Spatio-Temporal Generalized Autoregressive Conditional Heteroskedasticity Models

This thesis presents a spatio-temporal extension of the GARCH process with a specific spatial dependence structure. Different simulation and estimation techniques are developed. Assuming a circular spatial structure at each time point, gives a closed and finite set of variables at each point in time, making the spatio-temporal process adapted in the temporal dimension. This assumption makes likelihood estimation trivial and we obtain an analytical expression for estimators -- both using maximum likelihood and least squares estimation. On non-circular data, this procedure leads to biased estimates, but we suggest doing a parametric bootstrap bias correction, which turns out to be very effective and improve estimates substantially. We also suggest another approach to apply the circular model to non-circular data, by using a Gibbs sampler and an EM-algorithm.Denne avhandlingen presenterer en rom-tid- utvidelse av GARCH prosessen med en bestemt romlig avhengighetsstruktur. Ulike simulerings- og estimerings-metoder er utviklet. Forutsatt en sirkulær romlig struktur på hvert tidspunkt, gir et lukket og begrenset sett av variabler ved hvert punkt i tid, slik at rom-tid-prosess blir adaptert i tidsdimensjonen . Denne antakelsen gjør likelihood estimering trivielt og vi får et analytisk uttrykk for estimatorer - både ved hjelp av maximum likelihood- og minste-kvadratersestimering. På ikke-sirkulære data, fører denne prosedyren til estimatorer med bias, men vi viser at en parametrisk bootstrap skjevhetskorreksjon er svært effektivt og forbedrer estimater betydelig. Vi foreslår også en annen metode for å anvende den sirkulære modellen til ikke-sirkulære data, ved hjelp av en Gibbs sampler og en EM-algoritme.Master i StatistikkMAMN-STATSTAT39

Testing for asymmetric dependency structures in financial markets: regime-switching and local Gaussian correlation

This paper examines asymmetric and time-varying dependency structures between financial returns, using a novel approach consisting of a combination of regime-switching models and the local Gaussian correlation (LGC). We propose an LGC-based bootstrap test for whether the dependence structure in financial returns across different regimes is equal. We examine this test in a Monte Carlo study, where it shows good level and power properties. We argue that this approach is more intuitive than competing approaches, typically combining regime-switching models with copula theory. Furthermore, the LGC is a semi-parametric approach, hence avoids any parametric specification of the dependence structure. We illustrate our approach using returns from the US-UK stock markets and the US stock and government bond markets. Using a two-regime model for the US-UK stock returns, the test rejects equality of the dependence structure in the two regimes. Furthermore, we find evidence of lower tail dependence in the regime associated with financial downturns in the LGC structure. For a three-regime model fitted to US stock and bond returns, the test rejects equality of the dependence structures between all regime pairs. Furthermore, we find that the LGC has a primarily positive relationship in the time period 1980-2000, mostly a negative relationship from 2000 and onwards. In addition, the regime associated with bear markets indicates less, but asymmetric dependence, clearly documenting the loss of diversification benefits in times of crisis

A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using Template Model Builder

A very common way to estimate the parameters of a hidden Markov model (HMM) is the relatively straightforward computation of maximum likelihood (ML) estimates. For this task, most users rely on user-friendly implementation of the estimation routines via an interpreted programming language such as the statistical software environment R. Such an approach can easily require time-consuming computations, in particular for longer sequences of observations. In addition, selecting a suitable approach for deriving confidence intervals for the estimated parameters is not entirely obvious, and often the computationally intensive bootstrap methods have to be applied. In this tutorial, we illustrate how to speed up the computation of ML estimates significantly via the R package TMB. Moreover, this approach permits simple retrieval of standard errors at the same time. We illustrate the performance of our routines using different data sets: first, two smaller samples from a mobile application for tinnitus patients and a well-known data set of fetal lamb movements with 87 and 240 data points, respectively. Second, we rely on larger data sets of simulated data of sizes 2000 and 5000 for further analysis. This tutorial is accompanied by a collection of scripts, which are all available in the Supporting Information. These scripts allow any user with moderate programming experience to benefit quickly from the computational advantages of TMB.publishedVersio

Predicting density-dependent somatic growth in Norwegian spring-spawning herring

Density-dependent growth, which might influence the effects of fisheries on a population, is often ignored when management strategies are evaluated, mainly due to a lack of appropriate models readily available to be implemented. To improve on this, we investigated if somatic growth in Norwegian spring-spawning herring (Clupea harengus) depends on cohort density using a formulation of the von Bertalanffy growth function on cohorts from 1921 to 2014 and found a significant negative correlation between estimated asymptotic length and density. This clearly indicates density-dependent effects on growth, and we propose a model that can be used to predict the size-at-age of Norwegian spring-spawning herring as a function of herring density (the abundance of two successive cohorts) in short-term predictions of catch advice, and in Management strategy evaluations, including estimation of their reference points such as FMSY.publishedVersio

Space-time recapture dynamics of PIT-tagged Northeast Atlantic mackerel (Scomber scombrus) reveal size-dependent migratory behaviour

Based on GIS-mapping and semi-parametric modelling of recaptures from PIT-tag experiments in the North Sea nursery area (September 2011), the Celtic Seas spawning area (May-June 2014-2021) and the Icelandic Waters feeding area (August 2015-2019), we argue that the distribution of Northeast Atlantic (NEA) mackerel is influenced by a size-dependent migratory behaviour. The time-space recapture dynamics revealed that larger mackerel tended to migrate a longer distance between spawning and feeding areas, either through a western route from the Celtic Seas into the Icelandic Waters and the Greenland Sea or by following the main route northwards through the Faroe-Shetland Channel into the Norwegian Sea. This long-distance travel resulted in turn in delayed arrival in the North Sea wintering area. During the return spawning migration into the Celtic Seas, larger individuals remained in the front, likely heading to spawning grounds farther south than smaller conspecifics. Migration patterns also evolved with time at liberty as the mackerel grew older and larger, while possibly covering a progressively wider area over its annual migration cycle as suggested from the tagging data. However, the study also showed large inter-annual variability in the recapture patterns which likely reflect changes in environmental condition (prey availability and ocean current), NEA mackerel population demographics, and the spatial fishery dynamics.publishedVersio

Report of Working Group on Widely Distributed Stocks (WGWIDE).

As a consequence of the impact of the COVID pandemic on international travel which prevented the traditional meeting from taking place, the Working Group on Widely Distributed Stocks (WGWIDE) met online via WebEx hosted by ICES. Prior to the 2020 meeting, the generic ToRs for species and regional working groups were re-prioritised by ACOM to allow the WG to focus primarily on those ToRs most applicable to the provision of advice. WGWIDE reports on the status and considerations for management of Northeast Atlantic mackerel, blue whiting, Western and North Sea horse mackerel, Northeast Atlantic boarfish, Norwegian springspawning herring, striped red mullet (Subareas 6, 8 and Divisions 7.a-c, e-k and 9.a), and red gurnard (Subareas 3, 4, 5, 6, 7, and 8) stocks. Northeast Atlantic (NEA) Mackerel. This stock is highly migratory and widely distributed throughout the Northeast Atlantic with significant fisheries is most ICES subareas. A diverse range of fleets from smaller artisanal, handline vessels to large (100m+) factory freezer vessels and modern RSW trawlers and purse seiners take part in what is one of the most valuable European fisheries. The assessment conducted in 2020 is an update assessment, based on the configuration agreed during the most recent inter-benchmark exercise in 2019 and incorporates the most recent data available from sampling of the commercial catch in 2019, the final 2019 egg survey SSB estimate, an updated recruitment index and tagging time series along with 2020 survey data from the IESSNS swept area survey. Advice is given based on stock reference points which were updated during a management strategy evaluation carried out in 2020. Following a strong increase from 2007 to 2014, SSB has been declining although it remains well above MSY Btrigger. Fishing mortality has been below FMSY since 2016. There have been a number of large year classes since 2001 with above average recruitment over much of the most recent decade. Blue Whiting. This pelagic gadoid is widely distributed in the eastern part of the North Atlantic. The 2020 update assessment followed the protocol from the most recent inter-benchmark in 2016 and used preliminary catch data from 2020. Due to the cancellation of the 2020 acoustic survey, this data was not available. The effect on the assessment was minimal and limited to increases in uncertainty of the terminal year estimates. The SSB continues to decrease from the most recent maximum in 2017 mainly due to below average recruitment since 2017, although it remains above MSY Btrigger. Fishing mortality has been above FMSY since 2014. Norwegian Spring Spawning Herring. This is one of the largest herring stocks in the world. It is highly migratory, spawning along the Norwegian coast and feeding throughout much of the Norwegian Sea. The 2020 assessment is based on an implementation of the XSAM assessment model introduced at the benchmark in 2016. This years’ assessment indicates that the stock is continuing to decline from the peak in 2008 of 7Mt to just above MSY Btrigger due to successive years of average or below average recruitment. Catch advice for 2021 is given on the basis of the agreed management plan and represents a substantial increase over the 2020 advice due to an upward revision in the estimate of the 2016 year-class which is considered to be the most significant year-class since 2004

Spatio-Temporal Generalized Autoregressive Conditional Heteroskedasticity Models

This thesis presents a spatio-temporal extension of the GARCH process with a specific spatial dependence structure. Different simulation and estimation techniques are developed. Assuming a circular spatial structure at each time point, gives a closed and finite set of variables at each point in time, making the spatio-temporal process adapted in the temporal dimension. This assumption makes likelihood estimation trivial and we obtain an analytical expression for estimators -- both using maximum likelihood and least squares estimation. On non-circular data, this procedure leads to biased estimates, but we suggest doing a parametric bootstrap bias correction, which turns out to be very effective and improve estimates substantially. We also suggest another approach to apply the circular model to non-circular data, by using a Gibbs sampler and an EM-algorithm

Volatility modelling in time and space

This thesis contributes to the scientific community in several aspects. We introduce both spatial- and spatio-temporal extensions to the family of GARCH and ARMA-GARCH models and present asymptotic statistics for the quasi maximum likelihood estimators [QMLE] for the GARCH extensions. An important property of these extensions are their spatial- and spatio-temporal stationarity, which is part of the model specifications. The models all exist on an equidistant d-dimensional grid, be it purely spatial or spatiotemporal. Volatility modelling is important in finance, but we also present applications from other fields of study, e.g. climate, meteorology and even cell biology. In stationary spatial statistics on infinite lattices, a boundary problem arises. This is dealt with, in two of the papers, by assuming a circular model. This means wrapping the spatial part of the grid of observation onto a torus surface by connecting opposing edges, and effectively removing the boundaries so that each site’s neighbours are observed. The torus space is good for visualization and the point is that we regard sites on opposite sides of the rectangle we observe as neighbours. Circulation changes the area of observation from infinite to being closed and finite, and proving asymptotic results becomes easier. Consistency and asymptotic normality of the QMLE is established in the circular situation for GARCH models. The circular model can be used as an approximation of an infinite grid model, in which the circular estimator will be biased. In this setting, we suggest a parametric bootstrap bias correction to compensate for the false links between boundary sites due to circulation. In simulation studies, this approach provides good results for both GARCH and ARMA-GARCH models. For ARMA-GARCH, it is not uncommon to fit an ARMA model to data and a GARCH model to its residuals, but simultaneously estimating all parameters is better. We show by a simulation experiment that the variance of the ARMA-part of the QMLE can be reduced by doing this. The second paper of this thesis is an application of non-stationary GARCH modelling in climate research. We investigate how volatility has developed in a daily temperature series at Svalbard Airport over the last 44 years. During this period the temperature there has increased intensively. We model the volatility using a GARCH model with a trend, where the slope depends on the day of the year. Except for the summer, we find a decreasing temperature variability, i.e. a negative trend. The temperature on Svalbard is getting higher and more stable at the same time and we believe this is due to the reduced sea ice extent in the region. Without the circulation, on an infinite grid and in a potentially purely spatial setting, we turn to half-space GARCH models in the final paper. These models use an ordering of the spatial locations, extending non-deterministic time series to space. The MLE used is based on a modified likelihood, and we show that it is consistent and asymptotically Gaussian. Instead of the standard Lyapunov condition for existence of a stationary solution, a generalization of Nelson’s criteria is used

Decline in temperature variability on Svalbard

The variability in the temperature on Svalbard, Norway, has been decreasing over the last four decades. This may be due to the reduction in sea ice, transitioning the regional climate to a more stable, coastal one.We quantify this transition in terms of decreasing volatility in a daily average temperature time series at Svalbard Airport from 1976 to 2019. We use two different approaches: a nonstochastic model and a time-dependent generalized autoregressive conditional heteroskedasticity (GARCH) model. These parametric approaches include a time-dependent trend, where the slope depends on the day of the year. For Svalbard, the slope has a minimum in late August and the steepest slope during winter is estimated to be 20.18C2 yr21. The nonstochastic model, for which the conditional and unconditional variances are the same, only depends on the marginal distribution and is perhaps the easiest to interpret. The GARCH model extends the nonstochastic model by including short-range temporal dependence in the volatility and is thus more locally adapted. Volatility modeling is important for a complete statistical description of the temperature dynamics on Svalbard as an Arctic representative. In combination with increasing temperatures, the volatility reduction makes the extremely cold days during winter occur less frequently. Although we focus exclusively on the Svalbard Airport series, the models should be suitable for other temperature or climatic time series

Barents Sea Capelin - Report of the Joint Russian-Norwegian Working Group on Arctic Fisheries (JRN-AFWG) 2022

publishedVersio