dynamic factor model for consumer confidence

8/14/2019 Dynamic factor model for consumer confidence

http://slidepdf.com/reader/full/dynamic-factor-model-for-consumer-confidence 1/29

Erasmus Universiteit Rotterdam

Econometrics Institute

MSc in Econometrics and ManagementThesis:

Dynamic Factor Models for Consumer

Confidence in the US, the UK and

Germany∗

Dirk Nachbar†

August 25, 2005

Abstract

In this paper I investigate the effect of several macroeconomic variableson consumer confidence indices from the US, the UK and Germany. Giventhe large number of variables which might be highly correlated I opt for adynamic factor model to reduce the dimension of the data. The model’sforecasts will be compared to a simple AR model. In addition partial leastsquares will be considered as an alternative.

∗I would like to thank Dick van Dijk for his inspirational, critical and supportive help.†Student number 288993dn; address: Skladanowskystr. 5, 13156 Berlin, Germany, Email:

[email protected]

1



Contents

1 Introduction 4

2 Factor Model 4

2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Partial Least Squares . . . . . . . . . . . . . . . . . . . . . . 72.3 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Simulation with Information Criteria . . . . . . . . . . . . . 9

3 Data 9

3.1 Consumer Indices . . . . . . . . . . . . . . . . . . . . . . . . 93.1.1 US . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1.2 UK and Germany . . . . . . . . . . . . . . . . . . . 10

3.2 Explanatory variables . . . . . . . . . . . . . . . . . . . . . 10

4 Results 11

4.1 US . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2 UK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2.1 Sub-sample evaluation . . . . . . . . . . . . . . . . . 134.3 Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3.1 Structural Breaks in German data . . . . . . . . . . 13

5 Conclusion 14

List of Tables

1 The six US indices . . . . . . . . . . . . . . . . . . . . . . . 102 Statistics for the US indices . . . . . . . . . . . . . . . . . . 16

3 Summary statistics for UK and German index . . . . . . . . 164 US. Forecasting Performance of PCA based DFM . . . . . . 175 US. Performance of PLS . . . . . . . . . . . . . . . . . . . . 196 US. Performance of 3-variable model . . . . . . . . . . . . . 207 US. Correlation matrix for PC and PLS . . . . . . . . . . . 208 UK. Forecasting performance . . . . . . . . . . . . . . . . . 229 UK. Correlation between first/second PC and PLS factors . 2210 Germany. Forecasting performance . . . . . . . . . . . . . . 2411 Germany. Correlation between factors . . . . . . . . . . . . 2412 Data I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513 Data II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2614 Data III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2715 Data IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

16 Data V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

List of Figures

1 RMSE for IC1 and PC1 . . . . . . . . . . . . . . . . . . . . 162 US. R2 for each variable regressed on the first and the sec-

ond PC factor . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2



3 US. R2 for each variable regressed on the PLS factors, start-ing top left with the first PLS factor for USCNFCONQ andgoing to bottom right with the first PLS factor for USUM-CONSH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 UK. R2 for each variable regressed on the first and thesecond PC factor . . . . . . . . . . . . . . . . . . . . . . . . 21

5 UK. R2 for each variable regressed on the first and secondPLS factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6 Germany. R2 for each variable regressed on the first andthe second PC factor . . . . . . . . . . . . . . . . . . . . . . 23

7 Germany. R2 for each variable regressed on the first andsecond PLS factor . . . . . . . . . . . . . . . . . . . . . . . 23

3



1 Introduction

Consumer confidence is measured by a monthly index derived from ques-tionnaires posed to a sample of nationals. Policy analysts, investors andeconomists have become increasingly interested in these indices as theycan be seen as leading indicators for consumption and other economicactivities. The questions in these consumer surveys pertain to past andpresent states as well as future expectations. The indices are weightedaverages of the scaled answers to these questions. There is a reasonablylarge literature on the correlation between theses indices and, for instance,consumption.

However, in this paper I analyse whether consumer confidence can beexplained and predicted by macroeconomic variables as consumers are in-fluenced by many economic variables, through different channels. In par-ticular I will use many variables to predict consumer confidence/sentiment

indices in the UK, the US and Germany.Jansen and Nahuis [6], for instance, analyse the causality betweenstock market indices and consumer confidence in 11 EU countries. Theyfind that stock market indices Granger-cause consumer confidence in nineout of 11 countries. Interestingly, Germany is an exception, which justifiesthe inclusion of it in this paper.

The forecasting method applied here is via dynamic factor models,which extract common factors from the data and so minimise the dimen-sion of the data matrix. This method is compared to partial least squares,which correlate the variables with the index, and to simple autoregressivemodels. Dynamic factors models are in the centre of this investigationsince they are more widely applied than partial least squares.

The results of this investigation are not as persuasive as could beexpected from related work with dynamic factor models (DFMs). Partial

least squares, also, do not improve on average the forecasting performance.One conclusion is that the choice of the data matters more than previouslyassumed in the literature.

The outline of the paper is as follows. Section 2 presents the generalfactor model and describes its computation. The next section discussesthe data and its characteristics. Section 4 presents the results of theforecasting procedures.

2 Factor Model

2.1 General

Factor models have been around since the 1970s, but only recently they

have been extended to a dynamic context. In addition their forecastingability is a topic of relatively recent interest. This has been because of increased computing power, which is necessary for large models and theirsimulation in Monte Carlo studies.

The basic challenge in DFMs is the assumption about the error termsin the models. Different assumptions, as in any econometric framework,lead to different specifications and estimation procedures. Obviously, one

4



would want to allow the error terms to be flexible, i.e. correlated overtime and regressors.

Stock and Watson (henceforth SW) [10] present the approximate DFMwhich relates the variable to be forecast to a set of predictors. They callthe dynamic factors diffusion indexes (DI). SW’s model looks like this:

yt+1 = β F t + γ (L)yt + t+1, (1)

Xt = ΛtF t + et,

where yt+1 is the zero-mean series to be forecast, F t = (f t ,...,f t−q) isthe vector of lagged factors of the variables in the T ×N matrix Xt (T isthe number of observations and N is the number of variables), γ and β arecoefficients, Λt are the factor loadings, t is the disturbance and et is thefactor error. This is just a static representation of the DFM, since we donot assume an infinite distributed lag for the factors. However it makes

computation easy as we can estimate the factors by principal components(PC).Stock and Watson [9] show how principal component analysis (PCA)

can be used in a DFM, when the number of regressors is large. Theypresent the assumptions about the factors, errors and the forecasting equa-tion.

The assumption for the factor(s) (loadings) are:

• The matrix ΛΛ converges to the identity matrix.

• The covariance matrix of the factors is diagonal and its elements aredecreasing with the index.

• Each element of the factor loadings is finite.

• The sample covariance matrix of the factors converges to its true

covariance matrix for large T .These assumptions allow the factors to be serially correlated. The as-sumptions about the errors in the factor model, et are:

• The errors can be weakly correlated across time.

• The errors can be weakly correlated across series.

• The fourth moment should be finite.

The assumptions about the forecasting equation are:

• The covariance matrix of the factors and the other predictors (au-toregressive terms) is a positive definite matrix.

• The sample covariance matrices of the factors and other predictorsconverge to their true covariance matrices for large T .

• The factors and predictors are not correlated with the forecastingerror for large T .

• The forecasting error converges to σ2 for large T .

• The coefficients β and γ are finite.

5



Classical PCA derives the factors by by finding first the eigenvectors of X

X, Λ̂ and then forming the factor as1

F̂ = XΛ̂N. (2)

Essentially N can become very large (N >> T ), but the factors diminishthe dimension of the predictors. Obviously, extracting the factors is onlythe first step for building a DFM, it has to be followed by estimating thecoefficients in equation (1) by OLS.

A crucial question is how many factors are needed to represent theinformation in Xt in equation (1). Bai and Ng [1] examine the optimalnumber of factors more closely. They specify the model as:

xit = λi F t + eit, (3)

where F t are the common factors, λi are the factor loadings and eit is

the idiosyncratic component. Minimising the sum of squared residuals of equation (3) is equivalent to maximising tr(F k(XX

)F k), where k isthe number of factors. The estimator can also be derived as

F̂ k = F̄ k(F̄ kF̄ k/T )1/2, (4)

where the factors and loadings are normalised: Λ̄kΛ̄k = I k and F̄ k =XΛ̄k/N . Here Λ̄k is

√N times the eigenvectors corresponding to the

k largest eigenvalues of X

X. Bai and Ng test the features of manyinformation criteria to test for the ”true” value of factors. The ones withthe best properties are:

P C 1 = V (k, F̂ k) + kσ2

N + T

N T ln

N T

N + T (5)

P C 2 = V (k, F̂ k) + kσ2

N + T N T

ln C 2NT

IC 1 = ln(V (k, F̂ k)) + k

N + T

N T

ln

N T

N + T

IC 2 = ln(V (k, F̂ k)) + k

N + T

N T

ln C 2NT ,

where V (k, F̂ k) = minΛ1

NT

N

i=1

T

t=1(xit−λk

i F̂ k)2 and C NT = min(√

N ,√

T ).They also compare these criteria to conventional AICs and BICs whichare less applicable in this framework. In an empirical study Bai and Ngfind for 4883 stock series 2 (!) as the optimal number of factors.

Chan and SW [3] derive a framework for forecast combination withDFMs. The application of combination forecasts is fairly straight forwardand empirical studies show that combined forecasts improve upon single

forecasts in general. The combination of forecasts is also possible in aBayesian framework where Bayes factors are used to select models.

DFMs are a good method in case one has a lot of variables and onewants not to go through the tedious task of selecting and deselectingvariables from a large data set. Obviously deriving few factors from alarge data set reduces the informational content of the data substantially.

1X stands for Xt

6



In addition these variables and their derived factors have to fulfill certainassumptions (see above), which can make estimation difficult in case theyare not fulfilled. It should also be noted again that the SW framework is

just an approximation.For an estimation of factors via spectral densities the reader is referred

to Forni et al. [4].

2.2 Partial Least Squares

As was mentioned in the introduction there is another method to deter-mine factors from many regressors. The method is called Partial LeastSquares (PLS) and dates back to Wold, [11]. PLS circumvents the prob-lem of non-relatedness of the PC factor F t with the dependent variable ytin equation (1). The disadvantage of PLS is that although easy to imple-ment it takes a lot more computing time. Also there is no clear technique

of how many PLS factors are to be chosen.The first PLS factor is derived as follows

F 1t ∝N i=1

Cov(yit, xit)xit. (6)

Then yt and xit are regressed on this factor and the residuals are recorded:e1,t and e1,it. With these residuals the next factor is created (the residualsensure orthogonality).

F 2t ∝N i=1

Cov(e1,t, e1,it)e1,it. (7)

This is done for the next factors iteratively. These two factors (or possibly just the first) are then put into equation (1) instead of the PC factors.Lin and Tsay [7] compare PLS with principal components, ridge regressionand combination of forecasts. PLS with three components does well topredict US macroeconomic time series.

There is a second possibility to form PLS factors2, which allows theseparate inclusion of lags of the dependent variable in the forecastingequation (1). Instead of putting the dependent variable and the regressorsin the first factor in equation (9), one first regresses the dependent variableand the regressors on yt−1,...,yt−q and then uses these residuals for thefirst factor:

F 21t ∝N i=1

Cov(e0,t, e0,it)e0,it, (8)

where e0,t and e0,it are the residuals of the dependent variable and theregressors on the q lags of the dependent variable, respectively. The secondfactor is formed as in the previous method, just it will not be the same.

This method performs marginally better than the first PLS methodas the forecasting performance is better for the second method, which istrue for our empirical investigation. q will be determined by a simple

2This method was suggested by Christiaan Heij.

7



regression of yt on its lags and then one chooses q according to the BICminimum.

I will not use the Bai and Ng information criteria to choose the numberof PLS factors, but rather compare the root mean squared errors of modelswith a different number of PLS factors to determine the optimal numberof factors.

2.3 Forecasting

In my own estimation I follow SW’s work. SW apply their approximateDFM to 6-, 12- and 24-step forecasts of eight monthly US macroeconomictime series using 215 predictors. They present three specifications:

• DI-AR, Lags: lags of yt and the factors,

• DI-AR: many lags of yt, one lag of the factors,

• DI: one lag of the factors, no lag of yt.

The lag length and the number of factors are all chosen by BIC. SW’sresults show that the two last specifications work best.

The first model I will use for forecasting consumer indices is the fol-lowing:

yt+h|t = α +

Ii=1

Koptk=1

β ikF k,t−i+1 +

M m=1

γ myt−m+1 + y,t, (9)

where K opt is the number of factors. F t and yt are directly regressed

on yt+h. This approach has the advantage that it is easy to implementand one circumvents doing h iterative forecasts. Macrellino and SW [8]compare direct with iterated forecasts empirically. In general iteratedforecasts fare better than direct forecasts, however if BIC chooses the laglength (i.e. parsimonious models), direct forecasts can do well.

I will also forecast the first difference of the consumer index, for thisthe first difference will also appear as a regressor. Finally forecasts of thel-month difference will be made. This means:

yt+l − yt = α +

Ii=1

Koptk=1

β ikF k,t−i+1 +

M m=1

γ m∆yt−m+1 + y,t. (10)

The number of factors is chosen by the Bai-NG approach. First, the re-

gressors are multiplied by themselves:X

t = XtX

t . Then the eigenvaluesand eigenvectors of Xt are extracted (in decreasing order). V (k, F̂ ) in

equation (8) is calculated as

E

T t=1

(Xt − F̂ λ)2

T

. (11)

8



This is done for k = 1,...,kmax and σ2 is calculated as E(T

t=1X2t /T ).

Then the information criteria are computed as in (5). The next subsectiondoes a MC study to determine which information criterion to choose.

In order to compare my forecasts I will also estimate a simple ARmodel:

yt+h|t = α +

M m=1

γ myt−m+1 + y,t, (12)

for h-step ahead forecasts.All models are estimated by OLS.

2.4 Simulation with Information Criteria

To assess which of the information criteria in equation (5) to choose, Irun a small Monte Carlo study in which I simulate 50 data sets consisting

of an independent variable and an explanatory matrix. First two series(x1t, x2t) are generated according to an AR(1) and next yt is generatedas an AR(1) plus the two series x1t and x2t. Then from x1t 25 series aregenerated which are x1t times a random number plus noise, the same isdone for x2t. These 50 series are then our prediction matrix X. Afterthat yt and X are estimated in 2 DFMs where IC1 and PC1 choose k in aestimation/forecast program and the root mean squared (forecast) error(RMSE) is returned. BIC chooses between nine models: I and M runfrom 1 till 3. This is run 50 times for a sample size of 100. The RMSE iscalculated as:

RMSE =

1

50

100t=51

(yt|t−1 − yt)2 (13)

The RMSEs for IC1 and PC1 are exactly the same (i.e. IC1 and PC1choose the same number of factors), that is why I do the same simulationwith three factors. Everything is the same, just x1t and x3t appear 16times and x2 appears 17 times, so that we still have 50 variables in X.The results can be seen in figure 1 (RMSEs are sorted for better visibility).PC1 outperforms IC1. The mean RMSE of IC1 is 1.1548 and the meanRMSE of PC1 is 1.0586 (so IC1 is 9% worse). In general PC1 choosesmore parsimonious models. Because of this result I will use PC1 as myinformation criterion later in the empirical study.

3 Data

In this section the dependent and explanatory variables are presented.

All data start in January 1985, so that on average we have 20 years of observations (240 data points).

3.1 Consumer Indices

The Directorate General for Economic and Financial Affairs conducts reg-ular harmonised surveys for different sectors of the economies in the Eu-ropean Union (EU). These surveys allow comparisons among different

9



Before the factors are estimated the logs and first difference are appliedto the variables4. After that the variables have been standardised:

xsti =xti − x̂ti

Var(xti), (14)

where x̂ti is the mean of a single variable. There was no screening foroutliers since the three transformations usually eradicate outliers.

For the US we have 50 variables, for the UK 102 and for Germany 52.

4 Results

In order to determine whether a DFM performs well in forecasting I do 3-,6- and 12-step ahead forecasts according to equation (12) for t = 50,...,T .The starting month is February 1985 (January is lost because of first

differencing). The first 50 months are used as starting sample (until April1989) and then the sample and forecasting period moves one period aheadeach time (until beginning of 2005). I then calculate the RMSE:

RMSE =

1

T − 50− h

T t=50+h

(yt+h|t − yt+h)2, (15)

where h is the forecast horizon and yt+h|t is estimated from a DFM. TheRMSE of the DFM is divided by the RMSE of a corresponding simple ARmodel for yt.

The number of factors is chosen by PC1, and BIC chooses the lags/modelfor the DFM and the AR model. Every time a forecast is made BICchooses among 9 DFMs. In equation (12) I can be from 1 till 3 and M

from 1 till 3, as well. In the AR model M can be between 1 and 3 (BIC),equation (15). Furthermore, I also do forecasts of the first difference andof the l-month difference of the consumer index.

4.1 US

I estimate RMSEs for all six US indices and compare them to simple ARmodels. PC1 and BIC very often choose fairly small models, that meansone factor and one lag in F t and yt. Table 4 shows the results of 3-, 6-,and 12-ahead forecasts. The forecast of the first difference of the indicesis most persuasive as only two out of 18 relative RMSEs are above 1. Theother forecasts are good as well, but always the relative RMSE is veryclose to 1.

Now we look at the performance of the second PLS model. The de-pendent variable and the regressors are regressed on the first and secondlag of yt. Table 7 shows the correlation between the PCA and PLS5 fac-tors. The PCA factor is negatively correlated with all PLS factors. Table5 shows the forecasting performance of PLS. PLS’s performance is simi-lar to that of a PCA based DFM, but PCA outperforms PLS, although

4based on judgemental evaluation5PLS(1) is for the first index andsoforth.

11



some relative RMSE are quite low (e.g. 6-step ahead for USCNPSIT firstdifference).

In order to assess which variables the factors load on, I regress eachvariable on a constant and a single factor, then I record the R2. Figure2 shows the R2 for each variable with the PC factor. The first PC factorloads most on financial data and the second one loads on price indicesand monetary data. Figure 3, similarly, shows the loadings of each firstPLS factor6 on each variable. The first PLS factors look similar to thePC first factor.

It is also possible to handpick some variables and put them in a fore-casting model and then compare the performance to the other models.

yt+h|t = α +

Ii=1

J j=1

β ijxj,t−i+1 +

M m=1

γ myt−m+1 + y,t, (16)

where xj,t is only a subset of X. The equations for the first differenceand the l-month difference are formed accordingly. Choosing these vari-ables I opt for a semi-judgmental process. I look first at the correlationmatrix between the indices and the many variables and then choose thosewhich have high correlation and make economic sense or have been seenas leading indicators in the literature. For the US I found these threevariables:

• 31. Housing Starts

• 34. Purchasing Managers Index

• 35. Spot Oil Price

This model on average does not improve upon the factor models, but ithas some very low relative RMSE for the 12-step ahead forecast of the

first difference.

4.2 UK

For the UK I have only one index to forecast. All the results are given inTable 8. Here only the PCA based DFM has two relative RMSE below 1for the forecast of the level index.

For the PLS factor yt and the regressors were regressed on yt−1 only.The correlation between the PC and the PLS factors is given in Table 9.The highest correlation is between the first PC factor and the second PLSfactor. Figure 4 and 5 show the loadings of each variable on the PC andPLS factors. The first PC factor loads heavily on the financial variablesand the employment data. The second PC factor loads on the same databut less heavily. The first PLS factor loads less on financial data than the

first PC factor.Looking for single predictors, I extract one out of the 102 variables:

• 102. FTSE non financial share price index

This approach is only slightly better than the PLS or PCA approachapproach for the first difference and the l-month difference. Bold numbersindicate the lowest relative RMSE across models.

6Obviously every index has its own PLS factor.

12



5 Conclusion

In this paper the general factor model and its dynamic extension waspresented. To assess the predictive value of many variables for consumerindices, dynamic factor forecasting models were constructed and theirperformance relative to an AR model were computed. Furthermore, theefficiency of a PLS model was evaluated. However, the performance is notas persuasive as expected, for instance from the work of SW, althoughdifferent specifications were tried. In general one can say that the per-formance is highly dependent on the goodness of the variables which onechooses. For instance, it does make a difference how many variables of one type (employment, output) one includes in the data set as the factorsload more on those variables of which kind there are many in the dataset. If these variables have low predictive value for consumer confidence,then the forecasting performance is bad.

Overall, it seems that consumer confidence is affected by many factorswhich are not economically measurable. One can think, for instance, of political and societal events, such as war, sports, diplomatic crises etc.

14



References

[1] Bai, and Ng. Determining the Number of Factors in ApproximateFactor Models. Econometrica 70 (2002), 191–220.

[2] Bai, J. Estimating Multiple Breaks One at a Time. Econometric

Theory 13 (1997), 315–52.

[3] Chan, Stock, and Watson. A dynamic factor model framework forforecast combination. Spanish Economic Review 1 (1999), 91–121.

[4] Forni, Hallin, Lippi, and Reichlin. The Generalized Dynamic-Factor Model: Identification and Estimation. Review of Economics

and Statistics 82 (2000), 540–54.

[5] Hansen, B. The New Econometrics of Structural Change: DatingBreaks in U.S. Labour Productivity. Journal of Economic Perspec-

tives 15 (2001), 117–128.

[6] Jansen, and Nahuis. The stock market and consumer confidence:European evidence. Economic Letters 79 (2003), 89–98.

[7] Lin, J., and Tsay, S. Comparisons of Forecasting Methods withMany Predictors. Working paper, 2004.

[8] Macrellino, Stock, and Watson. A Comparison of Direct andIterated Multistep AR Methods for Forecasting Macroeconomic TimeSeries. Working paper, 2004.

[9] Stock, and Watson. Forecasting Using Principal ComponentsFrom a Large Number of Predictors. Journal of the American Sta-

tistical Association 97 (2002), 1167–79.

[10] Stock, and Watson. Macroeconomic Forecasting Using DiffusionIndexes. Journal of Business and Economic Statistics 20 (2002),147–162.

[11] Wold, H. Multivariate Analysis. Academic Press, New York, 1966,ch. Estimation of principal components and related models by itera-tive least squares, pp. 391–420.

15



Figure 1: RMSE for IC1 and PC1

CNFCONQ CNEXPT CNPSIT UMCONEH UMCONCH UMCONSHmean 101.134 95.588 109.457 84.758 103.986 92.278

standard dev. 22.924 12.984 42.805 10.734 8.356 9.448

skewness -0.201 -0.856 -0.059 -0.377 -0.652 -0.463kurtosis 2.455 3.609 2.251 3.515 3.383 3.519

CNFCONQ CNEXPT CNPSIT UMCONEH UMCONCH UMCONSHCNFCONQ 1.000

CNEXPT 0.821 1.000CNPSIT 0.966 0.644 1.000

UMCONEH 0.860 0.828 0.774 1.000UMCONCH 0.848 0.712 0.811 0.838 1.000UMCONSH 0.888 0.820 0.816 0.982 0.926 1.000

Table 2: Statistics for the US indices

UK Germanymean -8.626 -8.567

standard dev. 7.857 8.781skewness -0.352 -0.263

kurtosis 2.267 2.013

Table 3: Summary statistics for UK and German index

16



forecast of yt3-step 6-step 12-step

USCNFCONQ 0.999 1.005 0.995USCNEXPT 1.001 1.012 1.013

USCNPSIT 0.966 0.983 0.993

USUMCONEH 1.000 1.002 1.002USUMCONCH 0.995 1.002 1.002USUMCONSH 0.999 1.003 1.001

mean 0.993 1.001 1.001forecast of ∆yt

3-step 6-step 12-step


USCNPSIT 0.992 0.945 0.977USUMCONEH 0.939 0.949 0.941USUMCONCH 0.962 0.959 0.957USUMCONSH 0.940 0.947 0.943

mean 0.965 0.958 0.959

forecast of yt+l − yt3-step 6-step 12-step



mean 0.997 0.986 1.000

Table 4: US. Forecasting Performance of PCA based DFM

17



Figure 2: US. R2 for each variable regressed on the first and the second PCfactor

Figure 3: US. R2 for each variable regressed on the PLS factors, starting topleft with the first PLS factor for USCNFCONQ and going to bottom right withthe first PLS factor for USUMCONSH

18



forecast of yt3-step 6-step 12-step


USCNPSIT 0.954 0.993 0.982

USUMCONEH 0.978 1.007 1.012USUMCONCH 0.992 1.003 0.998USUMCONSH 0.987 0.997 1.004

mean 0.985 1.001 1.000forecast of ∆yt




mean 0.984 0.981 0.996

forecast of yt+l − yt3-step 6-step 12-step



mean 0.993 0.990 1.004

Table 5: US. Performance of PLS

19



Figure 4: UK. R2 for each variable regressed on the first and the second PCfactor

Figure 5: UK. R2 for each variable regressed on the first and second PLS factor

21



PCyt+h|t

3-step 6-step 12-step0.996 1.003 0.984

∆yt+h|t

3-step 6-step 12-step1.019 1.005 1.006

yt+l|t − yt3-month 6-month 12-month

1.006 1.020 1.081

PLS

yt+h|t

3-step 6-step 12-step1.015 1.011 1.009

∆yt+h|t

3-step 6-step 12-step1.010 1.003 1.004


1.015 1.018 1.110

1-variable

yt+h|t


1.007 1.008 1.019∆yt+h|t

3-step 6-step 12-step1.002 1.003 1.004


1.003 1.004 1.003

Table 8: UK. Forecasting performance

first PC second PC first PLS second PLS

first PC 1.000second PC 0.042 1.000

first PLS -0.307 -0.389 1.000second PLS 0.467 0.223 0.020 1.000

Table 9: UK. Correlation between first/second PC and PLS factors

22



Figure 6: Germany. R2 for each variable regressed on the first and the secondPC factor

Figure 7: Germany. R2 for each variable regressed on the first and second PLSfactor

23



PCyt+h|t

3-step 6-step 12-step0.994 0.987 0.995

∆yt+h|t

3-step 6-step 12-step0.999 1.021 1.019


1.003 1.006 0.991

PLS

yt+h|t

3-step 6-step 12-step0.990 0.994 0.982

∆yt+h|t

3-step 6-step 12-step1.007 1.020 0.994


1.011 1.023 1.020

2-variable

yt+h|t


0.950 0.967 0.964∆yt+h|t

3-step 6-step 12-step1.021 1.020 1.005


1.006 1.039 1.130

Table 10: Germany. Forecasting performance

first PC second PC first PLS second PLS

first PC 1.000second PC 0.006 1.000

first PLS -0.642 -0.116 1.000second PLS 0.729 0.096 -0.004 1.000

Table 11: Germany. Correlation between factors

24



T a b l e 1 3 : D a t a I I

i n d e x

d e s c r i p t i o n

m n e o m i c

s e a s o n a l l y

s o u r c e

a d j u s t e d

U S

4 3

P e r s o n a l S a v i n g , B i l . o f $

p m s a v e

X

F R E D I I

4 4

M 1 M o n

e y S t o c k ,

B i l . o f $

m 1 n s

F R E D I I

4 5

M 1 M o n

e y S t o c k ,

B i l . o f $

m 1 s l

X

F R E D I I

4 6

M 2 M o n

e y S t o c k ,

B i l . o f $

m 2 n s

F R E D I I

4 7

M 2 M o n

e y S t o c k ,

B i l . o f $

m 2 s l

X

F R E D I I

4 8

M 3 M o n

e y S t o c k ,

B i l . o f $

m 3 s l

X

F R E D I I

4 9

M 3 M o n

e y S t o c k ,

B i l . o f $

m 3 n s

F R E D I I

5 0

P r o d u c e r P r i c e I n d e x : A l l C o m m o d i t i e s , I n d e x

p p i a c o

F R E D I I

U K

1

A v e r a g e

R a t e s A g a i n s t S t e r l i n g : S t e r l i n g E

ff e c t i v e E x c h a n g e r a t e

A G B G

N a t i o n a l S t a t i s t i c s

2

S t e r l i n g

e x c h a n g e r a t e

A U S S


3

T o t a l C l a i m a n t c o u n t S A ( U K ) -

t h o u s a n d

s

B C J D

X


4

B O P : B a l a n c e : S A : T o t a l T r a d e i n G o o d s

B O K I

X


5

L o n g t e r

m i n d i c a t o r o f p r i c e s o f c o n s u m e r

g o o d s a n d s e r v i c e s

C D K O


6

R P I : P e r c e n t a g e c h a n g e o v e r 1 m o n t h - F o

o d

C D K P


7

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - A

l l i t e m s e x c . m o r t g a g e i n t e r e s t p a

y m e n t s

C D K Q


8

I O P : I n d

u s t r y C , D , E

: A l l p r o d u c t i o n i n d u s t r i e s

C K Y W


9

I O P : I n d

u s t r y C : M i n i n g & q u a r r y i n g

C K Y X


1 0

I O P : I n d

u s t r y D : M a n u f a c t u r i n g

C K Y Y


1 1

I O P : I n d

u s t r y E : E l e c t r i c i t y , g a s a n d w a t e r s u p p l y

C K Y Z


1 2

I O P : I n d

u s t r y C A 1 : E x t r a c t i o n o f o i l & g

a s :

C K Z O


1 3

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - a

l l i t e m s

C Z B H


1 4

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - a

l l i t e m s e x c l u d i n g h o u s i n g

C Z B I


1 5

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - S

e a s o n a l f o o d

C Z B P


1 6

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - F

o o d e x c l u d i n g s e a s o n a l

C Z B Q


1 7

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - H

o u s i n g

C Z C P


1 8

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - H

o u s e h o l d g o o d s

C Z D C


1 9

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - C

l o t h i n g a n d f o o t w e a r

C Z D O


2 0

R P I : P e r c e n t a g e c h a n g e o v e r 1 m o n t h -

A l l

i t e m s

C Z E Q


2 1


F o o

d a n d c a t e r i n g

C Z E R


2 2

P I : P e r c e

n t a g e c h a n g e o v e r 1 m o n t h -

S e a s o n a l f o o d

C Z E X


2 3


F o o

d e x c l u d i n g s e a s o n a l

C Z E Y


2 4


A l l

i t e m s e x c l u d i n g h o u s i n g

C Z F B


2 5


H o u s i n g

C Z F G


2 6


H o u s e h o l d g o o d s

C Z F I


2 7


C l o

t h i n g a n d f o o t w e a r

C Z F K


2 8

T a x & P

r i c e i n d e x : P e r c e n t a g e c h a n g e o v e r 1 m o n t h

C Z V K


2 9

T a x & P

r i c e i n d e x : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s

C Z V L


3 0


A l l

i t e m s e x c . M I P S + C o u n c i l T a x

D O F Y


3 1

R P I : P e r c e n t a g e c h a n g e o v e r 1 2 m o n t h s - A

l l i t e m s e x c . M I P S + C o u n c i l T a x

D O F Z


3 2

C B I I N D

U S T R I A L T R E N D S S U R V E Y : B

u s V o l O f O u t p u t E x p e c N e x t 4 M

o n t h s

E T C U


3 3

C B I I N D

U S T R I A L T R E N D S S U R V E Y : A

v D o m e s t i c P r i c e E x p e c N e x t 4 M

o n t h s

E T D Q

X


3 4

P a s s e n g e r c a r p r o d u c t i o n - t o t a l : t h o u s a n d s

F F A O

X


26



T a b l e 1 4 : D a t a I I I

i n d e x


m n e o m i c

s e a s o n a l l y

s o u r c e

a d j u s t e d

U K

3 5

P u r c h a s i n g p o w e r o f i n d e x

F J A K


3 6

I n t e r - b a n k : 3 m o n t h s : b i d r a t e

H S A J


3 7

a v e r a g e o f 4 U K B a n k s ’ r a t e s

I U M A A M I H

B a n k o f E n g l a n d

3 8

S t e r l i n g

i n t e r b a n k l e n d i n g r a t e , 3 m o n t h s

I U M A A M I J


3 9

B a n k o f

E n g l a n d r e p o r a t e

I U M A B E D R


4 0

E n d m o n t h l e v e l o f d i s c o u n t r a t e , 3 m o n t h

s T r e a s u r y b i l l s

I U M A J N B


4 1

y i e l d f r o m B r i t i s h G o v e r n m e n t S e c u r i t i e s , 1 0 y e a r s , i n fl a t i o n

I U M A M I Z C


4 2

y i e l d f r o m B r i t i s h G o v e r n m e n t S e c u r i t i e s , 1 0 y e a r s , N o m i n a l

I U M A M N Z C


4 3

y i e l d f r o m B r i t i s h G o v e r n m e n t S e c u r i t i e s , 1 0 y e a r s , r e a l

I U M A M R Z C


4 4

y i e l d f r o m B r i t i s h G o v e r n m e n t S e c u r i t i e s , 5 y e a r s , i n fl a t i o n

I U M A S I Z C


4 5

y i e l d f r o m B r i t i s h G o v e r n m e n t S e c u r i t i e s , 5 y e a r s , N o m i n a l

I U M A S N Z C


4 6

y i e l d f r o m B r i t i s h G o v e r n m e n t S e c u r i t i e s , 5 y e a r s , r e a l

I U M A S R Z C


4 7

S t e r l i n g

i n t e r b a n k l e n d i n g r a t e , 1 m o n t h

I U M A V N E A


4 8

S t e r l i n g

i n t e r b a n k l e n d i n g r a t e , 6 m o n t h s

I U M A V S M A


4 9

S t e r l i n g

i n t e r b a n k l e n d i n g r a t e , 1 w e e k

I U M A V W K A


5 0

S t e r l i n g

i n t e r b a n k l e n d i n g r a t e , 1 y e a r

I U M A V Y R A


5 1

A E I : W h o l e e c o n o m y N S A i n c b o n u s

L N M M


5 2

A E I : M a

n u f a c t u r i n g N S A i n c b o n u s

L N M N


5 3

A E I : P r o d u c t i o n N S A i n c b o n u s

L N M O


5 4

A E I : S e r v i c e s N S A i n c b o n u s :

L N M P


5 5

A E I : W h o l e e c o n o m y S A i n c b o n u s : % c h a n g e 3 m o n t h a v e r a g e

L N N C

X


5 6

U n i t W a

g e C o s t s : M a n u f a c t u r i n g i n d u s t r i e

s

L N N Q

X


5 7

O u t p u t p e r fi l l e d j o b : M a n u f a c t u r i n g I n d u

s t r i e s

L N N X

X


5 8

P r o d u c t i v i t y J o b s : M a n u f a c t u r i n g

L N O K

X


5 9

U K E m p

l o y e e j o b s ( S A ) : 3 m o n t h s a v e r a g

e -

M i n i n g , e n e r g y & w a t e r s u p p l y

L O M M

X


6 0

U K E m p

l o y e e j o b s ( S A ) : 3 m o n t h s a v e r a g e -

M a n u f a c t u r i n g i n d u s t r i e s

L O M N

X


6 1

A E I : W h o l e e c o n o m y N S A i n c b o n u s : % c h a n g e s i n g l e m o n t h

L O U J


6 2

A E I : M a

n u f a c t u r i n g N S A i n c b o n u s : % c h

a n g e s i n g l e m o n t h

L O U K


6 3

A E I : P r o d u c t i o n N S A i n c b o n u s : % c h a n g

e s i n g l e m o n t h

L O U L


6 4

A E I : S e r v i c e s N S A i n c b o n u s : % c h a n g e s i n g l e m o n t h

L O U M


6 5

I n t e r e s t

o n U S t r e a s u r y b i l l s ( 3 m o n t h s )

L U S T


6 6

L F S : I n

e m p l o y m e n t : U K : A l l : A g e d 1 6 + :

0 0 0 s

M G R Z

X


6 7

L F S : I n

e m p l o y m e n t : U K : M a l e : A g e d 1 6

a n d o v e r : T h o u s a n d s :

M G S A

X


6 8

L F S : I n

e m p l o y m e n t : U K : F e m a l e : A g e d 1

6 a n d o v e r : T h o u s a n d s

M G S B

X


6 9

L F S : U n

e m p l o y e d : U K : A l l : A g e d 1 6 + : 0 0

0 s

M G S C

X


7 0

L F S : U n

e m p l o y e d : U K : M a l e : A g e d 1 6 a n d o v e r : T h o u s a n d s

M G S D

X


7 1

L F S : U n

e m p l o y e d : U K : F e m a l e : A g e d 1 6 a n d o v e r : T h o u s a n d s

M G S E

X


7 2

L F S : E c o n o m i c a l l y a c t i v e : U K : A l l

M G S F

X


7 3

L F S : E c o n o m i c a l l y a c t i v e : U K : M a l e : T h o

u s a n d s

M G S G

X


7 4

L F S : E c o n o m i c a l l y a c t i v e : U K : F e m a l e : T h o u s a n d s

M G S H

X


7 5

L F S : E c o n i n a c t i v e : U K : A l l : A g e d 1 6 + : 0 0 0 s

M G S I

X


7 6

L F S : E c o n o m i c a l l y i n a c t i v e : U K : M a l e : A g e d 1 6 a n d o v e r : T h o u s a n d s

M G S J

X


7 7

L F S : E c o n o m i c a l l y i n a c t i v e : U K : F e m a l e :

A g e d 1 6 a n d o v e r : T h o u s a n d s

M G S K

X


27



T a b l e 1 5 : D a t a I V

i n d e x


m n e o m i c

s e a s o n

a l l y

s o u r c e

a d j u s t

e d

U K

7 8

L F S : P o p u l a t i o n a g e d 1 6 + : U K : A l l

M G S L


7 9

L F S : P o p u l a t i o n a g e d 1 6 a n d o v e r : U K : M

a l e : T h o u s a n d s

M G S M


8 0

L F S : P o p u l a t i o n a g e d 1 6 a n d o v e r : U K : F e m a l e : T h o u s a n d s

M G S N


8 1

L F S : E m

p l o y m e n t r a t e : U K : A l l : A g e d 1 6 - 5 9 / 6 4 :

%

M G S U

X


8 2

L F S : E m

p l o y m e n t r a t e : U K : M a l e : A g e d 1 6 - 6 4 : %

M G S V

X


8 3

L F S : E m

p l o y m e n t r a t e : U K : F e m a l e : A g e d 1 6 - 5 9 %

M G S W

X


8 4

L F S : U n

e m p l o y m e n t r a t e : U K : A l l : A g e d

1 6 a n d o v e r : %

M G S X

X


8 5

P P I : 7 2 0

9 2 0 0 0 0 0 : O u t p u t o f m a n u f a c t u r e d

p r o d u c t s

P L L U


8 6

P u b l i c S

e c t o r N e t C a s h R e q u i r e m e n t : m

R U R Q


8 7

E x c h a n g

e r a t e s f o r e u r o m o n t h l y a v e r a g e -

s t e r l i n g e u r o

T H A P


8 8

M o n e y s

t o c k M 4 : a n n u a l % c h a n g e

V Q J W

X


8 9

M o n e y s

t o c k M 0 : a n n u a l p e r c e n t a g e c h a n

g e

V Q M X

X


9 0

E m p l o y e

e j o b s : A l l j o b s : M a n u f a c t u r i n g I n

d s .

Y E J A

X


9 1

U K E m p

l o y e e j o b s ( S A ) : A l l j o b s -

M i n i n g

, E n e r g y & W a t e r

Y E J J

X


9 2

U K % I n

d e x o f E m p l o y e e j o b s ( S A ) : A l l j o b s -

M i n i n g , E n e r g y & W a t e r

Y E J K

X


9 3

U K % I n

d e x o f E m p l o y e e j o b s ( S A ) : A l l j o b s -

M a n u f a c t u r i n g

Y E J M

X


9 4

U K I N D

U S T R I A L P R O D U C T I O N S A D J

U K I 6 6 . . C

E

D a t a s t r e a m

9 5

U K I N D

U S T R I A L P R O D U C T I O N - I N

D U S T R Y E X C L C O N S T R U C T I O N V O L A

U K O P R 0 3 5 G

D a t a s t r e a m

9 6

U K I N D

U S T R I A L P R O D U C T I O N - I N

D U S T R Y E X C L C O N S T R U C T I O N V O L N

U K O P R 0 3 5 H

D a t a s t r e a m

9 7

U K C R U

D E O I L P R O D U C T I O N -

U N I T E D K I N G D O M V O L N

U K P C O B D . P

D a t a s t r e a m

9 8

U K C P I

- H O U S I N G N A D J

U K O C P 0 5 3 F

D a t a s t r e a m

9 9

U K N E W

O R D E R S O B T A I N E D -

N E W

H O U S I N G ( T O T A L ) C O N A

U K N O C H T T D

D a t a s t r e a m

1 0 0

U K R P I

- H O U S I N G N A D J

U K R P H O U S F

D a t a s t r e a m

1 0 1

U K R P I

- A L C O H O L I C D R I N K N A D J

U K R P A L C D F

D a t a s t r e a m

1 0 2

U K L E A

D I N G I N D I C A T O R : F T S E - A

N O

N F I N S H A R E P R I C E I N D E X

U K O L 0 7 8 4 R

D a t a s t r e a m

G e r m a n y

1

B D O N E

M O N T H F U N D S R A T E -

F R A N K F U R T ( h i g h e s t )

S U 0 1 0 4

B u n d e b a n k

2

B D T H R

E E M O N T H F U N D S R A T E - F R

A N K F U R T ( l o w e s t )

S U 0 1 0 8

B u n d e b a n k

3

B D T H R

E E M O N T H F U N D S R A T E - F R

A N K F U R T ( h i g h e s t )

S U 0 1 0 9

B u n d e b a n k

4

B D S I X

M O N T H F U N D S R A T E -

F R A N K F U R T ( l o w e s t )

S U 0 2 5 0

B u n d e b a n k

5

B D 1 2 M

O N T H F U N D S R A T E -

F R A N K

F U R T ( l o w e s t )

S U 0 2 5 3

B u n d e b a n k

6

B D U N E

M P L O Y M E N T L E S S U N F I L L E D

V A C A N C I E S ( W E S T ) S A D J

B D U N P V A C E

X

D a t a s t r e a m

7

B D U N E

M P L O Y M E N T L E S S U N F I L L E D

V A C A N C I E S ( W E S T ) N A D J

B D U N P V A C F

D a t a s t r e a m

8

B D U N E

M P L O Y M E N T L E V E L ( P A N B D

F R O M J A N 1 9 9 2 ) V O L A

B D U N P T O T O

D a t a s t r e a m

9

B D U N E

M P L O Y M E N T L E V E L ( P A N B D

F R O M S E P T 1 9 9 0 ) V O L N

B D U N P T O T P

D a t a s t r e a m

1 0

B D U N E

M P L O Y M E N T L E V E L -

F E M A L E ( W E S T ) N A D J

B D F E M U N P F

D a t a s t r e a m

1 1

B D U N E

M P L O Y M E N T L E V E L -

M A L E

( W E S T ) N A D J

B D M A L U N P F

D a t a s t r e a m

1 2

B D U N E

M P L O Y M E N T R A T E -

M A L E (

W E S T ) N A D J

B D M A L U N % F

D a t a s t r e a m

1 3

B D U N E

M P L O Y M E N T R A T E -

F E M A L E ( W E S T ) N A D J

B D F E M U N % F

D a t a s t r e a m

1 4

B D U N E

M P L O Y M E N T : % C I V I L I A N L A

B O U R

B D U N % T O T R

D a t a s t r e a m

1 5

B D I N D

U S T R I A L P R O D U C T I O N V O L A

B D E S I N P R G

D a t a s t r e a m

1 6

B D I N D

U S T R I A L P R O D U C T I O N V O L N

B D E S I N P R H

D a t a s t r e a m

1 7

B D I N D

U S T R I A L P R O D U C T I O N - C

O N S U M E R G O O D S V O L A

B D E S I S U R T

D a t a s t r e a m

28



T a b l e 1 6 : D a t a V

i n d e x


m n e o m i c

s e a s o n a l l y

s o u r c e

a d j u s t e d

G e r m a n y

1 8

B D I N D


O N S U M E R G O O D S V O L A

B D E S I S U R G

D a t a s t r e a m

1 9

B D I N D


O N S U M E R G O O D S V O L N

B D E S I S U R H

D a t a s t r e a m

2 0

B D C P I

S A D J

B D C O N P R C E

X

D a t a s t r e a m

2 1

B D C P I

N A D J

B D C O N P R C F

D a t a s t r e a m

2 2

B D C P I

N A D J

B D O C P 0 0 9 F

D a t a s t r e a m

2 3

B D F A C

T O R I N C O M E -

E X P E N D I T U R E C U R A

B D E S 3 1 7 0 B

D a t a s t r e a m

2 4

B D I N V

E S T M E N T I N C O M E : E X P E N D I T U R E C U R N

B D E U 3 1 6 9 A

D a t a s t r e a m

2 5

B D N O M

I N A L E F F E C T I V E T R A D E - W

E I G H T E D E X C H A N G E R A T E I N

D E X N A D J

B D I . . N

E U E

D a t a s t r e a m

2 6

B D R E A

L E F F E C T I V E E X C H A N G E R A

T E N A D J

B D O C C 0 1 1 F

D a t a s t r e a m

2 7

B D R E A

L E F F E C T I V E E X C H A N G E R A T E I N D E X -

C P I B A S E D S A D J

B D I . . R

E C E

X

D a t a s t r e a m

2 8

B D R E A

L E F F E C T I V E E X C H A N G E R A

T E S V O L N

B D O C C 0 1 1

D a t a s t r e a m

2 9

B D E F F

E C T I V E E X C H .

R A T E O F E U R O

A G A I N S T N A R R O W

G R O U P ,

R E A L N A D J

B D Y U W 9 0 5 F

D a t a s t r e a m

3 0

B D H O U

S I N G P E R M I T S G R A N T E D B S .

V O L A

B D H O U S I N G

D a t a s t r e a m

3 1

B D E M P L O Y M E N T -

M A N U F A C T U R I N

G V O L N

B D O E M 0 0 6 P

D a t a s t r e a m

3 2

B D E M P L O Y M E N T -

P A R T - T

I M E ( E C O

N O M I C R E A S O N ) V O L N

B D O E M 0 4 7 P

D a t a s t r e a m

3 3

B D R E T

A I L S U R V E Y : E M P L O Y M E N T -

G E R M A N Y N A D J

B D E U S R E M R

D a t a s t r e a m

3 4

B D S T A

N D A R D I Z E D U N E M P L O Y M E N T R A T E S A D J

B D O U N 0 1 4 Q

X

D a t a s t r e a m

3 5

B D T E R

M S O F T R A D E N A D J

B D T O T P R C F

D a t a s t r e a m

3 6

B D E X P

O R T S ( U S $ ) C U R N

B D O E X P U $ A

D a t a s t r e a m

3 7

B D E X P

O R T S ( I N U S $ ) C U R N

B D I 7 0 . . D

A

D a t a s t r e a m

3 8

B D E X P

O R T S ( F O B ) C U R N

B D E X P G D S A

D a t a s t r e a m

3 9

B D B O P

: G O O D S -

E X P O R T S C U R N

B D O B P 0 3 1 A

D a t a s t r e a m

4 0

B D B O P

: G O O D S -

I M P O R T S C U R N

B D O B P 0 4 3 A

D a t a s t r e a m

4 1

B D I M P

O R T S ( C I F ) C U R N

B D I M P G D S A

D a t a s t r e a m

4 2

B D D A X

S H A R E P R I C E I N D E X ,

E P N A

D J

B D S H R P R C F

D a t a s t r e a m

4 3

B D S H A

R E S : C D A X P E R F O R M A N C E I N D E X ( E N D 1 9 8 7 = 1 0 0 ) C U R N

B D W U 0 1 8 A A

D a t a s t r e a m

4 4

B D S H A

R E S : C D A X S H A R E P R I C E I N D

E X ( E N D 1 9 8 7 = 1 0 0 ) C U R N

B D W U 0 0 1 A A

D a t a s t r e a m

4 5

B D S H A

R E S : D A X P E R F O R M A N C E I N D

E X ( E N D 1 9 8 7 = 1 0 0 ) C U R N

B D W U 3 1 4 1 A

D a t a s t r e a m

4 6

B D B O P

: I N C O M E -

C R E D I T C U R N

B D O B P 0 2 4 A

D a t a s t r e a m

4 7

B D B O P

: I N C O M E -

D E B I T C U R N

B D O B P 0 3 6 A

D a t a s t r e a m

4 8

B D T A X

R E V E N U E - I N

C O M E T A X E S - T O T A L ( O L D L A N D E R ) C U R N

B D B U 1 0 0 9 A

D a t a s t r e a m

4 9

B D P P I

N A D J

B D I 6 3 . . .

F

D a t a s t r e a m

5 0

B D P P I

- A L L I T E M S N A D J

B D O P P 0 1 9 F

D a t a s t r e a m

5 1

B D P P I

- I N D U S T R I A L P R O D U C T S ( % Y O Y ) N A D J

B D P R O P R % F

D a t a s t r e a m

5 2

B D P P I : C O N S U M E R G O O D S N A D J

B D E S P P A 1 F

D a t a s t r e a m

29

dynamic factor model for consumer confidence

Documents