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

Transcription

1 Nowcasting GDP with Real-time Datasets: An ECM-MIDAS Approach, Thomas Goetz, J-P. Urbain Maastricht University October 2011 lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

2 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 frequency observations. Hence, it is reasonable to believe that the forecasting performance of a low-frequency series (e.g. quarterly) might be improved by making use of the additional information contained in the higher frequency variables. We focus on MIDAS, i.e. a restricted function of the high frequency variables instead of sometimes unfeasible unrestricted models. See Gyshels papers. (Maastricht University) Nowcasting GDP with MIDAS October / 30

3 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 approach gives more accurate forecast than alternative models both in Monte Carlo simulations and on empirical studies using the last available data (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 erent vintages in a real-time data approach. (Maastricht University) Nowcasting GDP with MIDAS October / 30

4 Motivation for ROF Let s then apply the nice idea of Stark and Croushore (2002), i.e. to estimate ROF, i.e. repeated observation forecasting. In practice, ROF consists, for each calendar date, to look at forecasts obtained from di erent vintages. Hence for every calendar date we have not only a single point forecast but a set of point forecasts from which we can study and plot the distribution. We "extend" the univariate analysis of Stark and Croushore (2002) by considering models with additional explanatory variables. Our ideas were: a better model should have a more concentrate distribution or say di erently, two models that are not signi cantly di erent if their ROF distribution have the same accuracy. It emerges that this is not so clear however. (Maastricht University) Nowcasting GDP with MIDAS October / 30

5 Data The dependent variable y t is the US quarterly real gross national product (ref. GNPC96), seasonally adjusted. We extract real time data sets from The series 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 the end-of-quarter vintages as quarterly vintages) in order to focus on the additional vintage-dimension originating from employing high-frequency regressors. Note that because we forecast growth rates of output, changes in base years is not an issue for our ROF analysis. The intercept will capture the di erence in the ECM such that we can compare the results for di erent vintages. (Maastricht University) Nowcasting GDP with MIDAS October / 30

6 Data For the regressors in x we consider, the monthly seasonally adjusted industrial production index (ref INDPRO) and the daily S&P 500 stock 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. (Maastricht University) Nowcasting GDP with MIDAS October / 30

7 Vintage representation Vintages Calendar time t, m 2 t, m 1 t, m. t 2, m 2 t 2, m 1 t 2, m 0 t 1, m 2 t 1, m 1 t 1, m 0 t, m 2 t, m 1 t, m 0 x t,m 2 t 2,m 2 x t,m 1 t 2,m 2 x t,m t 2,m 2 x t,m 2 t 2,m 1 x t,m 1 t 2,m 1 x t,m t 2,m 1 x t,m 2 t 2,m x t,m 1 t 2,m x t,m t 2,m ; y t t 2 x t,m 2 t 1,m 2 x t,m 1 t 1,m 2 x t,m t 1,m 2 x t,m 2 t 1,m 1 x t,m 1 t 1,m 1 x t,m t 1,m 1 x t,m 2 t 1,m x t,m 1 t 1,m x t,m t 1,m ; y t t 1 x t,m 1 t,m 2 x t,m t,m 2 x t,m t,m 1 nowcast y t t. (Maastricht University) Nowcasting GDP with MIDAS October / 30

8 Repeated observations forecasting approaches A common practice in empirical work is to use the last available time series to evaluate forecasts. This means that in a period T, June 2011 say, one collects the historical time series for yt T 1 where t = 2,..., T assuming a publication lag of one period. Subsequently, a one-step ahead point forecast for ŷ T might be obtained. For ROF, one take a particular calendar date t and look at the historical series yt v 1 for a set of vintages v = 1,..., V. We have a sequence of V (one step-ahead) forecasts for the same point ŷt v, v = 1,..., V, which can be reported on a graph. (Maastricht University) Nowcasting GDP with MIDAS October / 30

9 Three issues: Issue 1 forecast of y t t 1 Vintages Calendar time t, m 2 t, m 1 t, m. t 2, m 2 t 2, m 1 t 2, m 0 t 1, m 2 t 1, m 1 t 1, m 0 t, m 2 t, m 1 t, m 0 x t,m t 2,m 2 x t,m t 2,m 1 x t,m t 2,m ; y t t 2 x t,m t 1,m 2 x t,m t 1,m 1 x t,m t 1,m ; y t t 1. lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

10 Issue 2: Best timing for x. Indeed several vintages of x can be used for the same vintage of y. This means that we have an additional dimension compared to the previous ROF study. Issue 3: Nowcasting (Maastricht University) Nowcasting GDP with MIDAS October / 30

11 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). (Maastricht University) Nowcasting GDP with MIDAS October / 30

12 In order to compare whether one of the seven models dominates the others, we conduct the ROF for six randomly chosen dates. The dates are 1986Q3, 1991Q4, 1996Q1, 2001Q3, 2005Q2 and 2009Q1. Note that for the last date only 7 forecast errors can be computed due to the time period considered. For each method under consideration, the next 20 end-of-quarter vintages for both, the regressand and the regressors, are employed to compute 20 one-step-ahead forecasts which are visualized using a box-plot. It emerged that even after 20 quarters there is still a lot of revisions in the growth rates. This is emphasized in Figure 1 where far after the grey area (5 years) there is still some large movements in some dates. 1986Q3 is a good example. (Maastricht University) Nowcasting GDP with MIDAS October / 30

13 Date: 2001Q3 Date: 2005Q2 Date: 2009Q1 Date: 1986Q3 Date: 1991Q4 Date: 1996Q lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

14 PT_COINT_86Q3 PT_86Q3 AV_COINT_86Q3 AV_86Q3 MIDAS_COINT_86Q3 MIDAS_86Q3 AR(4)_86Q3 D86Q3_Q LAST_VINT_86Q3 lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

15 lain Hecq.000 PT_COINT_91Q4 PT_91Q4 AV_COINT_91Q4 AV_91Q4 MIDAS_COINT_91Q4 MIDAS_91Q4 AR(4)_91Q4 D91Q4_Q LAST_VINT_91Q4 (Maastricht University) Nowcasting GDP with MIDAS October / 30

16 PT_COINT_96Q1 PT_96Q1 AV_COINT_96Q1 AV_96Q1 MIDAS_COINT_96Q1 MIDAS_96Q1 AR(4)_96Q1 D96Q1_Q LAST_VINT_96Q1 lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

17 PT_COINT_01Q3 PT_01Q3 AV_COINT_01Q3 AV_01Q3 MIDAS_COINT_01Q3 MIDAS_01Q3 AR(4)_01Q3 D2001Q3_Q LAST_VINT_01Q3 lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

18 PT_COINT_05Q2 PT_05Q2 AV_COINT_05Q2 AV_05Q2 MIDAS_COINT_05Q2 MIDAS_05Q2 AR(4)_05Q2 D2005Q2_Q LAST_VINT_05Q2 (Maastricht University) Nowcasting GDP with MIDAS October / 30

19 PT_COINT_09Q1 PT_09Q1 AV_COINT_09Q1 AV_09Q1 MIDAS_COINT_09Q1 MIDAS_09Q1 AR(4)_09Q1 D2009Q1_Q LAST_VINT_09Q1 lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

20 Criteria for comparing forecasts 1 To have a less widespread distribution is not a criteria. For instance AR(4) might be more concentrated but not around the rst release neither 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. (Maastricht University) Nowcasting GDP with MIDAS October / 30

21 PT_COINT_86Q3 PT_86Q3 AV_COINT_86Q3 AV_86Q3 MIDAS_COINT_86Q3 MIDAS_86Q3 AR(4)_86Q3 D86Q3_Q LAST_VINT_86Q P P A A M M A D L PT_COINT_96Q1 PT_96Q1 AV_COINT_96Q1 AV_96Q1 MIDAS_COINT_96Q1 MIDAS_96Q1 AR(4)_96Q1 D96Q1_Q LAST_VINT_96Q PT PT AV AV MI MI AR D2 LA lain Hecq.010 PT_COINT_05Q2 PT_05Q2 AV_COINT_05Q2 AV_05Q2 MIDAS_COINT_05Q2 MIDAS_05Q2 AR(4)_05Q2 D2005Q2_Q LAST_VINT_05Q PT_COINT_09Q1 PT_09Q1 AV_COINT_09Q1 AV_09Q1 (Maastricht University) Nowcasting GDP with MIDAS October / 30

22 Criteria for comparing forecasts The comparison of forecast accuracy is not obvious. Indeed the performance of the several speci cation can di er when comparing with the nal realization or the realization on those speci c vintages. In summary, is a model better because it get closer to the nal gure or the value at the corresponding vintages? (Maastricht University) Nowcasting GDP with MIDAS October / 30

23 In order to have an intuitive idea of these di erences we compute for our seven models the RMSE over 20 quarters but we do it separately with respect to the nal value or the vintage values. For each of the six dates we rank the models from 1 (best) to 7 and we then average these values for the six dates. We proceed similarly when comparing with the realized vintage values. Table gives these sums PT_LR PT Av_LR Av Midas_LR Midas AR(4) last vint real vint Total (Maastricht University) Nowcasting GDP with MIDAS October / 30

24 Impact of regressor vintages For the regressors, we have focused so far on the vintages corresponding to the last month of a quarter. It might, however, be the case, that using the vintages corresponding to the rst or second month of a quarter yields considerably better forecasting performances than using the end-of-quarter vintages. If so, this might have an impact on how we should compute nowcasts of GDP (how many observations of the regressors we need to forecast). Even if it turns out that employing di erent monthly vintages does not lead to signi cantly di erent forecasting performance, we would have gained the insight that we can make use of the most recent observations without expecting a worse forecasting performance than when we, for instance, waited another month for revised data. (Maastricht University) Nowcasting GDP with MIDAS October / 30

25 In order to nd out whether employing a certain vintage yields considerably better forecasting performances, we consider ve candidate vintages per quarterly vintage for MIDAS models: The x-vintage two months, one month before that of y, the same vintage as y, the vintage of x one month and two months after the one of y. Now, similar to the previous section, but this time for each calendar date, a one-step-ahead forecast is computed employing real-time data and the RMSE computed. (Maastricht University) Nowcasting GDP with MIDAS October / 30

26 The Diebold-Mariano test are DM statistic x-1 same x+1 x+2 x x same x None of the di erent high-frequency vintages yields better forecasting performances than the others. Hence, we may freely choose which x-vintage to employ for a real-time data analysis and nowcasting. lain Hecq (Maastricht University) Nowcasting GDP with MIDAS October / 30

27 Nowcasting Given the outcome of the previous analysis, we construct nowcasts using the end-of-quarter vintages for the regressors. This way we are using the most recent observation possible in real-time. Note that nowcasts may also be done during the quarter by employing additional monthly vintages for the quarterly variable GDP or by simply using the most recent observation of GDP. (Maastricht University) Nowcasting GDP with MIDAS October / 30

28 (Maastricht University) Nowcasting GDP with MIDAS October / 30

29 Conclusion This paper combines the issues of working with variables that are sampled at mixed-frequencies and working with real-time data sets. Thereby, a wider range of models may be considered by the practitioner and it is proposed to assess the superiority of one model over 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 and box-plots of 20 one-step-ahead forecasts Di cult to determine what model does best. We can eliminate less good speci cation maybe. (Maastricht University) Nowcasting GDP with MIDAS October / 30

30 With respect to the model comparison, it was found that no model dominates the others for all dates considered. Unlike the mixed-frequency models, the ARIMA model focused on by Stark and Croushore (2002) is not able to react to recent changes in the growth rate of GDP due to its exclusive dependency on low-frequency information. However, the MIDAS model excluding a long-run term seems to yield reasonably 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 vintages considered show statistically similar forecasting performances such that the researcher can freely choose which one to employ and can, thereby, rely on the most recent information available in real-time to compute fore- or nowcasts. (Maastricht University) Nowcasting GDP with MIDAS October / 30