Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment

Abstract

In the context of Dynamic Factor Models (DFM), we compare point and interval estimates of the underlying unobserved factors extracted using small and big-data procedures. Our paper differs from previous works in the related literature in several ways. First, we focus on factor extraction rather than on prediction of a given variable in the system. Second, the comparisons are carried out by implementing the procedures considered to the same data. Third, we are interested not only on point estimates but also on confidence intervals for the factors. Based on a simulated system and the macroeconomic data set popularized by Stock and Watson (2012), we show that, for a given procedure, factor estimates based on different cross-sectional dimensions are highly correlated. On the other hand, given the cross-sectional dimension, the Maximum Likelihood Kalman filter and smoother (KFS) factor estimates are highly correlated with those obtained using hybrid Principal Components (PC) and KFS procedures. The PC estimates are somehow less correlated. Finally, the PC intervals based on asymptotic approximations are unrealistically tiny. Keywords January 2015 AbstractIn the context of Dynamic Factor Models (DFM), we compare point and interval estimates of the underlying unobserved factors extracted using small and big-data procedures. Our paper di¤ers from previous works in the related literature in several ways. First, we focus on factor extraction rather than on prediction of a given variable in the system. Second, the comparisons are carried out by implementing the procedures considered to the same data. Third, we are interested not only on point estimates but also on con…dence intervals for the factors. Based on a simulated system and the macroeconomic data set popularized by Stock and Watson (2012), we show that, for a given procedure, factor estimates based on di¤erent cross-sectional dimensions are highly correlated. On the other hand, given the cross-sectional dimension, the Maximum Likelihood Kalman …lter and smoother (KFS) factor estimates are highly correlated with those obtained using hybrid Principal Components (PC) and KFS procedures. The PC estimates are somehow less correlated. Finally, the PC intervals based on asymptotic approximations are unrealistically tiny.

Determining the number of factors after stationary univariate transformations

“…(1) to (3) with r = 1, Φ = 1 and σ 2 η = 1. The factor loadings are generated by 59, 18.70, 34.63 and 65.56 for N = 12, 50, 100 and 200, respectively;Bai and Ng (2006) and Poncela and Ruiz (2016) also generate the factor loadings by the same distribution. We consider several structures for the idiosyncratic noises.…”

Remittances in Mexico and their unobserved components

“…Therefore, in our factor representation the number of variables is N = 5, being a small DFM with Y t = (x t , y d t , y h t , e t , u h t ) , where x t represents the monthly flow of remittances, y d t denotes GDP of the home economy, y h t the industrial production index of the host economy, e t the real exchange rate between the home and the host economies, and u h t captures the unemployment rate of the host economy. We expect that the home economy 6 See Poncela and Ruiz (2016) for a review of the sample performance of several methods of estimation.…”

“…If the time series are not cointegrated, the estimation of common factors can be carried out by several procedures. SeePoncela and Ruiz (2016) for a review of the literature.8 SeeBai and Ng (2002) andStock and Watson (2002a) who indicate that var(∆Ft) and var(εt) must exist.…”

A nowcasting approach to generate timely estimates of Mexican economic activity: An application to the period of COVID-19

“…An open question in the literature on large DFMs is whether a large number of series is adequate for a particular forecasting objective. In that sense, preselecting variables has proven to reduce the error prediction with respect to using the complete dataset Boivin and Ng (2006); that is, not always by using a large set of variables, we can obtain closer factor estimates with respect to when we use fewer variables, especially under finite sample performance Poncela and Ruiz (2016). Even when the number of time series is moderate, approximately 15, we can accurately estimate the simulated common factors, as shown by Corona et al (2020) in a Monte Carlo analysis.…”