C02 - Mathematical Methods

• 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 Topic(s): Econometric and statistical methods JEL Code(s): C, C0, C01, C02, C1, C13, C5, C50, C51, C52, C53

• Classical Decomposition of Markowitz Portfolio Selection

  Staff Working Paper 2020-21 Christopher Demone, Olivia Di Matteo, Barbara Collignon

  In this study, we enhance Markowitz portfolio selection with graph theory for the analysis of two portfolios composed of either EU or US assets. Using a threshold-based decomposition of their respective covariance matrices, we perturb the level of risk in each portfolio and build the corresponding sets of graphs.

  Content Type(s): Staff research, Staff working papers Topic(s): Central bank research JEL Code(s): C, C0, C02

• Market Expectations and Option Prices: Evidence for the Can$/US$ Exchange Rate

  Staff Discussion Paper 2010-2 Alejandro García, Andrei Prokopiw

  Security prices contain valuable information that can be used to make a wide variety of economic decisions. To extract this information, a model is required that relates market prices to the desired information, and that ideally can be implemented using timely and low-cost methods.

  Content Type(s): Staff research, Staff discussion papers Topic(s): Econometric and statistical methods, Exchange rates, Financial markets JEL Code(s): C, C0, C00, C02, G, G1, G13