Structural changes in large economic datasets: A nonparametric homogeneity test☆
Introduction
There exists an established literature on the investigation of structural changes in large panel data for economic and financial time series, encompassing the identification of turning points in business cycles, or financial stress periods in stock markets. Examples of empirical application focusing on the changes in the cross section of macroeconomic variables are the studies by Canova (2004) and Stock and Watson (2014). The former proposes a joint testing procedure to identify convergence clubs in income per capita of the OECD countries while the latter studies the cross section of a large set of macroeconomic series to detect turning points in the US economy. Detecting those structural changes allows policy makers to intervene in a timely way to ensure economic and financial stability, and investors to efficiently manage their portfolios and risk exposition.
The paper attempts to contribute to this stream of literature by proposing a Bayesian nonparametric homogeneity test for distributional changes in large economic datasets. The proposed approach abstracts the distributional assumption and relies onPitman–Yor and Dirichlet process priors (Ferguson, 1973, Lo, 1984, Sethuraman, 1994), which are widely used in statistics and econometrics (Hirano, 2002, Griffin and Steel, 2011, Bassetti et al., 2014, Bassetti et al., 2018). Since simulation methods for posterior approximation can be heavily time consuming when dealing with high dimensional panels, we propose an asymptotic approximation of the Bayes factor (BF) to overcome this issue. We show that the approximated BF has an appealing representation which allows relating the homogeneity test to Shannon’s entropy of empirical distributions. Entropy is a measure of complexity which has been applied successfully in many economic and financial studies (Maasoumi and Racine, 2002, Billio et al., 2016, Gradojevic and Caric, 2017).
We provide an application on the FRED-QD macroeconomic dataset and show the ability of the homogeneity test to detect relevant structural changes in the US economy.
Section snippets
A nonparametric homogeneity test
Let be an i.i.d. sequence of real-valued samples, i.e. from the sequence of discrete distribution with , where is a sequence of probability parameters such that and , is a partition of the support such that , and . is the indicator function, which takes value if and 0, otherwise. The likelihood of the data is a product of multinomial distribution and can be written as
An application to the FRED-QD dataset
We apply the homogeneity test to detect structural breaks in the FRED-QD dataset (McCracken and Ng, 2016) which is a large US macroeconomic database containing 248 economic variables specifically designed for the empirical analysis of big data.1
Conclusions
This paper proposes a Bayesian nonparametric homogeneity test for distributional changes and provides an asymptotic approximation of the Bayes factor related to the Shannon entropy. The testing procedure is well suited for large datasets which usually require time-consuming posterior computation methods. In the application on the FRED-QD macroeconomic database, the homogeneity test detects distributional changes in correspondence with the most severe US economic turning points. We believe that
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2019, Economics LettersCitation Excerpt :Change point detection has been a prominent topic in biology, engineering and finance for decades. Extensive literature has explored the detection and estimation of change points, e.g., Aue and Horvath (2013), Jandhyala et al. (2013), Qin and Ma (2018), Eichinger and Kirch (2018) and Casarin and Costola (2019). Estimating multiple change points in time series has recently become a popular topic.
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The authors would like to thank the Editor and an anonymous referee for useful comments and suggestions. Michele Costola acknowledges financial support from the Research Center SAFE, funded by the State of Hessen initiative for research LOEWE. Roberto Casarin acknowledges financial support from the Venice center in Economic and Risk Analytics for public policies (VERA) at University Ca’ Foscari of Venice, funded by Italian Ministry of Education, Universities and Research (MIUR).