In this paper we analyze the performance of supremum augmented Dickey-Fuller (SADF), generalized SADF (GSADF), and backward SADF (BSADF) tests, as introduced by Phillips et al. (International Economic Review 56:1043-1078, 2015) for detecting and date-stamping financial bubbles. In Monte Carlo...

In this chapter, we first explain what we mean by a signal, and then we describe some characteristics such as energy, frequency, phase, power spectrum, etc. We show how to analyse it by the means of spectral analysis and Fourier transform. Moreover, as the Fourier transform does not provide any...

We propose a simple modification of the time series filter by Hamilton (2018b) that yields reliable and economically meaningful real-time output gap estimates. The original filter relies on 8-quarter ahead forecasts errors of an autoregression. While this approach yields a cyclical component of...