained from Tromsø7 were used as mediators (smoking, snuff, alcohol, and physical activity), while the outcome variables were body mass index (BMI), total/ high-density lipoprotein (HDL) cholesterol ratio, waist circumference, hypertension, diabetes. Mediation and mediated moderation analysis were performed with age as a moderator, stratified by sex. Results: ASES was significantly associated with all outcome variables. CVD risk factor level declined with an increase in ASES. These associations were mediated by differences in smoking habits, alcohol use and physical activity. The associations of ASES with total/HDL cholesterol ratio and waist circumference (women) were moderated by age, and the moderating effects were mediated by smoking and physical activity in both sexes. The largest mediated effects were seen in the associations of ASES with total/HDL cholesterol ratio, with the mediators accounting for 43% of the observed effects. Conclusions: Living in lower SES areas is associated with increased CVD risk due to unhealthy lifestyle behaviors, such as smoking, alcohol use and physical inactivity. These associations were stronger in women and among older participants

Empirisk analyse og stokastisk modellering av temporale fluktuasjoner i den norske pengemarkedsrenta

I denne oppgaven analyserer vi den norske pengemarkedsrenta NIBOR (3 mnd). Vi fokuserer spesielt p\aa\ modeller som beskriver den karakteristiske potenslovskaleringen vi ser i data. Eksempler p\aa\ slike modeller er stabile L\'{e}vy-prosesser, trunkerte stabile L\'{e}vy-prosesser og multifraktale prosesser. Vi finner at modellen Markov Switching Multifractal gjenskaper de viktigste strukturelle egenskapene til rentefluktasjonene samtidig som den er egnet til volatilitetsvarsling. Vi utf\o rer en statistisk test p\aa\ hvordan denne modellen takler prediksjonsproblemet