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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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 2 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 3 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 4 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 5 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 6 / 30
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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 7 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 8 / 30
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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 9 / 30
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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 10 / 30
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).
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 11 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 12 / 30
.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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 13 / 30
.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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 14 / 30
.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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 15 / 30
.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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 16 / 30
.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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 17 / 30
.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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 18 / 30
.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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 19 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 20 / 30
.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
PT_COINT_91Q4PT_91Q4AV_COINT_91Q4AV_91Q4MIDAS_COINT_91Q4MIDAS_91Q4AR(4)_91Q4D91Q4_QLAST_VINT_91Q4
.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
PT_COINT_96Q1PT_96Q1AV_COINT_96Q1AV_96Q1MIDAS_COINT_96Q1MIDAS_96Q1AR(4)_96Q1D96Q1_QLAST_VINT_96Q1
.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
PT_COINT_01Q3PT_01Q3AV_COINT_01Q3AV_01Q3MIDAS_COINT_01Q3MIDAS_01Q3AR(4)_01Q3D2001Q3_QLAST_VINT_01Q3
.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
PT_COINT_05Q2PT_05Q2AV_COINT_05Q2AV_05Q2MIDAS_COINT_05Q2MIDAS_05Q2AR(4)_05Q2D2005Q2_QLAST_VINT_05Q2
.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
PT_COINT_09Q1PT_09Q1AV_COINT_09Q1AV_09Q1MIDAS_COINT_09Q1MIDAS_09Q1AR(4)_09Q1D2009Q1_QLAST_VINT_09Q1
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 21 / 30
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?
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 22 / 30
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
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 23 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 24 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 25 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 26 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 27 / 30
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 28 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 29 / 30
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.
Alain Hecq (Maastricht University)Nowcasting GDP with MIDAS October 2011 30 / 30
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