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
Do Monetary Policy Shocks Affect the Neutral Rate of Interest? Staff working paper 2026-6 Danilo Leiva-Leon, Rodrigo Sekkel, Luis Uzeda Can monetary policy influence the neutral real interest rate (r-star)? Using a new statistical model, we show that interest rate hikes tend to lower r-star and long-run growth, but that monetary policy explains only a small share of the long-run decline in r-star. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C3, C32, C5, C51, E, E3, E32, E4, E44 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Monetary policy, Monetary policy framework and transmission, Monetary policy tools and implementation
CBDC in the Market for Payments at the Point of Sale: Equilibrium Impact and Incumbent Responses Staff working paper 2024-52 Walter Engert, Oleksandr Shcherbakov, André Stenzel We simulate introducing a central bank digital currency (CBDC) and consider consumer adoption, merchant acceptance and usage at the point of sale. Modest adoption frictions significantly inhibit CBDC market penetration along all three dimensions. Incumbent responses to restore pre-CBDC market shares are moderate to small and further reduce the impact of a CBDC. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C5, C51, D, D1, D12, E, E4, E42, L, L1, L14, L5, L52 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Money and payments, Digital assets and fintech, Payment and financial market infrastructures, Retail payments
The impact of a central bank digital currency on payments at the point of sale Staff analytical note 2024-27 Walter Engert, Oleksandr Shcherbakov, André Stenzel We simulate the impact of a central bank digital currency (CBDC) on consumer adoption, merchant acceptance and use of different payment methods. Modest frictions that deter consumer adoption of a CBDC inhibit its market penetration. Minor pricing responses by financial institutions and payment service providers further reduce the impact of a CBDC. Content Type(s): Staff research, Staff analytical notes JEL Code(s): C, C5, C51, D, D1, D12, E, E4, E42, L, L1, L14, L5, L52 Research Theme(s): Money and payments, Digital assets and fintech, Retail payments
Decomposing Systemic Risk: The Roles of Contagion and Common Exposures Staff working paper 2024-19 Grzegorz Halaj, Ruben Hipp We examine systemic risks within the Canadian banking sector, decomposing them into three contribution channels: contagion, common exposures, and idiosyncratic risk. Through a structural model, we dissect how interbank relationships and market conditions contribute to systemic risk, providing new insights for financial stability. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C3, C32, C5, C51, G, G2, G21, L, L1, L14 Research Theme(s): Financial system, Financial stability and systemic risk, Models and tools, Econometric, statistical and computational methods, Economic models
Forecasting Recessions in Canada: An Autoregressive Probit Model Approach Staff working paper 2024-10 Antoine Poulin-Moore, Kerem Tuzcuoglu We forecast recessions in Canada using an autoregressive (AR) probit model. The results highlight the short-term predictive power of the US economic activity and suggest that financial indicators are reliable predictors of Canadian recessions. In addition, the suggested model meaningfully improves the ability to forecast Canadian recessions, relative to a variety of probit models proposed in the Canadian literature. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C5, C51, C53, E, E3, E32 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Monetary policy, Real economy and forecasting
Making It Real: Bringing Research Models into Central Bank Projections Staff discussion paper 2023-29 Marc-André Gosselin, Sharon Kozicki Macroeconomic projections and risk analyses play an important role in guiding monetary policy decisions. Models are integral to this process. This paper discusses how the Bank of Canada brings research models and lessons learned from those models into the central bank projection environment. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C3, C32, C5, C51, E, E3, E37, E4, E47, E5, E52 Research Theme(s): Models and tools, Economic models, Monetary policy, Monetary policy framework and transmission, Real economy and forecasting
A Blueprint for the Fourth Generation of Bank of Canada Projection and Policy Analysis Models Staff discussion paper 2023-23 Donald Coletti The fourth generation of Bank of Canada projection and policy analysis models seeks to improve our understanding of inflation dynamics, the supply side of the economy and the underlying risks faced by policy-makers coming from uncertainty about how the economy functions. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C5, C50, C51, C52, C53, C54, C55 Research Theme(s): Models and tools, Economic models, Monetary policy, Inflation dynamics and pressures, Monetary policy framework and transmission, Real economy and forecasting
Risk Amplification Macro Model (RAMM) Technical report No. 123 Kerem Tuzcuoglu The Risk Amplification Macro Model (RAMM) is a new nonlinear two-country dynamic model that captures rare but severe adverse shocks. The RAMM can be used to assess the financial stability implications of both domestic and foreign-originated risk scenarios. Content Type(s): Staff research, Technical reports JEL Code(s): C, C5, C51, E, E3, E37, E4, E44, F, F4, F44 Research Theme(s): Financial system, Financial stability and systemic risk, Models and tools, Economic models, Monetary policy, Real economy and forecasting
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