Detecting irrelevant variables in possible proxies for the latent factors in macroeconomics and finance

This paper focuses on evaluating the observed and latent factors in macroeconomics and finance from a new angle. The null hypothesis is that some observed time series is not correlated with each latent factor. This issue is interesting since it can help us to detect irrelevant variables in possible proxies for the latent factors in the macroeconomics and finance field. In this sense, this paper can be seen as the preliminary work of Bai and Ng (2006b) or one of its supplements. Under the null hypothesis and some mild assumptions, the proposed statistic is asymptotically chi-squared distributed. Monte Carlo simulation study shows that the new method has desired performance. A real example is analyzed for illustration