Trends and cycles in macro series: The case of US real GDP

Guglielmo Maria Caporale,Luis Alberiko Gil‐Alana

doi:10.1111/boer.12278

Guglielmo Maria Caporale, Luis Alberiko Gil‐Alana

Open Access

https://doi.org/10.1111/boer.12278

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Abstract

AbstractThis paper proposes a new modeling framework capturing both the long‐run and the cyclical components of a time series. As an illustration, we apply it to four US macro series, namely, annual and quarterly real gross domestic product (GDP) and GDP per capita. The results indicate that the behavior of US GDP can be captured accurately by a model incorporating both stochastic trends and stochastic cycles that allows for some degree of persistence in the data. Both appear to be mean reverting, although the stochastic trend is nonstationary, while the cyclical component is stationary, with cycles repeating themselves every 6–10 years.

Highlights

In this paper we put forward a new modelling framework for macro series that allows for two singularities in the spectral density function, one corresponding to the long-run or zero frequency, the other to a non-zero frequency
The results indicate that the behaviour of US GDP can be captured accurately by a model incorporating both stochastic trends and stochastic cycles that allows for some degree of persistence in the dynamics of the series
Both appear to be mean-reverting, it is found that the stochastic trend is non-stationary whilst the cyclical component is stationary, with cycles repeating themselves every 6 – 10 years

Summary

Introduction

In this paper we put forward a new modelling framework for macro series that allows for two singularities (or poles) in the spectral density function, one corresponding to the long-run or zero frequency (i.e. to the long-run evolution of the series), the other to a non-zero frequency (and related to a cyclical pattern repeated approximately every 6 – 10 years). The results indicate that the behaviour of US GDP can be captured accurately by a model incorporating both stochastic trends and stochastic cycles that allows for some degree of persistence in the dynamics of the series. Both appear to be mean-reverting, it is found that the stochastic trend is non-stationary whilst the cyclical component is stationary, with cycles repeating themselves every 6 – 10 years.

Literature Review

A New Statistical Model for Trends and Cycles

Empirical Analysis We examine the following four series

Conclusions