To infinity and beyond: Efficient computation of ARCH() Models
(with Morten Ørregaard Nielsen)

  • Latest version is November 6, 2020
  • Reference: Nielsen and Noel (2020, QED working paper 1425).
  • The associated computer codes can be downloaded here.
  • Forthcoming in Journal of Time Series Analysis

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.

Working Papers

Information Transparency of Firm Financing
(with Amy Hongfei Sun)

Abstract: We propose a theory of optimal firm financing to explain why information transparency varies with external financing methods. Our model nests adverse selection and agency cost in an environment with ex ante heterogeneous firms. With our model, we prove the following: First, equity, transparent debt and opaque debt contracts arise endogenously and coexist as optimal contracts. Second, the equity contract is the most informationally transparent in the sense that it requires both business and financial information of a firm, followed by transparent debt requiring financial information, and then opaque debt with no firm-specific information attached. Third, the equilibrium can be one of two types, either pooling with only opaque debt or mixing with all three types. Finally, firm-specific characteristics such as quality and internal funds drive the optimal financing choice. Given a mediocre quality, a firm will always use opaque-debt financing regardless of its available funds. Given a good quality, as internal funds ranked from low to high, firms will respectively choose to finance with opaque debt, equity, transparent debt, and opaque debt.

WTO, tariffs negotiations and bargaining power
(work in progress)

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