Nielsen, M.Ø. & A.L. Noël (2021) To infinity and beyond: Efficient computation of ARCH(\infty) modelsJournal of Time Series Analysis 42, 338–354.

  • The associated computer codes can be downloaded here.

Abstract: This paper provides an exact algorithm for efficient computation of the time series of conditional variances, and hence the likelihood function, of models that have an ARCH(∞) representation. This class of models includes, e.g., the fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model. Our algorithm is a variation of the fast fractional difference algorithm of Jensen and Nielsen (2014). It takes advantage of the fast Fourier transform (FFT) to achieve an order of magnitude improvement in computational speed. The efficiency of the algorithm allows estimation (and simulation/bootstrapping) of ARCH(∞) models, even with very large data sets and without the truncation of the filter commonly applied in the literature. In Monte Carlo simulations, we show that the elimination of the truncation of the filter reduces the bias of the quasi-maximum-likelihood estimators and improves out-of-sample forecasting. Our results are illustrated in two empirical examples.


Information Transparency of Firm Financing (with Amy Hongfei Sun)

  • QED working paper 1459. Latest version 2021/05.

Abstract: We propose a theory of optimal firm financing given nested information problems of adverse selection and agency cost. We prove that there exists a unique perfect Bayesian equilibrium with novel features: First, three types of optimal contracts arise endogenously, i.e., equity, transparent debt and opaque debt. Equity and transparent debt are both informational transparent because these contracts require firms to take on a costly technology for verifying types. Opaque debt, however, merely reflects the general information of firms seeking external funds. Any signaling contract that does not involve costly verification does not survive the equilibrium. Second, the equilibrium is either pooling on opaque debt, or mixing with transparent and opaque financing. Third, debt weakly dominates equity. Finally, the optimal debt-to-equity ratio is unique for all firms in a pooling equilibrium, but only for a strict subset of firms in a mixing equilibrium.

Trade Bargaining Power, Multilateralism and Regional Trade Agreements
(work in progress)

Measurement Error and Consumption Inequality in Canada
(work in progress with Brant Abbott and Samuel Brien)