Estimation and Inference for Stochastic Volatility Models with Heavy-Tailed Distributions Staff working paper 2026-8 Gabriel Rodriguez Rondon, Jean-Marie Dufour, Md. Nazmul Ahsan Statistical inference--both estimation and testing--for stochastic volatility (SV) models is known to be challenging and computationally demanding. We propose simple and efficient estimators for SV models with conditionally heavy-tailed error distributions, particularly the Student’s t and Generalized Exponential Distributions (GED). The estimators rely on a small set of moment conditions derived from ARMA-type representations of SV models, with an option to apply “winsorization” to improve stability and finite-sample performance. Except for the degrees of-freedom parameter, closed-form expressions are available for all other parameters, extending Ahsan and Dufour (2019, 2021), thus eliminating the need for numerical optimization or initial values. We derive the estimators’ asymptotic distribution and show that, due to their analytical tractability, they support reliable, and even exact, simulation-based inference via Monte Carlo or bootstrap methods. We assess their performance through extensive simulations and demonstrate their practical relevance in financial return data, which strongly reject the normality assumption in favor of heavy-tailed models. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C1, C12, C13, C15, C2, C22, C5, C51, C53, C58 Research Theme(s): Financial markets and funds management, International markets and currencies, Models and tools, Econometric, statistical and computational methods, Economic models
Estimating the impacts on GDP of natural disasters in Canada Staff analytical note 2025-5 Tatjana Dahlhaus, Thibaut Duprey, Craig Johnston Extreme weather events contribute to increased volatility in both economic activity and prices, interfering with the assessment of the true underlying trends of the economy. With this in mind, we conduct a timely assessment of the impact of natural disasters on Canadian gross domestic product (GDP). Content Type(s): Staff research, Staff analytical notes JEL Code(s): B, B2, B23, C, C1, C13, C2, C23, E, E1, E17, E3, E37, E6, E62, H, H6 Research Theme(s): Monetary policy, Real economy and forecasting, Structural challenges, Climate change
Examining recent revisions to CPI-common Staff analytical note 2022-15 Elyse Sullivan Unusually large revisions to CPI-common in recent months stem from increased common movements across consumer price index components amid broad inflationary pressures. With recent revisions, CPI-common is more closely aligned with the Bank of Canada’s other two preferred measures of core inflation. However, caution is necessary when interpreting real-time estimates of CPI-common in the current environment. Content Type(s): Staff research, Staff analytical notes JEL Code(s): C, C1, C13, C18, E, E3, E31 Research Theme(s): Models and tools, Economic models, Monetary policy, Inflation dynamics and pressures
Calculating Effective Degrees of Freedom for Forecast Combinations and Ensemble Models Staff discussion paper 2022-19 James Younker This paper derives a calculation for the effective degrees of freedom of a forecast combination under a set of general conditions for linear models. Computing effective degrees of freedom shows that the complexity cost of a forecast combination is driven by the parameters in the weighting scheme and the weighted average of parameters in the auxiliary models. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C0, C01, C02, C1, C13, C5, C50, C51, C52, C53 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Monetary policy, Real economy and forecasting
Characterizing the Canadian Financial Cycle with Frequency Filtering Approaches Staff analytical note 2018-34 Andrew Lee-Poy In this note, I use two multivariate frequency filtering approaches to characterize the Canadian financial cycle by capturing fluctuations in the underlying variables with respect to a long-term trend. The first approach is a dynamically weighted composite, and the second is a stochastic cycle model. Content Type(s): Staff research, Staff analytical notes JEL Code(s): C, C0, C01, C1, C13, C14, C18, C3, C32, C5, C51, C52, E, E3, E32, E6, E66, G, G0, G01, G1, G18 Research Theme(s): Financial system, Financial stability and systemic risk, Models and tools, Econometric, statistical and computational methods, Economic models
Bootstrapping Mean Squared Errors of Robust Small-Area Estimators: Application to the Method-of-Payments Data Staff working paper 2018-28 Valéry Dongmo Jiongo, Pierre Nguimkeu This paper proposes a new bootstrap procedure for mean squared errors of robust small-area estimators. We formally prove the asymptotic validity of the proposed bootstrap method and examine its finite sample performance through Monte Carlo simulations. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C1, C13, C15, C8, C83, E, E4, E41 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Money and payments, Cash and bank notes
New Housing Registrations as a Leading Indicator of the BC Economy Staff discussion paper 2016-3 Calista Cheung, Dmitry Granovsky Housing starts and building permits data are commonly used as leading indicators of economic activity. In British Columbia, all new homes must be registered with the Homeowner Protection Office, a branch of BC Housing, before the issuance of building permits and the start of construction. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C1, C13, C5, C53, E, E3, E32, E37 Research Theme(s): Financial system, Household and business credit, Monetary policy, Real economy and forecasting