Open Collections

Zhang, Lin

University of British Columbia

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 models The 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.

Text

2024-03-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/87646

Statistics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/