A Canonical Correlation Approach for Selecting the Number of Dynamic Factors

Breitung, Jörg; Pigorsch, Uta

doi:10.1111/obes.12003

Cited by 35 publications

(31 citation statements)

References 29 publications

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“…As in the appendix of Breitung and Pigorsch (2013) it can be shown that as N → ∞ and T → ∞ the linear combination G r,t (or G s,t ) converges in probability to HG t , where H is some regular m 0 × m 0 matrix. Hence, G r,t yields a consistent estimator of the space spanned by G t .…”

Section: The Cca Estimatormentioning

confidence: 91%

Analyzing Business and Financial Cycles Using Multi-Level Factor Models

Breitung

Eickmeier

2014

SSRN Journal

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Research QuestionIn recent years (dynamic) factor models have become increasingly popular for macroeconomic analysis and forecasting in a data-rich environment. A serious limitation of the standard approximate factor model is that it assumes the common factors to affect all variables of the system. However, the efficiency of the Principal Component (PC) estimator for the common factors may deteriorate substantially if there are factors that load on subsets of variables only. Those factors may also be of independent interest. In an international context, for example, factors that load on variables associated with specific regions ("regional factors") could be (and have been) analyzed besides the global factors which link all variables in the model. Alternatively (or in addition), a block structure may represent economic, cultural or other characteristics. This paper addresses the question how such models can be estimated in a fast and easy way. ContributionThis paper makes several contributions. First, we provide a comprehensive comparison of existing estimation approaches for multi-level factor models and propose two very simple alternative estimation techniques based on sequential least squares and canonical correlations (which avoids any iterations). Second, we extend the sequential least squares estimation approach to a three-level factor model (with, for example, global, regional and variable-specific factors) with overlapping blocks of factors. Such factors structures are challenging as they cannot be estimated one level after another. A final contribution are three applications in which we study international comovements of business and financial cycles as well as asymmetries over the business cycle in the US. ResultsOur suggested estimation techniques provide (point) estimates in a tiny fraction of a second (in typical (macro) settings) compared to a Bayesian estimator that requires several hours. We also shows that based on Monte Carlo simulations that, in some circumstances, our proposed estimators tend to outperform alternative (two-step principal component and quasi maximum likelihood) estimation methods.In the first application we apply several estimation methodologies for twolevel factor models to an annual real activity dataset of more than 100 countries between 1960 and 2010. We estimate global and regional factors which turn out to be very similar across methods. We confirm Hirata et al.'s main finding that regional (business cycle) factors have become more important and global factors less important over time.In the second application, we use a large quarterly macro-financial dataset for 24 countries between 1995 and 2011. We estimate a global factor, regional factors, as well as variable-specific (macro and financial) factors. We find that financial variables strongly comove internationally, to a similar extent as macroeconomic variables. Macroeconomic and financial dynamics share common factors, but financial factors independent from macro factors also matter for financial variables. Finally, ...

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Section: The Cca Estimatormentioning

confidence: 91%

Analyzing Business and Financial Cycles Using Multi-Level Factor Models

Breitung

Eickmeier

2014

SSRN Journal

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“…It is important to note that the procedures for determining the number of factors considered in this paper are designed for what is known in the literature as static factors. Alternatively, several factor determination procedures have been proposed in the context of dynamic factors; see, for example Amengual and Watson (2007); Hallin and Liska (2007); Bai and Ng (2007); Jacobs and Otter (2008) and Breitung and Pigorsch (2013). The difference between static and dynamic factors is described by, for example, Bai and Ng (2008).…”

Section: Introductionmentioning

confidence: 99%

Determining the number of factors after stationary univariate transformations

2016

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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.

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“…The idea of the test is that a r×r semipositive definite matrix of rank q has q nonzero eigenvalues and that a sequence of test statistics on the ordered eigenvalues of the VAR's residual covariance matrix converges to zero if the considered rank is greater than the true one. Related approaches for selecting the number of dynamic factors in a DFM have been developed that we do not consider here but refer the reader to Barhoumi et al (2013) or Breitung and Pigorsch (2013) who give an overview.…”

Section: Methodsmentioning

confidence: 99%

How Many Factors and Shocks Cause Financial Stress?

Kappler

Schleer

2013

SSRN Journal

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Die Dis cus si on Pape rs die nen einer mög lichst schnel len Ver brei tung von neue ren For schungs arbei ten des ZEW. Die Bei trä ge lie gen in allei ni ger Ver ant wor tung der Auto ren und stel len nicht not wen di ger wei se die Mei nung des ZEW dar.Dis cus si on Papers are inten ded to make results of ZEW research prompt ly avai la ble to other eco no mists in order to encou ra ge dis cus si on and sug gesti ons for revi si ons. The aut hors are sole ly respon si ble for the con tents which do not neces sa ri ly repre sent the opi ni on of the ZEW. AbstractThe aim of this paper is to assess the dimension of factors and shocks that drive financial conditions, and in particular financial stress in the euro area. A second aim is to construct summary indices on the conditions and level of stress in financial markets with the aid of a dynamic factor model. By analysing 149 newly compiled monthly time series on financial market conditions in the euro area, our results suggest that the data respond quite differently to fundamental shocks to financial markets but the dimension of these shocks is rather limited. Consequently, countries or segments of the financial sector in the euro area react fairly heterogonously to such shocks. We estimate several common factors and by means of an exploratory analysis we give them an economic interpretation. We find that the existence of a "Periphery Banking Crisis" factor, a "Stress" factor and a "Yield Curve" factor explains the bulk of variation in recent euro area financial sector data.JEL Classification: C38, G01

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A Canonical Correlation Approach for Selecting the Number of Dynamic Factors

Cited by 35 publications

References 29 publications

Analyzing Business and Financial Cycles Using Multi-Level Factor Models

Analyzing Business and Financial Cycles Using Multi-Level Factor Models

Determining the number of factors after stationary univariate transformations

How Many Factors and Shocks Cause Financial Stress?

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