Econometrics Seminar: Lorenzo Trapani, University of Nottingham

Title: Determining the dimension of factor structures in nonstationary large datasets

2017.12.13 | Bodil Krog

Date Thu 01 Mar
Time 14:30 15:30
Location Fuglesangs Allé 4, 8210 Aarhus V, building 2630(K), room 101

Presenter: Lorenzo Trapani, University of Nottingham

Title: Determining the dimension of factor structures in nonstationary large datasets

Abstract: We propose a sequential, randomised testing procedure to determine the dimension of the common factor space in a large, possibly non-stationary, dataset. Our procedure is designed to determine, separately: (i) whether there are common factors with linear trends; (ii) whether there are common factors with stochastic trends (and how many there are); (iii) how many stationary common factors (if any) there are. As an ancillary result, our procedure can therefore also be used as a test for the stationarity or cointegration of a large dataset. The building block of the analysis is the fact that the first eigenvalues of the suitably scaled covariance matrix of the data (corresponding to the common factor part) diverge, whilst the others stay bounded. On the grounds of this, we propose a test for the null that the $p$-th eigenvalue diverges, using a randomised test statistic based directly on the estimated eigenvalue. The tests only requires minimal assumptions on the data, and no assumptions are required on factors, loadings or idiosyncratic errors; the randomised tests are then employed in a sequential procedure to determine the total number of factors. Monte Carlo evidence shows that our procedure has very good finite sample properties, clearly dominating competing approaches when no common factors are present.
      We illustrate our methodology through an application to US bond yields with different maturities observed over the last 30 years. A common linear trend and two common stochastic trends are found and identified as the level, slope and curvature factors driving the dynamics of the yield curve.

Area of Research: Theoretical and Time Series Econometrics

Organizers: Shin Kanaya and Agatha Murgoci

Econometrics and Business Statistics Seminar Series
14304 / i32