Identification of Common Factors in Multivariate Time Series Modeling

For multivariate time series modelling, it is essential to know the number of common factors that define the behaviour. The traditional approach to this problem is investigating the number of cointegration relations among the data by determining the trace and the maximum eigenvalue and obtaining the number of stationary long-run relations. Alternatively, this problem can be analyzed using dynamic factor models, which involves estimating the number of common factors, both stationary and not, that describe the behaviour of the data. In this context, we empirically analyze the power of such alternative approaches by applying them to time series that are simulated using known factorial models and to financial market data. The results show that when there are stationary common factors, when the number of observations is reduced and/or when the variables are part of more than one cointegration relation, the common factors test is more powerful than the usually applied cointegration tests. These results, together with the greater flexibility to identify the loading matrix of the data generating process, render dynamic factor models more suitable for use in multivariate time series analysis.