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Now- and forecasting the French GDP with a targeted dynamic factor model

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Marie Bessec (Banque de France)

Séminaire de l’OFCE - 2012

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Motivation

Growing interest in factor models to forecast macroeconomic variables in particular in Central Banks
Fed: Stock and Watson (1999, 2002), Giannone, Reichlin and Small (2008)
ECB: Giannone, Reichlin and Small (2008), Angelini et al. (2011),…
Banque de France: Barhoumi, Darné and Ferrara (2010)
Banca d’Italia: Altissimo et al. (2001, 2007)
Bundesbank: Schumacher (2007, 2010)

Problem of the number of variables N: Boivin & Ng (2006), Bai & Ng (2008)
in theory, N must be large
in practice, increasing N can be detrimental to the forecast

if the idiosyncratic components are large or correlated with each other
if a block of variables is driven by a factor less correlated to the forecast variable

Solution : Targeted predictors (Bai and Ng, 2008)

use of the LARS-EN algorithm to remove the irrelevant variables before the factor estimation

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Motivation

Previous applications in static factor models

Bai and Ng (2008): US inflation, industrial production,…
Charpin (2009): French GDP, h=1,0,-1
Schumacher (2010): German GDP, h=1,…,12

Aim of the paper: adapting the selection procedure in dynamic factor models to take into account the timeliness of indicators and the forecast horizon

Motivation: the dynamic factor model of Doz, Giannone and Reichlin (2011) and Giannone, Reichlin and Small (2008)

allows an update of GDP forecast with indicators released at a higher frequency
implementable on ragged edge data via the use of the Kalman filter

Application to the forecast of the French GDP: improvement on models estimated without pre-selection or with a pre-selection neglecting the timeliness of indicators and the forecast horizon

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4

T+1 M2

T+1 M1

T M3

T M2

T M1

T-1 M3

T-1 M2

T-1 M1

T-2 M3

T-2 M2

T-2 M1

X

Dec 2011

Jan 2012

Feb 2012

X

Nov 2011

X

Oct 2011

X

Sep 2011

X

Aug 2011

X

Jul 2011

X

Jun 2011

X

May 2011

X

Apr 2011

GDP

IPI

Manuf

Consump

Survey

4

Calendar: Forecast of quarter T

Forecasting, nowcasting and backcasting

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Specification: n variables x_t=(x_1t,x_2t,…,x_nt)’, r<< n factors, q≤r shocks

with u_t i.i.d. N(0,Ι_q) a white noise of dimension q (the dynamic shocks)

B is a r x q matrix

A₁,…,A_r are r x r matrices of parameters

Estimation: 2-step method of Doz, Giannone and Reichlin (2011)

Forecast

Forecast of F_t with the VAR → F_T+h|T
Forecast of y_twith

Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

5

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

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Step 1 : on the balanced subsample t = T₀,…,T-τ

estimation of Λ by PCA to x_t → F_t(préliminaire)
estimation of VAR on F_t→ A₁, A₂, …, A_p
estimation of B by PCA to the estimated covariance of the residuals of the VAR ζ_t

Step 2 : on the whole sample t = 1,…,T

Kalman filter and smoother → F_t|t, F_t|T

at iteration t : E(e_it²) = φ_i si x_it released,

∞ otherwise

VAR on F_t → F_T+h|T

tm	x₁	x₂	x₃	…	x_n
1	X		X
2	X	X	X
…	…	…	…
T₀-1	X	X	X
T₀	X	X	X	X	X
T₀+1	X	X	X	X	X
…	…	…	…	…	…
T-4	X	X	X	X	X
T-3	X	X	X	X	X
T-2	X		X		X
T-1	X		X
T	X

Estimation of Θ = (Λ, A₁, A₂, …, A_p,Φ,Σ_ζ,B) : Doz, Giannone et Reichlin (2011)

6

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

M. Bessec

June 2011

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Specification: n variables x_t=(x_1t,x_2t,…,x_nt)’, r<< n factors, q≤r shocks

with u_t i.i.d. N(0,Ι_q) a white noise of dimension q (the dynamic shocks)

B is a r x q matrix

A₁,…,A_r are r x r matrices of parameters

Estimation: 2-step method of Doz, Giannone and Reichlin (2011)

Forecast

Forecast of F_t with the VAR → F_T+h|T
Forecast of y_twith

Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

7

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

M. Bessec

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Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

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Let y_t be the variable to be forecast and x_t the predictors

EN criterion (Zou and Hastie, 2005)

Resolution with LARS algorithm

At the first iteration, all the coefficients are set to 0. In the following iterations, the variables are selected one by one according to their correlation with y_t while taking into account the correlation with the regressors already selected.

Remarks

instead of choosing λ₁, we define the number of regressors N_A to select among the N possible predictors
in this application, the LARS-EN algorithm is only used to select the N_A predictors

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

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Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

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The selection procedure needs to be adapted in the dynamic factor model

First, we do not consider a horizon specific model as usually done in the static approach ⇒ the targeted variable is the same ∀ h ⇒ a classical pre-selection procedure would lead to the same specification ∀ h

Second, short term indicators have different publication lags

survey and financial variables: 0 month
real indicators: 1 or 2 months

When ignoring the publication lags, the pre-selection would favor real indicators like IPI highly correlated to GDP but published with a significant delay.

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Static FM	Dynamic FM
Y_t+0 = δ F_t + ε_t for h=0 Y_t+1 = δ F_t + ε_t for h=1 Y_t+2 = δ F_t + ε_t for h=2	Y_t+h = δ F_t+h + ε_t∀ h

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Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

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Adaptation of the selection procedure in the dynamic factor model

1. Construction of a pseudo real time dataset for h

with x the monthly indicator and d the publication lag of x

2. Monthly series converted to quarterly data

with x^Q = the quarterly value in the third month of the quarter

unobserved otherwise

3. Application of the LARS-EN algorithm to this dataset

Example: manuf consumption in the 2^nd month of the quarter to be forecast

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

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June 2011

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

11

T+1 M2

T+1 M1

T M3

T M2

T M1

T-1 M3

T-1 M2

T-1 M1

T-2 M3

T-2 M2

T-2 M1

X

Dec 2011

Jan 2012

Feb 2012

X

Nov 2011

X

Oct 2011

X

Sep 2011

X

Aug 2011

X

Jul 2011

X

Jun 2011

X

May 2011

X

Apr 2011

PIB

IPI

Conso Manuf

Enquêtes

11

Calendar: Forecast of quarter T

?

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Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Example 1: forecast in the last month of the current quarter (M-2)

X a monthly indicator with d=0, Y a monthly indicator with d=1, Z a monthly indicator with d=2

t_Q	t_m	X	Y	Z
	1	X₁	Y₁	Z₁
	2	X₂	Y₂	Z₂
1	3	X₃	Y₃	Z₃
	4	X₄	Y₄	Z₄
	5	X₅	Y₅	Z₅
2	6	X₆	Y₆	Z₆
		…	…	…
	T-2	X_T-2	Y_T-2	Z_T-2
	T-1	X_T-1	Y_T-1	Z_T-1
T/3	T	X_T	Y_T	Z_T

full dataset

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	_∙
X₃	_∙	_∙
X₄	Y₄	Z₄
X₅	Y₅	_∙
X₆	_∙	_∙
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	_∙
X_T	_∙	_∙

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	Z_2\|1
X₃	Y_3\|2	Z_3\|1
X₄	Y₄	Z₄
X₅	Y₅	Z_5\|4
X₆	Y_6\|5	Z_6\|4
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	Z_T-1\|T-2
X_T	Y_T\|T-1	Z_T\|t-2

constructed dataset

real-time dataset

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

13

T+1 M2

T+1 M1

T M3

T M2

T M1

T-1 M3

T-1 M2

T-1 M1

T-2 M3

T-2 M2

T-2 M1

Dec 2011

Jan 2012

Feb 2012

Nov 2011

X

Oct 2011

X

Sep 2011

X

Aug 2011

X

Jul 2011

X

Jun 2011

X

May 2011

X

Apr 2011

PIB

IPI

Conso Manuf

Enquêtes

13

Calendar: Forecast of quarter T

?

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Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Example 2: forecast in the first month of the current quarter (M-4)

X a monthly indicator with d=0, Y a monthly indicator with d=1, Z a monthly indicator with d=2

t_Q	t_m	X	Y	Z
	1	X₁	Y₁	Z₁
	2	X₂	Y₂	Z₂
1	3	X₃	Y₃	Z₃
	4	X₄	Y₄	Z₄
	5	X₅	Y₅	Z₅
2	6	X₆	Y₆	Z₆
		…	…	…
	T-2	X_T-2	Y_T-2	Z_T-2
	T-1	X_T-1	Y_T-1	Z_T-1
T/3	T	X_T	Y_T	Z_T

full dataset

X	Y	Z
X₁	_∙	_∙
_∙	_∙	_∙
_∙	_∙	_∙
X₄	_∙	_∙
_∙	_∙	_∙
_∙	_∙	_∙
…	…	…
X_T-2	_∙	_∙
_∙	_∙	_∙
_∙	_∙	_∙

X	Y	Z
X₁	Y_1\|0	Z_1\|-1
X_2\|1	Y_2\|0	Z_2\|-1
X_3\|1	Y_3\|0	Z_3\|-1
X₄	Y_4\|3	Z_4\|2
X_5\|4	Y_5\|3	Z_5\|2
X_6\|4	Y_6\|3	Z_6\|2
…	…	…
X_T-2	Y_T-2\|T-3	Z_T-2\|T-4
X_T-1\|T-2	Y_T-1\|T-3	Z_T-1\|T-4
X_T\|T-2	Y_T\|T-3	Z_T\|t-4

constructed dataset

real-time dataset

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Dynamic factor model

LARS-EN algorithm

A real time pre-selection of indicators

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

X	Y	Z
X_1\|0	Y_1\|-1	Z_1\|-2
X_2\|0	Y_2\|-1	Z_2\|-2
X_3\|0	Y_3\|-1	Z_3\|-2
X_4\|3	Y_4\|2	Z_4\|1
X_5\|3	Y_5\|2	Z_5\|1
X_6\|3	Y_6\|2	Z_6\|1
…	…	…
X_T-2\|T-3	Y_T-2\|T-4	Z_T-2\|T-5
X_T-1\|T-3	Y_T-1\|T-4	Z_T-1\|T-5
X_T\|T-3	Y_T\|T-4	Z_T\|t-5

X	Y	Z
X_1\|-1	Y_1\|-2	Z_1\|--3
X_2\|-1	Y_2\|-2	Z_2\|--3
X_3\|-1	Y_3\|-2	Z_3\|--3
X_4\|2	Y_4\|1	Z_4\|0
X_5\|2	Y_5\|1	Z_5\|0
X_6\|2	Y_6\|1	Z_6\|0
…	…	…
X_T-2\|T-4	Y_T-2\|T-3	Z_T-2\|T-6
X_T-1\|T-4	Y_T-1\|T-3	Z_T-1\|T-6
X_T\|T-4	Y_T\|T-3	Z_T\|t-6

X	Y	Z
X₁	Y_1\|0	Z_1\|-1
X_2\|1	Y_2\|0	Z_2\|-1
X_3\|1	Y_3\|0	Z_3\|-1
X₄	Y_4\|3	Z_4\|2
X_5\|4	Y_5\|3	Z_5\|2
X_6\|4	Y_6\|3	Z_6\|2
…	…	…
X_T-2	Y_T-2\|T-3	Z_T-2\|T-4
X_T-1\|T-2	Y_T-1\|T-3	Z_T-1\|T-4
X_T\|T-2	Y_T\|T-3	Z_T\|t-4

X	Y	Z
X₁	Y₁	Z₁
X₂	Y_3\|1	Z_2\|1
X_3\|2	Y_3\|1	Z_3\|1
X₄	Y₄	Z₄
X₅	Y_5\|4	Z_5\|4
X_6\|5	Y_6\|4	Z_6\|4
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1\|T-2	Z_T-1\|T-2
X_T\|T-1	Y_T\|T-2	Z_T\|T-2

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	Z_2\|1
X₃	Y_3\|2	Z_3\|1
X₄	Y₄	Z₄
X₅	Y₅	Z_5\|4
X₆	Y_6\|5	Z_6\|4
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	Z_T-1\|T-2
X_T	Y_T\|t-1	Z_T\|T-2

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	Z₂
X₃	Y₃	Z_3\|2
X₄	Y₄	Z₄
X₅	Y₅	Z₅
X₆	Y₆	Z_6\|5
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	Z_T-1
X_T	Y_T	Z_T\|T-1

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	Z₂
X₃	Y₃	Z₃
X₄	Y₄	Z₄
X₅	Y₅	Z₅
X₆	Y₆	Z₆
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	Z_T-1
X_T	Y_T	Z_T

X	Y	Z
X_1\|-2	Y_1\|-3	Z_1\|--4
X_2\|-2	Y_2\|-3	Z_2\|--4
X_3\|-2	Y_3\|-3	Z_3\|--4
X_4\|1	Y_4\|0	Z_4\|-1
X_5\|1	Y_5\|0	Z_5\|-1
X_6\|1	Y_6\|0	Z_6\|-1
…	…	…
X_T-2\|T-5	Y_T-2\|T-4	Z_T-2\|T-7
X_T-1\|T-5	Y_T-1\|T-4	Z_T-1\|T-7
X_T\|T-5	Y_T\|T-4	Z_T\|t-7

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Survey variables in manufacturing industry, services, retail trade, construction and consumer surveys

Exchange rate of euro, key macroeconomic indicators in Germany and the US

Stock price indices, monetary aggregates, interest rates, spread, market volatility, price indices

Household consumption of manufactured goods, registrations of new vehicles, exports and imports of goods, industrial production, housing starts and building permits

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dataset

Pre-selection of variables

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June 2011

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Survey variables in manufacturing industry, services, retail trade, construction and consumer surveys

Exchange rate of euro, key macroeconomic indicators in Germany and the US

Stock price indices, monetary aggregates, interest rates, spread, market volatility, price indices

Household consumption of manufactured goods, registrations of new vehicles, exports and imports of goods, industrial production, housing starts and building permits

17

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dataset

Pre-selection of variables

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Survey variables in manufacturing industry, services, retail trade, construction and consumer surveys

Exchange rate of euro, key macroeconomic indicators in Germany and the US

Stock price indices, monetary aggregates, interest rates, spread, market volatility, price indices

Household consumption of manufactured goods, registrations of new vehicles, exports and imports of goods, industrial production, housing starts and building permits

18

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dataset

Pre-selection of variables

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dataset

Pre-selection of variables

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Selection of predictors (N_A=20 or 40)

Horizon Type	7	6	5	4	3	2	1	0
publication lag = 0	75%	80%	65%	90%	85%	63%	50%	50%
publication lag = 1	15%	15%	20%	10%	10%	20%	25%	25%
publication lag = 2	10%	5%	15%	0%	5%	18%	25%	25%
survey	40%	40%	40%	65%	55%	40%	38%	45%
nominal	30%	50%	50%	15%	25%	28%	20%	0%
international	20%	10%	10%	20%	20%	20%	13%	15%
real	10%	0%	0%	0%	0%	13%	30%	40%

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dataset

Pre-selection of indicators

T-1

T

T+1

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Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Dataset

Pre-selection of indicators

h	7	6	5	4	3	2	1	0
20000Q1 2010Q4	Business expectations (IFO)	General prod expect Industry	Business expectations (IFO)	Expected demand industry	IP manuf in US	IP manuf US	IP manuf	IP manuf
	General prod expect Industry	Business expectations (IFO)	General product expect Industry	IP manuf in US	Business expect Industry	Business expect Industry	IP other manuf	IP other manuf
	Business expectation (ZEW)	Stress index	Past fin situation Households	General prod expect Industry	Expected demand Industry	Expected demand Industry	Business expectationIndustry	IP Industry
	Exp financial sit Households	Exp Financial sit Households	Exp Financial sit Households	Business expectations (IFO)	General prod Exp Industry	General prod Exp Industry	IP Industry	Business expect Industry
	M1	Yield curve in France	Stress index	Business expectation (ZEW)	Business expectation (IFO)	Business expectations (IFO)	Unemployment	General production expect Industry
	past financial sit Households	Business expectation (ZEW)	SBF250	Stress index	Past production Building (D)	Unemployment US	General production exp Industry	Unemployment
	CUR Construction	Past financial sit Households	Order books Industry (D)	Business expect Services (D)	Business expectation (ZEW)	Past production Building (D)	Exports	Exp financial situation households
	General prod exp Industry (D)	Major purchase Households	CUR Construction	Exp Financial Sit Households	stress index	Business expectations (ZEW)	Past production Building (D)	Order books Building (D)
	CPI	General prod exp Industry (D)	Yield curve	Expected demand Services	Business expect Services (D)	Expected Financial sit Households	Order books Building (D)	Past production Building (D)
	Past financial sit Households (D)	CUR construction	Major purchase Households	Expect Orders Retail sales (D)	Order books Building (D)	Order books Building (D)	Exp financial situation Household	Consumption of manufactured goods
	Yield curve	Eurostoxx50	Past production Construction (D)	Dow Jones	Expected financial sit households	Business exp Services (D)	Consumption of manufactured goods	Employment US
	Major purchases Households	SBF 250	Business exp Industry (D)	Order books Building (D)	SBF250	Job vacancies	Job vacancies	Exports
	IP construction	Yield curve in US	Eurostoxx50	Major purchase Households	Eurostoxx50	Exp Employment Retail sales (D)	Business expectations (ZEW)	Business expectations (ZEW)
	Yield curve in US	Business expect Services (D)	DAX	DAX	Exp Employment Retail sales (D)	Major purchase Households	Employment US	Major purchase Households
	Consumption of textile	M1	M2	euro/uk	Major purchase Households	Consumption of manufactured goods	Major purchase Households	Job vacancies
	DAX	DAX	CPI	Exp Employment Retail sales (D)	Business exp Industry (D)	IP car	Consumption of goods	Consumption of goods
	IP manuf in US	IPC	M3	Past financial sit Households	10year interest rate	Dow Jones	Past financial situation Household	Expected eco situation households
	Business Expect building (D)	Real estate interest rate	M1	Past production Building (D)	M2 US	Employment	Expected economic situation households	Business expectations Service
	Current situation (ZEW)	Topix	1 year interest rate	Business exp Industry (D)	DAX	Business exp Industry (D)	Business expectation services	Consumption of household durables
	Eurostoxx50	Business expect Services	IP manuf in US	General prod exp Industry (D)	Past financial sit Households	Stress index	Business exp Industry (D)	M1

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Pseudo real time evaluation of the forecast

1) Recursive forecast in M-7, M-6, …, M-0 of 2000Q1 to 2010Q4 🡪 8 sets of forecasts conditional on the info in M-7,…,M-0 🡪 8 sets of forecast errors

2) Application of usual evaluation criteria to the forecast errors

Directional accuracy test of Pesaran et Timmermann

Limits : 1) omission of the impact of the revisions of data,

2) selection of the variables over the whole sample

T T+h

22

1990T1

2000T1

2010T4

Calendar

Pseudo-real time evaluation

Processes under competition

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

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23

Processes under competition

Factor model with a pre-selection in real time

with N_A = {20,40,60,80}
with λ₂ = {0.1,0.25,0.5,1.0,1.5}

Usual benchmarks: AR and RW with a drift
Factor model without pre-selection
Factor model with a pre-selection on the full dataset

with N_A = {20,40,60,80}
with λ₂ = {0.1,0.25,0.5,1.0,1.5}

Individual forecast / pooling of FM over N_A , λ₂, r , q and p → 160 specifications

Calendar

Pseudo-real time evaluation

Processes under competition

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

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Gradual improvement with the increase in monthly information

Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

The forecast is quite inaccurate 7 months before the release of GDP but the results improve gradually with the increase in monthly information…

… the forecast made a few days before the GDP release tracks GDP quite well.

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Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

N_A

h

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Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

N_A

h

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Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

N_A

h

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RMSFE comparison

28

Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Ratio of RMSE

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Impact of the timeliness and forecast horizon in the preselection

Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

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X	Y	Z
X_1\|0	Y_1\|-1	Z_1\|-2
X_2\|0	Y_2\|-1	Z_2\|-2
X_3\|0	Y_3\|-1	Z_3\|-2
X_4\|3	Y_4\|2	Z_4\|1
X_5\|3	Y_5\|2	Z_5\|1
X_6\|3	Y_6\|2	Z_6\|1
…	…	…
X_T-2\|T-3	Y_T-2\|T-4	Z_T-2\|T-5
X_T-1\|T-3	Y_T-1\|T-4	Z_T-1\|T-5
X_T\|T-3	Y_T\|T-4	Z_T\|t-5

X	Y	Z
X_1\|-1	Y_1\|-2	Z_1\|--3
X_2\|-1	Y_2\|-2	Z_2\|--3
X_3\|-1	Y_3\|-2	Z_3\|--3
X_4\|2	Y_4\|1	Z_4\|0
X_5\|2	Y_5\|1	Z_5\|0
X_6\|2	Y_6\|1	Z_6\|0
…	…	…
X_T-2\|T-4	Y_T-2\|T-3	Z_T-2\|T-6
X_T-1\|T-4	Y_T-1\|T-3	Z_T-1\|T-6
X_T\|T-4	Y_T\|T-3	Z_T\|t-6

X	Y	Z
X₁	Y_1\|0	Z_1\|-1
X_2\|1	Y_2\|0	Z_2\|-1
X_3\|1	Y_3\|0	Z_3\|-1
X₄	Y_4\|3	Z_4\|2
X_5\|4	Y_5\|3	Z_5\|2
X_6\|4	Y_6\|3	Z_6\|2
…	…	…
X_T-2	Y_T-2\|T-3	Z_T-2\|T-4
X_T-1\|T-2	Y_T-1\|T-3	Z_T-1\|T-4
X_T\|T-2	Y_T\|T-3	Z_T\|t-4

X	Y	Z
X₁	Y₁	Z₁
X₂	Y_3\|1	Z_2\|1
X_3\|2	Y_3\|1	Z_3\|1
X₄	Y₄	Z₄
X₅	Y_5\|4	Z_5\|4
X_6\|5	Y_6\|4	Z_6\|4
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1\|T-2	Z_T-1\|T-2
X_T\|T-1	Y_T\|T-2	Z_T\|T-2

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	Z_2\|1
X₃	Y_3\|2	Z_3\|1
X₄	Y₄	Z₄
X₅	Y₅	Z_5\|4
X₆	Y_6\|5	Z_6\|4
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	Z_T-1\|T-2
X_T	Y_T\|t-1	Z_T\|T-2

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	Z₂
X₃	Y₃	Z_3\|2
X₄	Y₄	Z₄
X₅	Y₅	Z₅
X₆	Y₆	Z_6\|5
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	Z_T-1
X_T	Y_T	Z_T\|T-1

X	Y	Z
X₁	Y₁	Z₁
X₂	Y₂	Z₂
X₃	Y₃	Z₃
X₄	Y₄	Z₄
X₅	Y₅	Z₅
X₆	Y₆	Z₆
…	…	…
X_T-2	Y_T-2	Z_T-2
X_T-1	Y_T-1	Z_T-1
X_T	Y_T	Z_T

X	Y	Z
X_1\|-2	Y_1\|-3	Z_1\|--4
X_2\|-2	Y_2\|-3	Z_2\|--4
X_3\|-2	Y_3\|-3	Z_3\|--4
X_4\|1	Y_4\|0	Z_4\|-1
X_5\|1	Y_5\|0	Z_5\|-1
X_6\|1	Y_6\|0	Z_6\|-1
…	…	…
X_T-2\|T-5	Y_T-2\|T-4	Z_T-2\|T-7
X_T-1\|T-5	Y_T-1\|T-4	Z_T-1\|T-7
X_T\|T-5	Y_T\|T-4	Z_T\|t-7

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Individual forecasts

Pooled forecasts

M. Bessec

June 2011

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31

Impact of the timeliness and forecast horizon in the preselection

Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

M. Bessec

June 2011

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32

Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

At the beginning of the forecasting exercise, the leftmost distribution corresponds to a pre-selection carried out with data in M-7. The distributions shift to the right as information is integrated in the selection, indicating that the forecasts deteriorate.

Symmetrically, shortly before the publication of GDP, the pre-selection conducted with full information leads to better results. Distributions now shift to the right when the pre-selection is performed with less information.

M. Bessec

June 2011

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33

Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

Motivations

Theoretical: a robust tool in the presence of misspecification and parameter instability (Timmermann, 2005, Clements and Hendry, 2004)

Empirical: SW (2004), Clark and McCracken (2010), Schumacher (2010)

Processes under competition

Factor model with a pre-selection in real time pooled over

N_A = {20,40,60,80}
λ₂ = {0.1,0.25,0.5,1.0,1.5}
r = {1,…,4}, q={1,2}, p = 1

Usual benchmarks: AR and RW with a drift

Factor model without pre-selection pooled over r = {1,…,4}, q={1,2}, p = 1

Factor model with a pre-selection on the full dataset pooled over N_A , λ₂ , r, p, q

M. Bessec

June 2011

34 of 37

RMSFE comparison

34

Individual forecasts

Pooled forecasts

Dynamic factor model with targeted predictors

Data

Experimental design

Out-of-sample results

M. Bessec

June 2011

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The Bai & Ng procedure is adapted to dynamic factor models

The selection is made on the information available at each horizon

Empirical results

financial and survey variables are predominant at larger horizons, real variables at shorter ones
improvement on models estimated without pre-selection
improvement on models estimated with a pre-selection neglecting the timeliness of the indicators and the forecast horizon

Potential extensions

a replication of this exercise on survey data to remove a potential impact on the results of the revisions of the data,
a comparison of our approach to the procedure of Rünstler (2010)

Main results and potential extensions

M. Bessec

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36

The Bai & Ng procedure is adapted to dynamic factor models

The selection is made on the information available at each horizon

Empirical results

financial and survey variables are predominant at larger horizons, real variables at shorter ones
improvement on models estimated without pre-selection
improvement on models estimated with a pre-selection neglecting the timeliness of the indicators and the forecast horizon

Potential extensions

a replication of this exercise on survey data to remove a potential impact on the results of the revisions of the data,
a comparison of our approach to the procedure of Rünstler (2010)

Main results and potential extensions

M. Bessec

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37

Main results and potential extensions

M. Bessec

X	Y	Z
X₁	Y_1\|0	Z_1\|-1
X_2\|1	Y_2\|0	Z_2\|-1
X_3\|1	Y_3\|0	Z_3\|-1
X₄	Y_4\|3	Z_4\|2
X_5\|4	Y_5\|3	Z_5\|2
X_6\|4	Y_6\|3	Z_6\|2
…	…	…
X_T-2	Y_T-2\|T-3	Z_T-2\|T-4
X_T-1\|T-2	Y_T-1\|T-3	Z_T-1\|T-4
X_T\|T-2	Y_T\|T-3	Z_T\|t-4

X	Y	Z
X_1\|0	Y_1\|-1	Z_1\|-2
X_2\|0	Y_2\|-1	Z_2\|-2
X_3\|0	Y_3\|-1	Z_3\|-2
X_4\|3	Y_4\|2	Z_4\|1
X_5\|3	Y_5\|2	Z_5\|1
X_6\|3	Y_6\|2	Z_6\|1
…	…	…
X_T-2\|T-3	Y_T-2\|T-4	Z_T-2\|T-5
X_T-1\|T-3	Y_T-1\|T-4	Z_T-1\|T-5
X_T\|T-3	Y_T\|T-4	Z_T\|t-5

X	Y	Z
X_1\|-1	Y_1\|-2	Z_1\|--3
X_2\|-1	Y_2\|-2	Z_2\|--3
X_3\|-1	Y_3\|-2	Z_3\|--3
X_4\|2	Y_4\|1	Z_4\|0
X_5\|2	Y_5\|1	Z_5\|0
X_6\|2	Y_6\|1	Z_6\|0
…	…	…
X_T-2\|T-4	Y_T-2\|T-3	Z_T-2\|T-6
X_T-1\|T-4	Y_T-1\|T-3	Z_T-1\|T-6
X_T\|T-4	Y_T\|T-3	Z_T\|t-6

X	Y	Z
X₁	Y_1\|0	Z_1\|-1
X_2\|1	Y_2\|0	Z_2\|-1
X_3\|1	Y_3\|0	Z_3\|-1
X₄	Y_4\|3	Z_4\|2
X_5\|4	Y_5\|3	Z_5\|2
X_6\|4	Y_6\|3	Z_6\|2
…	…	…
X_T-2	Y_T-2\|T-3	Z_T-2\|T-4
X_T-1\|T-2	Y_T-1\|T-3	Z_T-1\|T-4
X_T\|T-2	Y_T\|T-3	Z_T\|t-4

X	Y	Z
X_1\|-2	Y_1\|-3	Z_1\|--4
X_2\|-2	Y_2\|-3	Z_2\|--4
X_3\|-2	Y_3\|-3	Z_3\|--4
X_4\|1	Y_4\|0	Z_4\|-1
X_5\|1	Y_5\|0	Z_5\|-1
X_6\|1	Y_6\|0	Z_6\|-1
…	…	…
X_T-2\|T-5	Y_T-2\|T-4	Z_T-2\|T-7
X_T-1\|T-5	Y_T-1\|T-4	Z_T-1\|T-7
X_T\|T-5	Y_T\|T-4	Z_T\|t-7