Nowcasting GDP with Real-time Datasets: An ECM-MIDAS Approach · Nowcasting GDP with Real-time Datasets: An ECM-MIDAS Approach Alain Hecq , Thomas Goetz, J-P. Urbain Maastricht University

Nowcasting GDP with Real-time Datasets:An ECM-MIDAS Approach

Alain Hecq , Thomas Goetz, J-P. Urbain

Maastricht University

October 2011

Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 1 / 30

Motivation for MIDAS

Economic time series are available in mixed frequencies.

As an example, one can �nd daily stock prices and quarterly GDP.

Solutions: Average sampling or point in time sampling.

But loss of information due to the deletion of higher frequencyobservations.

Hence, it is reasonable to believe that the forecasting performance ofa low-frequency series (e.g. quarterly) might be improved by makinguse of the additional information contained in the higher frequencyvariables.

We focus on MIDAS, i.e. a restricted function of the high frequencyvariables instead of sometimes unfeasible unrestricted models. SeeGyshels�papers.


Motivation of this paper

We work in a MIDAS framework but add an ECM to usual models in�rst di¤erences to take into account the presence of cointegration.

Like almost everybody with his own "new" modeling, our approachgives more accurate forecast than alternative models both in MonteCarlo simulations and on empirical studies using the last availabledata (for the growth rate of the GDP).

But these are strange results at some point: not everybody can win!

Hence our idea was to compare the performance of di¤erent models,not just for the more recent historical vintage but using the di¤erentvintages in a real-time data approach.


Motivation for ROF

Let�s then apply the nice idea of Stark and Croushore (2002), i.e. toestimate ROF, i.e. repeated observation forecasting.

In practice, ROF consists, for each calendar date, to look at forecastsobtained from di¤erent vintages.

Hence for every calendar date we have not only a single point forecastbut a set of point forecasts from which we can study and plot thedistribution.

We "extend" the univariate analysis of Stark and Croushore (2002) byconsidering models with additional explanatory variables.

Our ideas were: a better model should have a more concentratedistribution or say di¤erently, two models that are not signi�cantlydi¤erent if their ROF distribution have the same accuracy.

It emerges that this is not so clear however.


Data

The dependent variable yt is the US quarterly real gross nationalproduct (ref. GNPC96), seasonally adjusted.

We extract real time data sets from http://alfred.stlouisfed.org/. Theseries is observed from 1960Q1 until 2010Q3.

There are monthly vintages from July 1986 to December 2010 but we�rst disregard the additional monthly vintages (i.e. keep theend-of-quarter vintages as quarterly vintages) in order to focus on theadditional vintage-dimension originating from employinghigh-frequency regressors.

Note that because we forecast growth rates of output, changes inbase years is not an issue for our ROF analysis. The intercept willcapture the di¤erence in the ECM such that we can compare theresults for di¤erent vintages.


Data

For the regressors in x we consider, the monthly seasonally adjustedindustrial production index (ref INDPRO) and the daily S&P 500stock index (ref. SP500).

We have 3 observations on IPI per quarter and 60 daily prices.

We want to make the model as simple as possible. Factor MIDAS is�ne but we do not want to work with 500 real-time series.


Vintage representation

VintagesCalendar time t,m� 2 t,m� 1 t,m...

...

t � 2,m� 2t � 2,m� 1t � 2,m� 0

x t ,m�2t�2,m�2 x t ,m�1t�2,m�2 x t ,mt�2,m�2x t ,m�2t�2,m�1 x t ,m�1t�2,m�1 x t ,mt�2,m�1x t ,m�2t�2,m x t ,m�1t�2,m x t ,mt�2,m ; y

tt�2

t � 1,m� 2t � 1,m� 1t � 1,m� 0

x t ,m�2t�1,m�2 x t ,m�1t�1,m�2 x t ,mt�1,m�2x t ,m�2t�1,m�1 x t ,m�1t�1,m�1 x t ,mt�1,m�1x t ,m�2t�1,m x t ,m�1t�1,m x t ,mt�1,m ; y

tt�1

t,m� 2t,m� 1t,m� 0

� x t ,m�1t ,m�2 x t ,mt ,m�2� � x t ,mt ,m�1� � nowcast y tt


Repeated observations forecasting approaches

A common practice in empirical work is to use the last available timeseries to evaluate forecasts.

This means that in a period T , June 2011 say, one collects thehistorical time series for yTt�1 where t = 2, . . . ,T assuming apublication lag of one period.

Subsequently, a one-step ahead point forecast for yT might beobtained.

For ROF, one take a particular calendar date t� and look at thehistorical series y vt��1 for a set of vintages v = 1, . . . ,V .We have a sequence of V (one step-ahead) forecasts for the samepoint y vt� , v = 1, . . . ,V , which can be reported on a graph.


Three issues:

Issue 1 forecast of y tt�1Vintages

Calendar time t,m� 2 t,m� 1 t,m...

...t � 2,m� 2t � 2,m� 1t � 2,m� 0

x t ,mt�2,m�2x t ,mt�2,m�1x t ,mt�2,m ; y

tt�2

t � 1,m� 2t � 1,m� 1t � 1,m� 0

x t ,mt�1,m�2x t ,mt�1,m�1x t ,mt�1,m ; y

tt�1

t,m� 2t,m� 1t,m� 0


Issue 2: Best timing for x . Indeed several vintages of x can be usedfor the same vintage of y . This means that we have an additionaldimension compared to the previous ROF study.

Issue 3: Nowcasting


Models

we have the following seven models:

1 MIDAS, long-run relationship included,2 MIDAS, long-run relationship excluded,3 Average sampling; long-run relationship included,4 Average sampling; long-run relationship excluded,5 Point-in-Time sampling; long-run relationship included,6 Point-in-Time sampling; long-run relationship excluded,7 ARIMA(4, 1, 0).


In order to compare whether one of the seven models dominates theothers, we conduct the ROF for six randomly chosen dates.

The dates are 1986Q3, 1991Q4, 1996Q1, 2001Q3, 2005Q2 and2009Q1. Note that for the last date only 7 forecast errors can becomputed due to the time period considered.

For each method under consideration, the next 20 end-of-quartervintages for both, the regressand and the regressors, are employed tocompute 20 one-step-ahead forecasts which are visualized using abox-plot.

It emerged that even after 20 quarters there is still a lot of revisions inthe growth rates. This is emphasized in Figure 1 where far after thegrey area (5 years) there is still some large movements in some dates.1986Q3 is a good example.


.020

.015

.010

.005

.000

.005

.010

.015

25 50 75 100 125 150 175 200 225 250 275

Date: 2001Q3Date: 2005Q2Date: 2009Q1Date: 1986Q3Date: 1991Q4Date: 1996Q1


.002

.000

.002

.004

.006

.008

.010

.012

PT_COIN

T_86Q

3

PT_86Q

3

AV_COIN

T_86Q

3

AV_86Q

3

MIDAS_C

OINT_8

6Q3

MIDAS_8

6Q3

AR(4)_8

6Q3

D86Q3_

Q

LAST_V

INT_8

6Q3


.000

.001

.002

.003

.004

.005

.006

.007

.008

.009

PT_COIN

T_91Q

4

PT_91Q

4

AV_COIN

T_91Q

4

AV_91Q

4

MIDAS_C

OINT_9

1Q4

MIDAS_9

1Q4

AR(4)_9

1Q4

D91Q4_

Q

LAST_V

INT_9

1Q4


.001

.002

.003

.004

.005

.006

.007

.008

.009

.010

PT_COIN

T_96Q

1

PT_96Q

1

AV_COIN

T_96Q

1

AV_96Q

1

MIDAS_C

OINT_9

6Q1

MIDAS_9

6Q1

AR(4)_9

6Q1

D96Q1_

Q

LAST_V

INT_9

6Q1


.008

.006

.004

.002

.000

.002

.004

.006

.008

PT_COIN

T_01Q

3

PT_01Q

3

AV_COIN

T_01Q

3

AV_01Q

3

MIDAS_C

OINT_0

1Q3

MIDAS_0

1Q3

AR(4)_0

1Q3

D2001

Q3_Q

LAST_V

INT_0

1Q3


.002

.004

.006

.008

.010

.012

.014

PT_COIN

T_05Q

2

PT_05Q

2

AV_COIN

T_05Q

2

AV_05Q

2

MIDAS_C

OINT_0

5Q2

MIDAS_0

5Q2

AR(4)_0

5Q2

D2005

Q2_Q

LAST_V

INT_0

5Q2


.025

.020

.015

.010

.005

.000

.005

PT_COIN

T_09Q

1

PT_09Q

1

AV_COIN

T_09Q

1

AV_09Q

1

MIDAS_C

OINT_0

9Q1

MIDAS_0

9Q1

AR(4)_0

9Q1

D2009

Q1_Q

LAST_V

INT_0

9Q1


Criteria for comparing forecasts

1 To have a less widespread distribution is not a criteria. For instanceAR(4) might be more concentrated but not around the �rst releaseneither the �nal estimate.

2 To be around the real time �rst release is not a criteria because the�rst release is not necessarily around the �nal estimate.

3 To be around the �nal estimate is not a fair criteria. Might be by luck.


.002

.000

.002

.004

.006

.008

.010

.012

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

PT_COINT_86Q3PT_86Q3AV_COINT_86Q3AV_86Q3MIDAS_COINT_86Q3MIDAS_86Q3AR(4)_86Q3D86Q3_QLAST_VINT_86Q3

.000

.001

.002

.003

.004

.005

.006

.007

.008

.009

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


.001

.002

.003

.004

.005

.006

.007

.008

.009

.010

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


.008

.006

.004

.002

.000

.002

.004

.006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


.002

.004

.006

.008

.010

.012

.014

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


.024

.020

.016

.012

.008

.004

.000

.004

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20



Criteria for comparing forecasts

The comparison of forecast accuracy is not obvious.

Indeed the performance of the several speci�cation can di¤er whencomparing with the �nal realization or the realization on thosespeci�c vintages.

In summary, is a model better because it get closer to the �nal �gureor the value at the corresponding vintages?


In order to have an intuitive idea of these di¤erences we compute forour seven models the RMSE over 20 quarters but we do it separatelywith respect to the �nal value or the vintage values.

For each of the six dates we rank the models from 1 (best) to 7 andwe then average these values for the six dates. We proceed similarlywhen comparing with the realized vintage values.

Table gives these sums

PT_LR PT Av_LR Av Midas_LR Midas AR(4)last vint 19 24 25 23 36 16 25real vint 14 21 26 22 29 22 34Total 33 45 51 45 65 38 59


Impact of regressor vintages

For the regressors, we have focused so far on the vintagescorresponding to the last month of a quarter.

It might, however, be the case, that using the vintages correspondingto the �rst or second month of a quarter yields considerably betterforecasting performances than using the end-of-quarter vintages.

If so, this might have an impact on how we should compute nowcastsof GDP (how many observations of the regressors we need toforecast).

Even if it turns out that employing di¤erent monthly vintages doesnot lead to signi�cantly di¤erent forecasting performance, we wouldhave gained the insight that we can make use of the most recentobservations without expecting a worse forecasting performance thanwhen we, for instance, waited another month for revised data.


In order to �nd out whether employing a certain vintage yieldsconsiderably better forecasting performances, we consider �vecandidate vintages per quarterly vintage for MIDAS models:

The x-vintage two months, one month before that of y , the samevintage as y , the vintage of x one month and two months after theone of y .

Now, similar to the previous section, but this time for each calendardate, a one-step-ahead forecast is computed employing real-time dataand the RMSE computed.


The Diebold-Mariano test are

DM statistic x-1 same x+1 x+2x-2 -0.65 -0.79 -0.61 -0.44x-1 -0.41 -0.03 0.11same 0.46 0.45x+1 0.24

None of the di¤erent high-frequency vintages yields better forecastingperformances than the others.

Hence, we may freely choose which x-vintage to employ for areal-time data analysis and nowcasting.


Nowcasting

Given the outcome of the previous analysis, we construct nowcastsusing the end-of-quarter vintages for the regressors.

This way we are using the most recent observation possible inreal-time.

Note that nowcasts may also be done during the quarter by employingadditional monthly vintages for the quarterly variable GDP or bysimply using the most recent observation of GDP.



Conclusion

This paper combines the issues of working with variables that aresampled at mixed-frequencies and working with real-time data sets.

Thereby, a wider range of models may be considered by thepractitioner and it is proposed to assess the superiority of one modelover the other by means of the repeated observations forecasting(ROF) approach introduced in Stark and Croushore (2002).

The performance of seven models was assessed by means of ROF andbox-plots of 20 one-step-ahead forecasts

Di¢ cult to determine what model does best.

We can eliminate less good speci�cation maybe.


With respect to the model comparison, it was found that no modeldominates the others for all dates considered.

Unlike the mixed-frequency models, the ARIMA model focused on byStark and Croushore (2002) is not able to react to recent changes inthe growth rate of GDP due to its exclusive dependency onlow-frequency information.

However, the MIDAS model excluding a long-run term seems to yieldreasonably good forecasting performances for all dates and, thereby,presents a robust choice to the researcher.

Employing this model it was found that all high-frequency vintagesconsidered show statistically similar forecasting performances suchthat the researcher can freely choose which one to employ and can,thereby, rely on the most recent information available in real-time tocompute fore- or nowcasts.


Documents

Nowcasting GDP with Real-time Datasets: An ECM-MIDAS Approach · Nowcasting GDP with Real-time Datasets: An ECM-MIDAS Approach Alain Hecq , Thomas Goetz, J-P. Urbain Maastricht University