Markov-Switching Common Dynamic Factor Model with Mixed-Frequency Data

In this paper, we consider a coincident economic indicator model with regime-switching dynamics and with the time series observed at different frequencies, for instance, at monthly and quarterly frequencies. Until now the only solution was to drop the lower frequency series and to estimate the model based only on the higher frequency series. This approach leads to the significant information losses. We propose an approach allowing to overcome this problem and to estimate a nonlinear dynamic common factor with the missing observations taking advantage of all the information available.Common dynamic factor; Markov switching; Mixed frequency data; Kalman filter; Composite economic indicator

Fitting dynamic factor models to non-stationary time series

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time, by proposing a deterministic time variation of its loadings. In this respect we generalise existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a "double-asymptotic" framework of both cross-section and time dimension tending to infinity. A simulation study illustrates the performance of our estimators.econometrics;

Tracking Down the Business Cycle: A Dynamic Factor Model For Germany 1820-1913

We use a Bayesian dynamic factor model to measure Germany’s pre World War I economic activity. The procedure makes better use of existing time series data than historical national accounting. To investigate industrialization we propose to look at comovement between sectors. We find that Germany’s industrial sector developed earlier than stated in the literature, since after the 1860s agricultural time series do not comove with the business cycle anymore. Also, the bulk of comovement between 1820 and 1913 can be traced back to five out of 18 series representing industrial production, investment and demand for industrial inputs. Our factor is impressingly confirmed by a stock price index, leading the factor by 1-2 years. We also find evidence for early market integration in the 1820s and 1830s. Our business cycle dating aims to resolve the debate on German business cycle history. Given the often unsatisfactory quality of national accounting data for the 19th century we show the advantage of dynamic factor models in making efficient use of rare historical time series.Business Cycle Chronology; Imperial Germany; Dynamic Factor Models; Industrialization.

Functional dynamic factor models with application to yield curve forecasting

Accurate forecasting of zero coupon bond yields for a continuum of maturities is paramount to bond portfolio management and derivative security pricing. Yet a universal model for yield curve forecasting has been elusive, and prior attempts often resulted in a trade-off between goodness of fit and consistency with economic theory. To address this, herein we propose a novel formulation which connects the dynamic factor model (DFM) framework with concepts from functional data analysis: a DFM with functional factor loading curves. This results in a model capable of forecasting functional time series. Further, in the yield curve context we show that the model retains economic interpretation. Model estimation is achieved through an expectation-maximization algorithm, where the time series parameters and factor loading curves are simultaneously estimated in a single step. Efficient computing is implemented and a data-driven smoothing parameter is nicely incorporated. We show that our model performs very well on forecasting actual yield data compared with existing approaches, especially in regard to profit-based assessment for an innovative trading exercise. We further illustrate the viability of our model to applications outside of yield forecasting.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS551 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Forecasting Business Cycles in a Small Open Economy: A Dynamic Factor Model for Singapore

We apply multivariate statistical methods to a large dataset of Singapore’s macroeconomic variables and global economic indicators with the objective of forecasting business cycles in a small open economy. The empirical results suggest that three common factors are present in the time series at the quarterly frequency, which can be interpreted as world, regional and domestic economic cycles. This leads us to estimate a factor-augmented vector autoregressive (FAVAR) model for the purpose of optimally forecasting real economic activity in Singapore. By taking explicit account of the common factor dynamics, we find that iterative forecasts generated by this model are significantly more accurate than direct multi-step predictions based on the identified factors as well as forecasts from univariate and vector autoregressions.business cycles; principal components; dynamic factor model; factor-augmented VAR; forecasting; Singapore

Forecasting the U.S. term structure of interest rates using a macroeconomic smooth dynamic factor model

We extend the class of dynamic factor yield curve models for the inclusion of macro-economic factors. We benefit from recent developments in the dynamic factor literature for extracting the common factors from a large panel of macroeconomic series and for estimating the parameters in the model. We include these factors into a dynamic factor model for the yield curve, in which we model the salient structure of the yield curve by imposing smoothness restrictions on the yield factor loadings via cubic spline functions. We carry out a likelihood-based analysis in which we jointly consider a factor model for the yield curve, a factor model for the macroeconomic series, and their dynamic interactions with the latent dynamic factors. We illustrate the methodology by forecasting the U.S. term structure of interest rates. For this empirical study we use a monthly time series panel of unsmoothed Fama-Bliss zero yields for treasuries of different maturities between 1970 and 2009, which we combine with a macro panel of 110 series over the same sample period. We show that the relation between the macroeconomic factors and yield curve data has an intuitive interpretation, and that there is interdependence between the yield and macroeconomic factors. Finally, we perform an extensive out-of-sample forecasting study. Our main conclusion is that macroeconomic variables can lead to more accurate yield curve forecasts

Bayesian Inference on Dynamic Models with Latent Factors

In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction.Bayesian Dynamic Models, Simulation Based Inference, Particle Filters, Latent Factors, Business Cycle

Deep Dynamic Factor Models

We propose a novel deep neural net framework - that we refer to as Deep Dynamic Factor Model (D2FM) -, to encode the information available, from hundreds of macroeconomic and financial time-series into a handful of unobserved latent states. While similar in spirit to traditional dynamic factor models (DFMs), differently from those, this new class of models allows for nonlinearities between factors and observables due to the deep neural net structure. However, by design, the latent states of the model can still be interpreted as in a standard factor model. In an empirical application to the forecast and nowcast of economic conditions in the US, we show the potential of this framework in dealing with high dimensional, mixed frequencies and asynchronously published time series data. In a fully real-time out-of-sample exercise with US data, the D2FM improves over the performances of a state-of-the-art DFM