A Bayesian nonlinear stationary model with multiple frequencies for business cycle analysis

TL;DR

This paper introduces a Bayesian nonlinear model for analyzing multiple business cycles with different frequencies, capturing key empirical features, and providing probabilistic inference on cycle timing and characteristics.

Contribution

It presents a novel nonlinear Bayesian model that captures multiple business cycle frequencies, with a tailored MCMC estimation method and empirical validation on Polish GDP data.

Findings

Identification of investment and inventory cycles in Polish GDP

Support for stochastic variability in cycle amplitude and phase

Capture of business cycle asymmetries

Abstract

We design a novel, nonlinear single-source-of-error model for analysis of multiple business cycles. The model's specification is intended to capture key empirical characteristics of business cycle data by allowing for simultaneous cycles of different types and lengths, as well as time-variable amplitude and phase shift. The model is shown to feature relevant theoretical properties, including stationarity and pseudo-cyclical autocovariance function, and enables a decomposition of overall cyclic fluctuations into separate frequency-specific components. We develop a Bayesian framework for estimation and inference in the model, along with an MCMC procedure for posterior sampling, combining the Gibbs sampler and the Metropolis-Hastings algorithm, suitably adapted to address encountered numerical issues. Empirical results obtained from the model applied to the Polish GDP growth rates imply co-existence of two types of economic fluctuations: the investment and inventory cycles, and support the stochastic variability of the amplitude and phase shift, also capturing some business cycle asymmetries. Finally, the Bayesian framework enables a fully probabilistic inference on the business cycle clocks and dating, which seems the most relevant approach in view of economic uncertainties.