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)

Abstract: We propose a theory of optimal firm financing to explain variety in financial contracts and why some are more informationally transparent than others. Our model nests adverse selection and agency cost in an environment with ex-ante heterogeneous firms. With this model, we prove the following results: First, in equilibrium the optimal financial contracts can be of three types: equity, transparent debt and opaque debt. Equity and transparent debt are both contracts that reveal firm-specific information (e.g. productivity and survival rate), whereas opaque debt is a contract that merely reflects general information of fund-seeking firms. Second, the equilibrium is either pooling on opaque debt or mixing with transparent and opaque financing. Third, debt is more versatile than equity because it can be used by all firms to implement the optimal contract, some strictly better off with transparent debt and others with opaque debt. In contrast, equity can only be optimal for firms of high quality and low internal funds. Even so, these firms find themselves indifferent between financing with equity and transparent debt. Finally, the optimal debt-to-equity ratio is not a smooth function of the firm characteristics and may even map into an interval for certain types of firms.

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)