Determining the number of factors after stationary univariate transformations

Abstract

A very common practice when extracting factors from non-stationary multivariate time series is to differentiate each variable in the system. As a consequence, the ratio between variances and the dynamic dependence of the common and idiosyncratic differentiated components may change with respect to the original components. In this paper, we analyze the effects of these changes on the finite sample properties of several procedures to determine the number of factors. In particular, we consider the information criteria of Bai and Ng (Econometrica 70 (1) idiosyncratic noises. Furthermore, we also analyze the role of the number of factors in the original non-stationary system as well as of its temporal and cross-sectional dimensions. Finally, we implement the different procedures to determine the number of common factors in a system of inflation rates in 15 euro area countries.

A dynamic factor model for the Mexican economy: are common trends useful when predicting economic activity?

“…Moreover, in the context of non-stationary DFMs, Ergemen and Rodriguez-Caballero (2016) use the procedure given by Hallin and Liska (2007) to determine the number of regional and global factors allowing fractional differencing in Y t . However, and following Corona et al (2017a), they show that the finite sample performance of the proposed procedures in this paper exhibits a good performance when we use data in first differences or levels and the common factors are I(1). …”

“…The results indicate thatr ER ¼r GR ¼ 2 andr ED ¼ 5. 13 Given that Onatski (2010) is more robust in the presence of non-stationarity, see Corona et al (2017a), we work with this number of factors.…”

Estimating Non-stationary Common Factors: Implications for Risk Sharing

“…Furthermore, using the "differencing and recumulating" estimator implemented with the 2SKS procedure, named KSP in the graph, generates even smaller correlations, mainly when γ = − 0.8. Note that, when the serial dependence of the idiosyncratic components is such that γ < 0.5, the variance of the differenced idiosyncratic component, σ 2 e , is larger than the corresponding variance of the original component, σ 2 ε ; see, for example, Corona et al (2017). Consequently, the performance of the procedures using data in first differences deteriorates in this case.…”

“…In the context of determination of the number of factors, Corona et al (2017) conclude that if ε t is stationary, with autoregressive parameters smaller than 0.5 while F t is non-stationary, then overdifferencing the idiosyncratic components may introduce distortions on the determination of the number of factors given that the relation between the variances of the common and idiosyncratic components is modified with the variances of F t decreasing and the variances of e t increasing in relation to the variance of F t and ε t , respectively. Recall as well that some procedures do not yield consistent estimates when the idiosyncratic noises are I (1).…”

“…Unit root tests are performed for the GDP and consumption gaps for all countries and, overall, we can consider that the series are I (1). In order to determine the number of common factors, we implement the procedure proposed by Onatski (2010) and choose r = 5 regardless whether it is implemented to data in levels or first differences; see Corona et al (2017) for a comparison on alternative procedures to determine the number of common factors in non-stationary DFMs.…”