🗊 Презентация Basics of factor models

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Basics of factor models, слайд №1 Basics of factor models, слайд №2 Basics of factor models, слайд №3 Basics of factor models, слайд №4 Basics of factor models, слайд №5 Basics of factor models, слайд №6 Basics of factor models, слайд №7 Basics of factor models, слайд №8 Basics of factor models, слайд №9 Basics of factor models, слайд №10 Basics of factor models, слайд №11 Basics of factor models, слайд №12 Basics of factor models, слайд №13 Basics of factor models, слайд №14 Basics of factor models, слайд №15 Basics of factor models, слайд №16 Basics of factor models, слайд №17 Basics of factor models, слайд №18 Basics of factor models, слайд №19 Basics of factor models, слайд №20 Basics of factor models, слайд №21 Basics of factor models, слайд №22 Basics of factor models, слайд №23 Basics of factor models, слайд №24 Basics of factor models, слайд №25 Basics of factor models, слайд №26 Basics of factor models, слайд №27 Basics of factor models, слайд №28 Basics of factor models, слайд №29 Basics of factor models, слайд №30 Basics of factor models, слайд №31 Basics of factor models, слайд №32 Basics of factor models, слайд №33 Basics of factor models, слайд №34 Basics of factor models, слайд №35 Basics of factor models, слайд №36 Basics of factor models, слайд №37 Basics of factor models, слайд №38 Basics of factor models, слайд №39 Basics of factor models, слайд №40 Basics of factor models, слайд №41 Basics of factor models, слайд №42 Basics of factor models, слайд №43 Basics of factor models, слайд №44 Basics of factor models, слайд №45 Basics of factor models, слайд №46 Basics of factor models, слайд №47 Basics of factor models, слайд №48 Basics of factor models, слайд №49 Basics of factor models, слайд №50 Basics of factor models, слайд №51 Basics of factor models, слайд №52 Basics of factor models, слайд №53 Basics of factor models, слайд №54 Basics of factor models, слайд №55 Basics of factor models, слайд №56 Basics of factor models, слайд №57 Basics of factor models, слайд №58 Basics of factor models, слайд №59 Basics of factor models, слайд №60 Basics of factor models, слайд №61 Basics of factor models, слайд №62 Basics of factor models, слайд №63 Basics of factor models, слайд №64 Basics of factor models, слайд №65 Basics of factor models, слайд №66 Basics of factor models, слайд №67
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Слайды и текст этой презентации

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Basics of factor models, слайд №1
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Why factor models?
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Why factor models?

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Why factor models?
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Why factor models?

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What can be done with factor models?
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What can be done with factor models?

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An introduction to factor models
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An introduction to factor models

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Some extensions
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Some extensions

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Representation
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Representation

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Representation
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Representation

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Basics of factor models, слайд №9
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Basics of factor models, слайд №10
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Basics of factor models, слайд №11
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Basics of factor models, слайд №12
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Identification
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Identification

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Basics of factor models, слайд №14
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Basics of factor models, слайд №15
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Factor models and VARs
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Factor models and VARs

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Basics of factor models, слайд №17
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Estimation by the Kalman filter
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Estimation by the Kalman filter

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Basics of factor models, слайд №19
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Basics of factor models, слайд №20
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Non-parametric, large N, factor models
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Non-parametric, large N, factor models

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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 ×...
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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.

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The SW approach - PCA
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The SW approach - PCA

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The SW approach - Choice of r
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The SW approach - Choice of r

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The SW approach - Properties of PCA
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The SW approach - Properties of PCA

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The SW approach - Properties of PCA
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The SW approach - Properties of PCA

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The SW approach - Properties of PCA based forecasts
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The SW approach - Properties of PCA based forecasts

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The FHLR approach - DPCA
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The FHLR approach - DPCA

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The FHLR approach - static and dynamic factors
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The FHLR approach - static and dynamic factors

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The FHLR approach - Choice of q
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The FHLR approach - Choice of q

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The FHLR approach - Forecasting
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The FHLR approach - Forecasting

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Parametric estimation - quasi MLE
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Parametric estimation - quasi MLE

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Parametric estimation - quasi MLE
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Parametric estimation - quasi MLE

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Parametric estimation - Subspace algorithms (SSS)
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Parametric estimation - Subspace algorithms (SSS)

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Parametric estimation - SSS
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Parametric estimation - SSS

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Parametric estimation - SSS forecasts
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Parametric estimation - SSS forecasts

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Factor estimation methods - Monte Carlo Comparison
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Factor estimation methods - Monte Carlo Comparison

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Factor estimation methods - MC Comparison, summary
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Factor estimation methods - MC Comparison, summary

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Factor models - Forecasting performance Really many papers on forecasting with factor models in the past l5 years, starting with Stock and Watson...
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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.

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Factor models - Forecasting performance
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Factor models - Forecasting performance

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Structural Factor Augmented VAR (FAVAR)
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Structural Factor Augmented VAR (FAVAR)

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Structural FAVAR
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Structural FAVAR

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Structural FAVAR - Monetary policy shock identification
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Structural FAVAR - Monetary policy shock identification

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Structural FAVAR - Monetary policy shock identification
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Structural FAVAR - Monetary policy shock identification

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Structural FAVAR - Monetary policy shock identification
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Structural FAVAR - Monetary policy shock identification

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Structural FAVAR - Monetary policy (FFR) shock
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Structural FAVAR - Monetary policy (FFR) shock

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Structural FAVAR - Monetary policy (FFR) shock
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Structural FAVAR - Monetary policy (FFR) shock

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Structural FAVAR - Monetary policy (FFR) shock
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Structural FAVAR - Monetary policy (FFR) shock

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Structural FAVAR: Summary
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Structural FAVAR: Summary

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References
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References

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Basics of factor models, слайд №51
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Basics of factor models, слайд №52
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Basics of factor models, слайд №53
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Basics of factor models, слайд №54
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Basics of factor models, слайд №55
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Stock, J.H. and Watson, M. W. (20l5), “Factor Models for Macroeconomics," in J. B. Taylor and H. Uhlig (eds), Handbook of Macroeconomics, Vol....
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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.

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The FHLR approach - DPCA
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The FHLR approach - DPCA

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The FHLR approach - DPCA
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The FHLR approach - DPCA

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Parametric estimation - Subspace algorithms (SSS)
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Parametric estimation - Subspace algorithms (SSS)

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Parametric estimation - SSS, T asymptotics
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Parametric estimation - SSS, T asymptotics

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Parametric estimation - SSS, T and N asymptotics
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Parametric estimation - SSS, T and N asymptotics

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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...
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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

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Factor estimation methods - MC Comparison Second group of experiments: as in 1-10 but with each idiosyncratic error being an AR(1) process with...
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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.

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Factor estimation methods - MC Comparison
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Factor estimation methods - MC Comparison

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Factor estimation methods - MC Comparison, N=T=50 Single ARMA factor (exp. 1-8): looking at correlations, SSS clearly outperforms PCA and DPCA. Gains...
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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).

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Factor estimation methods - MC Comparison, N=T=50
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Factor estimation methods - MC Comparison, N=T=50

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Factor estimation methods - MC Comparison, other results
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Factor estimation methods - MC Comparison, other results

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