Презентация Basics of factor models онлайн

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Содержание слайда: Why factor models?

Содержание слайда: Why factor models?

Содержание слайда: What can be done with factor models?

Содержание слайда: An introduction to factor models

Содержание слайда: Some extensions

Содержание слайда: Representation

Содержание слайда: Representation

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Содержание слайда: Identification

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Содержание слайда: Factor models and VARs

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Содержание слайда: Estimation by the Kalman filter

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Содержание слайда: Non-parametric, large N, factor models

Содержание слайда: The SW approach - PCA The Stock and Watson (2002a,2002b) factor model is Xt = Λft ‡ ξt , where: Xt is N × 1 vector of stationary variables ft is r × 1 vector of common factors, can be correlated over time Λ is N × r matrix of loadings ξt is N × 1 vector of idiosyncratic disturbances, can be mildly cross-sectionally and temporally correlated conditions on Λ and ξt guarantee that the factors are pervasive (affect most variables) while idiosyncratic errors are not.

Содержание слайда: The SW approach - PCA

Содержание слайда: The SW approach - Choice of r

Содержание слайда: The SW approach - Properties of PCA

Содержание слайда: The SW approach - Properties of PCA

Содержание слайда: The SW approach - Properties of PCA based forecasts

Содержание слайда: The FHLR approach - DPCA

Содержание слайда: The FHLR approach - static and dynamic factors

Содержание слайда: The FHLR approach - Choice of q

Содержание слайда: The FHLR approach - Forecasting

Содержание слайда: Parametric estimation - quasi MLE

Содержание слайда: Parametric estimation - quasi MLE

Содержание слайда: Parametric estimation - Subspace algorithms (SSS)

Содержание слайда: Parametric estimation - SSS

Содержание слайда: Parametric estimation - SSS forecasts

Содержание слайда: Factor estimation methods - Monte Carlo Comparison

Содержание слайда: Factor estimation methods - MC Comparison, summary

Содержание слайда: Factor models - Forecasting performance Really many papers on forecasting with factor models in the past l5 years, starting with Stock and Watson (2002b) for the USA and Marcellino, Stock and Watson (2003) for the euro area. Banerjee, Marcellino and Masten (2006) provide results for ten Eastern European countries. Eickmeier and Ziegler (2008) provide nice summary (meta-analysis), see also Stock and Watson (2006) for a survey of the earlier results. Recently used also for nowcasting, i.e., predicting current economic conditions (before official data is released). More on this in the next lecture.

Содержание слайда: Factor models - Forecasting performance

Содержание слайда: Structural Factor Augmented VAR (FAVAR)

Содержание слайда: Structural FAVAR

Содержание слайда: Structural FAVAR - Monetary policy shock identification

Содержание слайда: Structural FAVAR - Monetary policy shock identification

Содержание слайда: Structural FAVAR - Monetary policy shock identification

Содержание слайда: Structural FAVAR - Monetary policy (FFR) shock

Содержание слайда: Structural FAVAR - Monetary policy (FFR) shock

Содержание слайда: Structural FAVAR - Monetary policy (FFR) shock

Содержание слайда: Structural FAVAR: Summary

Содержание слайда: References

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Содержание слайда: Stock, J.H. and Watson, M. W. (20l5), “Factor Models for Macroeconomics," in J. B. Taylor and H. Uhlig (eds), Handbook of Macroeconomics, Vol. 2, North Holland.

Содержание слайда: The FHLR approach - DPCA

Содержание слайда: The FHLR approach - DPCA

Содержание слайда: Parametric estimation - Subspace algorithms (SSS)

Содержание слайда: Parametric estimation - SSS, T asymptotics

Содержание слайда: Parametric estimation - SSS, T and N asymptotics

Содержание слайда: Factor estimation methods - MC Comparison First set of experiments: a single VARMA factor with di"erent specifications: 1a1 =0.2, b1 = 0.4¡ 2 a1 =0.7, bl =0.2¡ 3 a1 =0.3, a2 = 0.1, b1 = 0.15, b2 = 0.15¡ 4 a1 = 0.5, a2 = 0.3, b1 = 0.2, b2 = 0.2¡ 5 a1 = 0.2, b1 = —0.4¡ 6 a1 = 0.7, b1 = —0.2¡ 7 a1 = 0.3, a2 = 0.1, b1 = —0.15, b2 = —0.15¡ 8 a1 = 0.5, a2 = 0.3, b1 = —0.2, b2 = —0.2. 9 As 1but C = C0 + C1L. 10 As 1but one factor assumed instead of p + q

Содержание слайда: Factor estimation methods - MC Comparison Second group of experiments: as in 1-10 but with each idiosyncratic error being an AR(1) process with coefficient 0.2 (exp. 11-20). Experiments with cross correlation yield similar ranking of methods. Third group of experiments: 3 dimensional VAR(1) for the factors with diagonal matrix with elements equal to 0.5 (exp. 21). Fourth group of experiments: as 1-21 but the C matrix is U(0,1) rather than N(0,1). Fifth group of experiments: as 1-21 but using s = 1instead of s = m.

Содержание слайда: Factor estimation methods - MC Comparison

Содержание слайда: Factor estimation methods - MC Comparison, N=T=50 Single ARMA factor (exp. 1-8): looking at correlations, SSS clearly outperforms PCA and DPCA. Gains wrt PCA rather limited, 5-10%, but systematic. Larger gains wrt DPCA, about 20%. Little evidence of correlation of idiosyncratic component , but rejection probabilities of LM(4) test systematically larger for DPCA. Serially correlated idiosyncratic errors (exp. 11-18): no major changes. Low rejection rate of LM(4) test due to low power for T = 50. Dynamic effect of factor (exp. 9 and l9): serious deterioration of SSS, a drop of about 25% in the correlation values. DPCA improves but it is still beaten by PCA. Choice of s matters: for s =1SSS becomes comparable with PCA (Table 9).

Содержание слайда: Factor estimation methods - MC Comparison, N=T=50

Содержание слайда: Factor estimation methods - MC Comparison, other results