First Advisor

Dacian N. Daescu

Term of Graduation

Winter 2020

Date of Publication


Document Type

Closed Dissertation

Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences


Mathematics and Statistics




Mathematics, Econometrics



Physical Description

1 online resource (xi, 136 pages)


New methodologies for diagnostic analysis and adaptive tuning based on sensitivity information of the Multivariate Stochastic Volatility (MSV) model are established in this dissertation. The main focus is on obtaining optimal conditional volatilities from a time series set of financial data observed in the market by specifying a State-Space model with error covariance adaptive tuning of the MSV model. Variational Data Assimilation methods are used in this research as tools for obtaining the optimal a posteriori estimates of the multivariate series of volatilities. Calculus of Variations techniques are then applied to a forecast score function to derive the sensitivities of the forecasted volatilities in terms of the input parameters. In summary, this dissertation achieves the development of these new methodologies by

1.Developing the sensitivity information of the multivariate conditional volatilities to observations, covariance specifications and prior estimates,

2.Developing tools for assessing multivariate volatility forecasts. For each time period, sensitivity information provides forecasted volatility diagnostics of the MSV model to give guidance on model performance, and

3.Developing an adaptive tuning procedure based on the multivariate volatility sensitivity information to update the observation error covariance matrix during each assimilation with the main objective of providing improved results in an online manner.

Applications of the new sensitivity diagnostics and adaptive tuning procedures of the MSV model are explored in two experiments. The first experiment is a proof-of-concept experiment where a multivariate series of volatilities is simulated through the specification of a MSV model and serves as a placeholder for true volatilities. The MSV model is then estimated on the resulting time series dataset and the adaptive tuning procedure is performed to demonstrate superior estimation results over the current literature methodologies. In the second experiment, a time series set of Foreign Exchange (FX) rate data is used to estimate the MSV model to provide a time series of conditional volatility estimates of each FX rate. The sensitivity information of each FX rate's conditional volatility forecasts is implemented to derive model performance diagnostics, while the adaptive tuning procedure is implemented to provide improved conditional volatility estimates. Furthermore, an objective assessment and validation of the newly developed methodology is achieved by using an extended data set that is independent on the training set used to calibrate the model.


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