Natalia Nolde


Research Classification

Research Interests

Statistics and Probabilities
Applications in finance, insurance, geosciences
Multivariate extreme value theory
Risk assessment

Relevant Thesis-Based Degree Programs



Master's students
Doctoral students
Any time / year round

Financial risk analytics
Multivariate extreme value theory

I support public scholarship, e.g. through the Public Scholars Initiative, and am available to supervise students and Postdocs interested in collaborating with external partners as part of their research.
I support experiential learning experiences, such as internships and work placements, for my graduate students and Postdocs.

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Great Supervisor Week Mentions

Each year graduate students are encouraged to give kudos to their supervisors through social media and our website as part of #GreatSupervisorWeek. Below are students who mentioned this supervisor since the initiative was started in 2017.


My supervisors are extremely supportive. Natalia is a wonderful supervisor as she has a level of emotional intelligence that I have not seen in most people. Both her and Harry have always put my goals at the forefront and helped me achieve them. Their doors have always been open to me and they have been extremely generous with their time and their advice. I have learned so much from working with them throughout my time in my master's program. It has been an immense pleasure and I look forward to having an opportunity to collaborate with them in the future.

Abdullah Farouk (2019)


Graduate Student Supervision

Doctoral Student Supervision

Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.

Margin-closed and regime-switching multivariate time series models (2024)

Multivariate time series models are widely applied in many fields. The traditional multivariate time series models have some drawbacks in high dimensions. These include the large parameter set, interpretation of parameters, and possibly lack of flexibility in modeling and analyzing marginal distributions.The contributions of this thesis are (a) finding conditions under which any sub-process of a vector autoregressive (VAR) process is also autoregressive and has the same Markov order as the original process; (b) building multivariate regime-switching models whose sub-processes are regime-switching processes having the same Markov order as the original process; (c) studying autoregressive models with explanatory variables, with application to scenario analysis in finance.For modeling using copulas, it is typical to first model univariate margins and then the multivariate dependence between the marginal components. We derive the conditions for when multivariate stationary Gaussian vector autoregressive (VAR) time series have lower-dimensional VAR or AR margins. The property allows one to fit the sub-processes of multivariate time series before assembling them by fitting the dependence between the sub-processes. The use of the conditions for closure under margins also leads to models with fewer parameters than unrestricted VAR modelsThe margin-closed Gaussian VAR models can be extended to margin-closed regime-switching multivariate time series models. This is useful when regime switches are rare and the state of the regime is constant over stretches of time. In each regime, the margin-closed regime-switching models have non-Gaussian univariate margins for each univariate component and the multivariate Gaussian copula of the stationary joint distribution of a margin-closed VAR model. The property of closure under margins enables a multi-stage estimation procedure and inference on the latent regimes based on lower-dimensional selected sub-processes.A scenario analysis is performed for time series of the estimated distance to default of companies, based on the margin-closed regime-switching multivariate time series model. The autoregressive exogenous input (ARX) models are fit to the distance to default and macroeconomic explanatory variables in poor macroeconomic condition. Based on the estimated ARX models, the scenario analysis investigates the behavior of the average distance to default by sectors under stressful macroeconomic conditions.

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Forecasting of nonlinear extreme quantiles using copula models (2017)

Forecasts of extreme events are useful in order to prepare for disaster. Such forecasts are usefully communicated as an upper quantile function, and in the presence of predictors, can be estimated using quantile regression techniques. This dissertation proposes methodology that seeks to produce forecasts that (1) are consistent in the sense that the quantile functions are valid (non-decreasing); (2) are flexible enough to capture the dependence between the predictors and the response; and (3) can reliably extrapolate into the tail of the upper quantile function. To address these goals, a family of proper scoring rules is first established that measure the goodness of upper quantile function forecasts. To build a model of the conditional quantile function, a method that uses pair-copula Bayesian networks or vine copulas is proposed. This model is fit using a new class of estimators called the composite nonlinear quantile regression (CNQR) family of estimators, which optimize the scores from the previous scoring rules. In addition, a new parametric copula family is introduced that allows for a non-constant conditional extreme value index, and another parametric family is introduced that reduces a heavy-tailed response to a light tail upon conditioning. Taken together, this work is able to produce forecasts satisfying the three goals. This means that the resulting forecasts of extremes are more reliable than other methods, because they more adequately capture the insight that predictors hold on extreme outcomes. This work is applied to forecasting extreme flows of the Bow River at Banff, Alberta, for flood preparation, but can be used to forecast extremes of any continuous response when predictors are present.

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Master's Student Supervision

Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.

Extreme value approach to CoVaR estimation (2019)

The global financial crisis of 2007-2009 revealed the importance of systemic risk: the risk that may destabilize the global economy due to financial contagion. Accurate assessment of systemic risk would not only enable regulators to introduce suitable policies to mitigate the risk, but also allow individual institutions to monitor and mitigate their vulnerability. An effective measure of systemic risk should be able to capture the co-movements between a financial system (or market) and individual financial institutions. One popular measure of systemic risk is CoVaR. In this thesis, a methodology is proposed to compute dynamic forecasts of CoVaR semi-parametrically within the classical framework of multivariate extreme value theory (EVT). According to the definition, CoVaR can be viewed as a high quantile of a conditional distribution where the conditioning event corresponds to large losses of an institution. The idea of our methodology is to relate this conditional distribution to the tail dependence function. We develop an EVT-based framework to estimate CoVaR statically by combining parametric modelling of the tail dependence function to address the issue of data sparsity in the joint tail regions and semi-parametric univariate tail estimation techniques. The performance of the methodology is illustrated via simulation studies and real data examples.

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Modeling operational risk using the truncation approach (2018)

Banks that use the advanced measurement approach to model operational risk may struggle to develop an internal process that produces stable regulatory capital over time. Large decreases in regulatory capital are scrutinized by regulators while large increases may force banks to set aside more assets than necessary. A major source of this instability arises from the loss severity selection process, especially when the selected distribution families for severity risk categories change year-to-year. In this report, we examine the process of selecting severity distributions from a candidate distribution list within the guidelines of the advanced measurement approach, propose useful tools to aid in selecting an appropriate severity distribution, and analyze the effect of selection criteria on regulatory capital. The log sinh-arcsinh distribution family is added to a list of common candidate severity distributions used by industry. This 4-parameter family solves issues introduced by the 4-parameter g-and-h distribution without sacrificing flexibility and shows promise in outperforming 2-parameter families, reducing the frequency of severity distribution families changing year-to-year. Distribution parameters are estimated using the maximum likelihood approach from loss data truncated at a known minimum reporting threshold. Our severity distribution selection process combines truncation probability estimates with Akaike Information Criterion (AIC), Bayesian Information Criterion, modified Anderson-Darling, QQ-plots, and predictive measures such as the quantile scoring function and out-of-sample AIC, and we discuss some of the challenges associated with this process. We then simulate operational losses and calculate regulatory capital, comparing the effect on regulatory capital of selecting loss severity distributions using AIC versus quantile score. A combination of these two criteria is recommended when selecting loss severity distributions.

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Risk region estimation for light-tailed multivariate samples (2018)

Estimation of multivariate quantile regions with very small probabilities, referred toas risk regions in this report, plays an important part in various applications. Yet,it is a difficult problem since such regions contain hardly any or no data. Existingmethods address the problem only for heavy-tailed distributions or for bivariatedistributions with non-degenerate exponent measure that do not include the casesof asymptotic independence.In this report, we propose a more flexible framework to supplement existingapproaches to risk region estimation by allowing tails of the underlying distributionto be light as well as covering situations of tail independence. In particular,we concentrate on a class of distributions assumed to have a density function withhomothetic level sets. In simulation studies, reasonable performance of our proposedmethod is demonstrated. We also present two real-life applications to furtherillustrate the flexibility and performance of our method.

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A flexible inference method for an autoregressive stochastic volatility model with an application to risk management (2017)

The Autoregressive Stochastic Volatility (ARSV) model is a discrete-time stochastic volatility model that can model the financial returns time series and volatilities. This model is relevant for risk management. However, existing inference methods have various limitations on model assumptions. In this report we discuss a new inference method that allows flexible model assumption for innovation of the ARSV model. We also present the application of ARSV model to risk management, and compare the ARSV model with another commonly used model for financial time series, namely the GARCH model.

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On the choice of scoring functions for forecast comparisons (2017)

Forecasting of risk measures is an important part of risk management for financial institutions. Value-at-Risk and Expected Shortfall are two commonly used risk measures and accurately predicting these risk measures enables financial institutions to plan adequately for possible losses. Point forecasts from different methods can be compared using consistent scoring functions, provided the underlying functional to be forecasted is elicitable. It has been shown that the choice of a scoring function from the family of consistent scoring functions does not influence the ranking of forecasting methods as long as the underlying model is correctly specified and nested information sets are used. However, in practice, these conditions do not hold, which may lead to discrepancies in the ranking of methods under different scoring functions.We investigate the choice of scoring functions in the face of model misspecification, parameter estimation error and nonnested information sets. We concentrate on the family of homogeneous consistent scoring functions for Value-at-Risk and the pair of Value-at-Risk and Expected Shortfall and identify conditions required for existence of the expectation of these scoring functions. We also assess the finite-sample properties of the Diebold-Mario Test, as well as examine how these scoring functions penalize for over-prediction and under-prediction with the aid of simulation studies.

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