Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models

Watson, Mark W.; Engle, Robert F.

doi:10.1016/0304-4076(83)90066-0

Cited by 408 publications

(276 citation statements)

References 11 publications

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“…In the case of the DFM, the algorithm alternates between the use of the Kalman smoother to estimate the common factors given a set of parameters (E-step), and multivariate regressions (corrected for the uncertainty in the estimation of the common factors) to estimate the parameters given the factors (M-step), see e.g. Watson and Engle (1983) or Shumway and Stoffer (1982). (…”

Section: Dynamic Factor Modelsmentioning

confidence: 99%

Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections

Banbura

Giannone

Lenza

2015

International Journal of Forecasting

123

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In 2014 all ECB publications feature a motif taken from the €20 banknote.NOTE: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily refl ect those of the ECB. AbstractThis paper describes an algorithm to compute the distribution of conditional forecasts, i.e. projections of a set of variables of interest on future paths of some other variables, in dynamic systems. The algorithm is based on Kalman filtering methods and is computationally viable for large models that can be cast in a linear state space representation. We build large vector autoregressions (VARs) and a large dynamic factor model (DFM) for a quarterly data set of 26 euro area macroeconomic and financial indicators. Both approaches deliver similar forecasts and scenario assessments. In addition, conditional forecasts shed light on the stability of the dynamic relationships in the euro area during the recent episodes of financial turmoil and indicate that only a small number of sources drive the bulk of the fluctuations in the euro area economy. JEL Classification: C11, C13, C33, C53Keywords: Vector Autoregression, Bayesian Shrinkage, Dynamic Factor Model, Conditional Forecast, Large Cross-Sections.ECB Working Paper 1733, September 2014 1 Non-technical summaryVector autoregressions (VARs) are very flexible and general models and provide a reliable empirical benchmark for alternative econometric representations such as dynamic stochastic general equilibrium (DSGE) models, which are more grounded in theory but, at the same time, impose more structure on the data.Recent literature has shown that VARs are viable tools also for large sets of data. In this paper we construct a large VAR for the euro area and we apply it to unconditional forecasting as well as for conditional forecasts and scenarios. These, along with structural analysis (assessing the effects of structural shocks), have been the main applications of VARs. Whereas large VARs have been used for unconditional forecasting and structural analysis, limited attention has been devoted as yet to conditional forecasting. This is because popular algorithms for deriving conditional forecasts have been computationally challenging for large data sets. We overcome this problem by computing the conditional forecasts recursively using Kalman filtering techniques.Conditional forecasts and, in particular, scenarios are projections of a set of variables of interest on future paths of some other variables. This is in contrast to unconditional forecasts, where no knowledge of the future path of any variables is assumed. The prior knowledge, albeit imperfect, of the future evolution of some economic variables may carry information for the outlook of other variables. For example, future fiscal packages would affect the future evolution of economic activity and, thus, might provide important off-model information. Moreover, it may be of interest to assess the impact of specific future events on a ...

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Section: Dynamic Factor Modelsmentioning

confidence: 99%

Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections

Banbura

Giannone

Lenza

2015

International Journal of Forecasting

123

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“…The parameters are usually estimated by Maximum Likelihood (ML) maximizing the one-step-ahead decomposition of the log-Gaussian likelihood; see Engle and Watson (1981) and Watson and Engle (1983). The maximization of the log-likelihood entails nonlinear optimization which restricts the number of parameters that can be estimated and, consequently, the number of series that can be handled when estimating the underlying factors.…”

Section: Kalman …Lter and Smoothingmentioning

confidence: 99%

Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment

Poncela¹,

Ruiz²

2016

Advances in Econometrics

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In the context of Dynamic Factor Models (DFM), we compare point and interval estimates of the underlying unobserved factors extracted using small and big-data procedures. Our paper differs from previous works in the related literature in several ways. First, we focus on factor extraction rather than on prediction of a given variable in the system. Second, the comparisons are carried out by implementing the procedures considered to the same data. Third, we are interested not only on point estimates but also on confidence intervals for the factors. Based on a simulated system and the macroeconomic data set popularized by Stock and Watson (2012), we show that, for a given procedure, factor estimates based on different cross-sectional dimensions are highly correlated. On the other hand, given the cross-sectional dimension, the Maximum Likelihood Kalman filter and smoother (KFS) factor estimates are highly correlated with those obtained using hybrid Principal Components (PC) and KFS procedures. The PC estimates are somehow less correlated. Finally, the PC intervals based on asymptotic approximations are unrealistically tiny. Keywords January 2015 AbstractIn the context of Dynamic Factor Models (DFM), we compare point and interval estimates of the underlying unobserved factors extracted using small and big-data procedures. Our paper di¤ers from previous works in the related literature in several ways. First, we focus on factor extraction rather than on prediction of a given variable in the system. Second, the comparisons are carried out by implementing the procedures considered to the same data. Third, we are interested not only on point estimates but also on con…dence intervals for the factors. Based on a simulated system and the macroeconomic data set popularized by Stock and Watson (2012), we show that, for a given procedure, factor estimates based on di¤erent cross-sectional dimensions are highly correlated. On the other hand, given the cross-sectional dimension, the Maximum Likelihood Kalman …lter and smoother (KFS) factor estimates are highly correlated with those obtained using hybrid Principal Components (PC) and KFS procedures. The PC estimates are somehow less correlated. Finally, the PC intervals based on asymptotic approximations are unrealistically tiny.

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“…To generate the results in this paper we used the BFGS algorithm to perform the optimization; see, for example, Nocedal and Wright (1999). An alternative approach would be to use the EM algorithm as developed for state space models by Watson and Engle (1983).…”

Section: Parameter Estimation and Signal Extractionmentioning

confidence: 99%

“…Early contributions to this literature can be found in Sargent and Sims (1977), Geweke (1977), Geweke and Singleton (1981), Engle and Watson (1981), Watson and Engle (1983), Connor and Korajczyk (1993) and Gregory, Head, and Raynauld (1997). Most of these papers consider time series panels with limited panel dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…These methods are typically applied to high dimensional panels of time series. Exact maximum likelihood methods such as proposed in Watson and Engle (1983) have traditionally been dismissed as computationally too intensive for such high dimensional panels. Exceptions are studies such as Quah and Sargent (1993) and Doz, Giannone, and Reichlin (2010) who consider moderately sized panels of economic time series in their studies.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model

Koopman

Wel

2013

International Journal of Forecasting

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Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models

Cited by 408 publications

References 11 publications

Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections

Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections

Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment

Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model

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