Real-Time Forecasting of Inflation and Output Growth in the Presence of Data Revisions Michael Clements Ana Beatriz Galvão Warwick/Queen Mary September 2010 Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 1 / 27
Data Revisions and Real-Time Data Data Vintages of US real output growth: 2003:Q1 2003:Q2 2003:Q3 2003:Q4 2004:Q1 2004:Q2 2004:Q3 2004:Q4 2005:Q1 2005:Q2 2005:Q3 2005:Q4 2002:01 1.23 1.23 1.23 1.23 1.15 1.15 0.84 0.84 0.84 0.84 0.68 0.68 2002:02 0.31 0.31 0.31 0.31 0.47 0.47 0.59 0.59 0.59 0.59 0.54 0.54 2002:03 0.99 0.99 0.99 0.99 0.83 0.83 0.64 0.64 0.64 0.64 0.59 0.59 2002:04 0.19 0.34 0.34 0.34 0.32 0.32 0.18 0.18 0.18 0.18 0.05 0.05 2003:01 . 0.40 0.35 0.35 0.49 0.49 0.48 0.48 0.48 0.48 0.42 0.42 2003:02 . . 0.59 0.81 0.76 0.76 1.01 1.01 1.01 1.01 0.90 0.90 2003:03 . . . 1.73 1.97 1.97 1.79 1.79 1.79 1.79 1.75 1.75 2003:04 . . . . 0.99 1.01 1.03 1.03 1.03 1.03 0.88 0.88 2004:01 . . . . . 1.02 1.10 1.10 1.10 1.10 1.04 1.04 2004:02 . . . . . . 0.75 0.81 0.81 0.81 0.86 0.86 2004:03 . . . . . . . 0.91 0.98 0.98 0.97 0.97 2004:04 . . . . . . . . 0.77 0.94 0.81 0.81 2005:01 . . . . . . . . . 0.76 0.93 0.93 2005:02 . . . . . . . . . . 0.84 0.81 2005:03 . . . . . . . . . . . 0.93 Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 2 / 27
Data Revisions on Output Growth and Inflation Mean Standard Deviation Autocorrelation (1st) + + + + + + t 1 t 14 09 Q 1 t 1 t 14 09 Q 1 t 1 t 14 09 Q 1 y y y y y y y y y t t t t t t t t t Output growth 1965Q3-1985Q2 0.76 0.79 0.81 1.08 1.07 1.08 0.28 0.29 0.29 1985Q3-2006:Q4 0.68 0.68 0.75 0.43 0.52 0.50 0.33 0.33 0.23 GDP Deflator 1965Q3-1985Q2 1.45 1.43 1.41 0.59 0.59 0.59 0.70 0.75 0.80 1985Q3-2006:Q4 0.58 0.65 0.60 0.28 0.27 0.23 0.57 0.55 0.56 PCE Deflator 1965Q3-1985Q2 1.40 1.39 1.38 0.63 0.64 0.65 0.83 0.83 0.84 1985Q3-2006:Q4 0.64 0.69 0.64 0.38 0.35 0.30 0.49 0.60 0.56 Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 3 / 27
Real-Time Data and Forecasting I • The use of ‘final-revised’ data may exaggerate the predictive power of explanatory variables to what could have been achieved at the time using the then available data (‘real-time data’): Diebold and Rudebush (1991), Robertson and Tallman (1998), Orphanides (2001), Croushore and Stark (2001, 2003), Faust, Rogers and Wright (2003), and Orphanides and van Norden (2005). This paper: what is the best way (minimises mean squared error) of incorporating data vintages in real-time forecasting of output growth and inflation with AR and ADL models? Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 4 / 27
Real-Time Data and Forecasting II Ways of organizing data vintages for real-time forecasting: 1 Use the values from the latest available vintage of data to estimate the forecasting model: end-of-sample vintage approach - EOS data (Koenig, Dolmas and Piger, 2003). 2 Vintages are incorporated such that the forecasting model is estimated with data that mimics the vintage-data structure on the real-time forecast loss function - RTV (real-time vintage) data . • For example, if forecasts of y T + 2 T + 1 are computed using two lags y T + 1 T and y T + 1 T − 1 , then the forecast model should be estimated using y t + 1 t on the LHS and y t t − 1 and y t t − 2 on RHS with both vintage (superscript) and observed date (subscript) varying from t = 2 up to t = T . Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 5 / 27
Real-Time Data and Data Revisions I • We are able to show that the use of EOS data to estimate AR forecasting models delivers estimates that do not minimise the real-time mean squared forecast error. • If RTV data is employed instead, we are able to obtain consistent estimates of the optimal AR coefficients, that is, the values that minimise the population MSE. • The implications of the use of EOS instead of RTV data are based on a model of the data revision process . Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 6 / 27
Real-Time Data and Data Revisions II • Many authors have build models to characterize the dynamics of data revisions (Harvey et al, 1983; Howrey, 1984, Sargent, 1989; Patterson, 1995; Cunningham et al, 2007; Jacobs and van Norden, 2007). • Instead of using a model of data revisions to measure the ‘true data’, we use the model to establish how revisions characteristics affect the optimal way of organizing real-time data, that is, how large are MSE differences between RTV and EOS data. • In this paper, we use a model that decomposes the observed data into true underlying value, and data revisions that add news and noise (Jacobs and van Norden, 2007). Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 7 / 27
Implications: RTV versus EOS data • The gains from the use of RTV instead of EOS data to estimate AR forecasting models depend on how large are the variances of data revisions in comparison to the variance of the underlying data, and also how the revisions’ variances decay with each data revision. • The gains are larger when the estimation sample is small and revisions primarily add news, and the underlying process is reasonable persistent. Relative MSE ratios are measured with a monte carlo exercise using the model of data revisions calibrated to output growth and inflation revisions. • Even when considering a model of data revisions based on a VAR of multiple vintages estimated to macro data, monte carlo results also suggest MSE gains of around 2-3%. Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 8 / 27
Forecasting output growth and inflation • When forecasting output growth and inflation in the 1985-2008 period, the use RTV data improves forecasts of AR models with EOS data in around 1-4% of RMSFE. • When adding economic indicators, which are also subject to data revisions, to the forecasting model (ADL), the use of RTV data reduces RMSFE up to 8% (larger gains when nowcasting and using data from 1980 onwards in the estimation). Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 9 / 27
Statistical Framework I � � � y t + 1 , . . . , y t + l • Observed data estimates: y t = ; True value: � y t t t � � � � � = 0 ε t + 1 , . . . , ε t + l ε t + s • Noise revisions: ε t = ; Cov , � y t t t t � � � � � = 0 v t + 1 , . . . , v t + l v t + s , y t + s • News revisions: v t = ; Cov t t t t y t = i � y t + v t + ε t p l ∑ ∑ � y t = ρ 0 + ρ i � y t − i + R 1 η 1 t + σ v i η 2 t , i i = 1 underlying i = 1 news σ v 1 σ v 2 . . . σ v l η 2 t ,1 σ ε 1 η 3 t ,1 σ v 2 η 2 t ,2 σ ε 2 η 3 t ,2 ... v t = − ; ε t = η 2 t , l σ ε l η 3 t , l 0 σ v l Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 10 / 27
Statistical Framework II • The Statistical Model is modified to allow for revisions that have non-zero mean such that they change the unconditional mean of � y t when they add news. • The model can be also modified to accommodate the periodic pattern of BEA annual revisions (published in July) together with the revision pattern from ‘advance’ estimates y t + 1 up to ‘final’ t estimates y t + 2 . t • Even though our analytical results are for this specific statistical framework, the implications are general since our main requirement is stationarity of the underlying � y t and the revision processes. We also exploit a data revision processes based on a VAR model in the monte carlo evaluation. Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 11 / 27
Optimal AR Parameters in Population I • Parameters that minimise the real-time quadratic loss function. • Forecasts are computed using the latest available data from the T + 1 vintage: � � � y T + 1 y T + 1 , y T + 1 T − 1 , . . . , y T + 1 = . T T T − p + 1 • The optimal parameters are the ones that solve: � � 2 y T + 1 + f ( φ ∗ 0 , φ ∗ ) = arg min − φ 0 − φ � y T + 1 , T + 1 T that are: � � − 1 � � φ ∗ yv + Σ � y + Σ � = Σ � y + Σ v + Σ � yv + Σ ε Σ � ρ � � yv � � φ ∗ 1 − φ ∗� i = µ � 0 y Clements/Galvão (Warwick/Queen Mary) Real-Time Forecasting and Data Revisions September 2010 12 / 27
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