Error Statistics for the Survey of Professional Forecasters for Moodys AAA Rate [QA,PPs] Release Date: 09/01/2009 Tom Stark Assistant Director and Manager Real-Time Data Research Center Economic Research Department Federal Reserve Bank of Philadelphia 1. OVERVIEW. This document reports error statistics for median projections from the Survey of Professional Forecasters (SPF), conducted since 1990 by the Federal Reserve Bank of Philadelphia. We provide the results in a series of tables and, in the PDF version of this document, a number of charts. The tables show the survey variable forecast and, importantly, the transformation of the data that we used to generate the statistics. (The transformation is usually a quarter-over-quarter growth rate, expressed in annualized percentage points. However, some variables, such as interest rates, the unemployment rate, and housing starts are untransformed and, thus, expressed in their natural units.) The paragraphs below explain the format of the tables and charts and the methods used to compute the statistics. These paragraphs are general. The same discussion applies to all variables in the survey. 2. DESCRIPTION OF TABLES. Table 1 reports error statistics for various forecast horizons, sample periods, and choices of the real-time historical value that we used to assess accuracy. In each quarterly survey, we ask our panelists for their projections for the current quarter and the next four quarters. The current quarter is defined as the quarter in which we conducted the survey. Our tables provide error statistics separately for each quarter of this five-quarter horizon, beginning with the current quarter (denoted H = 1) and ending with the quarter that is four quarters in the future (H = 5). For each horizon, we report the mean forecast error [ME(S)], the mean absolute forecast error [MAE(S)], and the root-mean-square error [RMSE(S)]. All are standard measures of accuracy, though the academic literature generally places the most weight on the latter. We define a forecast error as the difference between the historical value and the forecast. The mean error for each horizon is simply the average of the forecast errors at that horizon, constructed over the sample period shown in Table 1. Other things the same, a forecast with a mean error close to zero is better than one with a mean error far from zero. The mean absolute error is the sample average of the absolute value of the errors. Many analysts prefer this measure to the mean error because it does not allow large positive errors to offset large negative errors. In this sense, the mean absolute error gives a cleaner estimate of the size of the errors. Decision makers, however, may care not only about the average size of the errors but also about their variability, as measured by variance. Our last measure of accuracy is one that reflects the influence of the mean error and the variance of the error. The root-mean-square error for the SPF [RMSE(S)], the measure most often used by analysts and academicians, is the square root of the the average squared error. The lower the root-mean-square error, the more accurate the forecast. 2.1. Benchmark Models. The forecast error statistics from the SPF are of interest in their own right. However, it is often more interesting to compare such statistics with those of alternative, or benchmark, forecasts. Table 1 reports four such comparisons. It shows the ratio of the root-mean-square error of the SPF forecast to that of four benchmark models. The benchmark models are statistical equations that we estimate on the data. We use the equations to generate projections for the same horizons included in the survey. In effect, we imagine standing back in time at each date when a survey was conducted and generating a separate forecast with each benchmark model. We do this in the same way that a survey panelist would have done using his own model. A RMSE ratio below unity indicates that the SPF consensus (median) forecast has a root-mean-square error lower than that of the benchmark. This means the SPF is more accurate. We now describe the benchmark models. The first is perhaps the simplest of all possible benchmarks: A no-change model. In this model, the forecast for quarter T, the one-step-ahead or current-quarter forecast, is simply the historical value for the prior quarter (T - 1). There is, in other words, no change in the forecast compared with the historical value. Moreover, the forecast for the remaining quarters of the horizon is the same as the forecast for the current quarter. We denote the relative RMSE ratio for this benchmark as RMSE(S/NC), using NC to indicate no change. The second and third benchmark models generate projections using one or more historical observations of the the variable forecast, weighted by coefficients estimated from the data. Such autoregressive (AR) models can be formulated in two ways. We can estimate one model to generate the forecasts at all horizons, using an iteration method to generate the projections beyond the current quarter (IAR), or we can directly estimate a new model for each forecast horizon (DAR). The latter formulation has been shown to reduce the bias in a forecast when the underlying model is characterized by certain types of misspecification. The root-mean-square error ratios are denoted RMSE(S/IAR) and RMSE(S/DAR), respectively. The one- through five-step-ahead projections of the benchmark models use information on the quarterly average of the variable forecast. The latest historical observation is for the quarter that is one quarter before the quarter of the first projection in the horizon. In contrast, the panelists generate their projections with the help of additional information. They submit their projections near the middle of each quarter and hence have access to some monthly indicators for the first month of each quarter, when those data are released before the survey deadline. This puts the projections of panelists for some variables at an advantage relative to the corresponding benchmark projections. Moreover, the panelists may also examine the very recent historical values of such monthly indicators in forming their projections for quarterly averages. Such monthly statistical momentum represents an advantage not shared by the benchmark models, which use only quarterly averages. For survey variables whose observations are reported at a monthly frequency, such as interest rates, industrial production, housing starts, and unemployment, we estimate and forecast a fourth benchmark model, the DARM. This model adds recent monthly historical values to the specification of the DAR model. For the projections for unemployment, nonfarm payroll employment, and interest rates, we add the values of monthly observations, beginning with that for the first month of the first quarter of the forecast horizon. These values should be in the information set of the survey panelists at the time they formed their projections. In contrast, for variables such as housing starts and industrial production, we include only lagged values of monthly observations. For such variables, the panelists would not have known the monthly observation for the first month of the first quarter of the forecast horizon. In general, we find that adding monthly observations to the benchmark DAR models improves accuracy. Indeed, for the projections for interest rates and the unemployment rate, the accuracy of the benchmark DARM projections rivals that of the SPF projections. 2.2. Real-Time Data. All benchmark models are estimated on a rolling, fixed window of 60 real-time quarterly observations. Lag lengths, based on either the Akaike information criterion (AIC) or the Schwarz information criterion (SIC), are re-estimated each period. The tables below indicate whether the lag length was was chosen by the AIC or SIC. We would like to make the comparison between the SPF forecast and the forecasts of each benchmark as fair as possible. Therefore, we must subject the benchmark models to the same data environment the survey panelists faced when they made their projections. This is important because macroeconomic data are revised often, and we do not want the benchmark models to use a data set that differs from the one our panelists would have used. We estimate and forecast the benchmark models with real-time data from the Philadelphia Fed real-time data set, using the vintage of data that the survey panelists would have had at the time they generated their own projections. (For more information on the Philadelphia Fed real-time data set, go to www.philadelphiafed.org/econ/forecast/real-time-data/.) An open question in the literature on forecasting is: What version or vintage of the data should we use to compute the errors? A closely related question is: What version of the data are professional forecasters trying to predict? Our computations take no strong position on these questions. Rather, in Table 1, we evaluate the projections (SPF and benchmark) with five alternative measures of the historical values, all from the Philadelphia Fed real-time data set. These measures range from the initial-release values to the values as we know them today. All together, we compute the forecast error statistics using the following five alternative measures of historical values: (1) The initial or first-release value; (2) The revised value as it appears one quarter after the initial release; (3) The revised value as it appears five quarters after the initial release; (4) The revised value as it appears nine quarters after the initial release; (5) The revised value as it appears today. Each measure of the historical value has advantages and disadvantages. The initial-release value is the first measure released by government statistical agencies. A forecaster might be very interested in this measure because it enables him to evaluate his latest forecast soon after he generated it. However, early releases of the data are often subject to large measurement error. Subsequent releases [(2) - (5)] are more accurate, but they are available much later than the initial release. As we go from the first measure to the fifth, we get more reliability, at the cost of higher delays in availability. The last two columns in Table 1 report the number of observations that we used to compute the error statistics. Some observations are omitted because the data are missing in the real-time data set, such as occurred when federal government statistical agencies closed in late 1995. 2.3. Recent Projections and Realizations. Tables 2 to 7 provide information on recent projections and realizations. They show how we align the data prior to computing the forecast errors that form the backbone of the computations in Table 1. Any forecast error can be written as the equation given by error = realization - forecast. For our computations, we must be more precise because, for each projection (SPF and benchmarks), we have different periods forecast (T) different forecast horizons (h), and several measures of the realization (m). Thus, we can define the forecast error more precisely as error( T, h, m ) = realization( T, m ) - forecast( T, h ). Tables 2 to 7 are organized along these lines. Table 2 shows recent forecasts from the SPF. Each column gives the projection for a different horizon or forecast step (h), beginning with that for the current quarter, defined as the quarter in which we conducted the survey. The dates (T) given in the rows show the periods forecast. These also correspond to the dates that we conducted the survey. Tables 3 to 6 report the recent projections of the four benchmark models. These are organized in the same way as Table 2. Table 7 reports recent values of the five alternative realizations (m) we use to compute the error statistics. 2.4. Qualifications. We note two minor qualifications to the methods discussed above. The first concerns the vintage of data that we used to estimate and forecast the benchmark models for CPI inflation. The second concerns the five measures of realizations used for the unemployment rate, nonfarm payroll employment, and CPI inflation. To estimate and forecast the benchmark models for CPI inflation, we use the vintage of data that would have been available in the middle of each quarter. This predates by one month the vintage that SPF panelists would have had at their disposal when they formed their projections. The effect is likely small because revisions to the CPI are generally small. To compute the realizations for unemployment, nonfarm payroll employment, and CPI inflation, we use the vintages associated with the middle of each quarter. The measure that we call initial comes from this vintage, even though the initial estimate was available one month earlier. Thus, for these variables, our initial estimate reflects some revision by government statistical agencies. The effect for unemployment and CPI inflation is likely small. The effect could be somewhat larger for nonfarm payroll employment. 3. DESCRIPTION OF GRAPHS. 3.1. Root-Mean-Square Errors. For each sample period shown in Table 1, we provide graphs of the root-mean-square error for the SPF forecast. There is one page for each sample period. On each page, we plot (for each forecast horizon) the RMSE on the y-axis. The x-axis shows the measure of the historical value that we used to compute the RMSE. These range from the value on its initial release to the value one quarter later to the value as we know it now (at the time we made the computation). The graphs provide a tremendous amount of information. If we focus on a particular graph, we can see how a change in the measure of the realization (x-axis) affects the root-mean-square-error measure of accuracy. The effect is pronounced for some variables, such as real GDP and some of its components. For others, there is little or no effect. For example, because the historical data on interest rates are not revised, the estimated RMSE is the same in each case. If we compare a particular point on one graph with the same point on another, we see how the forecast horizon affects accuracy. In general, the RMSE rises (accuracy falls) as the forecast horizon lengthens. Finally, if we compare a graph on one page with the corresponding graph on another page, we see how our estimates of accuracy in the SPF change with the sample period. Periods characterized by a high degree of economic turbulence will generally produce large RMSEs. 3.2. Fan Charts. The last chart plots recent historical values and the latest SPF forecast. It also shows confidence intervals for the forecast, based on back-of-the-envelope calculations. The historical values and the SPF forecast are those associated with the latest vintage of data and survey, respectively, available at the time we ran our computer programs. The confidence intervals are constructed under the assumption that the historical forecast errors over the sample (shown in the footnote) follow a normal distribution with a mean of zero and a variance given by the root-mean-square error. The latter is estimated over the aforementioned sample, using the measure of history listed in the footnote. ---------------------------------------------------------------------------------- Table 1. Forecast Error Statistics for SPF Variable: BOND (Moodys AAA Rate [QA,PPs]) ---------------------------------------------------------------------------------- Computed Over Various Sample Periods Various Measures of Realizations Transformation: Level Lag Length for IAR(p), DAR(p), and DARM(p) Models: AIC Last Updated: 09/01/2009 10:22 ---------------------------------------------------------------------------------- H ME(S) MAE(S) RMSE(S) RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) Nspf N History: Initial Release 1991:04-2007:01 1 -0.06 0.11 0.15 0.50 0.49 0.49 1.03 62 62 2 -0.17 0.36 0.43 0.89 0.82 0.83 1.03 62 62 3 -0.28 0.54 0.63 1.02 0.90 0.86 0.98 62 62 4 -0.35 0.65 0.76 1.04 0.86 0.83 0.93 62 62 5 -0.44 0.74 0.85 1.07 0.82 0.82 0.86 62 62 1991:04-1996:04 1 -0.04 0.11 0.13 0.37 0.38 0.38 0.83 21 21 2 -0.13 0.41 0.48 0.79 0.72 0.70 0.94 21 21 3 -0.21 0.62 0.72 0.91 0.78 0.73 0.85 21 21 4 -0.28 0.73 0.84 0.93 0.72 0.67 0.77 21 21 5 -0.41 0.78 0.91 0.95 0.65 0.62 0.67 21 21 1997:01-2007:01 1 -0.08 0.12 0.16 0.60 0.56 0.56 1.14 41 41 2 -0.20 0.34 0.40 0.99 0.93 1.00 1.11 41 41 3 -0.31 0.50 0.58 1.13 1.05 1.03 1.14 41 41 4 -0.39 0.60 0.71 1.15 1.04 1.07 1.13 41 41 5 -0.45 0.72 0.82 1.17 1.02 1.13 1.14 41 41 H ME(S) MAE(S) RMSE(S) RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) Nspf N History: One Qtr After Initial Release 1991:04-2007:01 1 -0.06 0.11 0.15 0.50 0.49 0.49 1.03 62 62 2 -0.17 0.36 0.43 0.89 0.82 0.83 1.03 62 62 3 -0.28 0.54 0.63 1.02 0.90 0.86 0.98 62 62 4 -0.35 0.65 0.76 1.04 0.86 0.83 0.93 62 62 5 -0.44 0.74 0.85 1.07 0.82 0.82 0.86 62 62 1991:04-1996:04 1 -0.04 0.11 0.13 0.37 0.38 0.38 0.83 21 21 2 -0.13 0.41 0.48 0.79 0.72 0.70 0.94 21 21 3 -0.21 0.62 0.72 0.91 0.78 0.73 0.85 21 21 4 -0.28 0.73 0.84 0.93 0.72 0.67 0.77 21 21 5 -0.41 0.78 0.91 0.95 0.65 0.62 0.67 21 21 1997:01-2007:01 1 -0.08 0.12 0.16 0.60 0.56 0.56 1.14 41 41 2 -0.20 0.34 0.40 0.99 0.93 1.00 1.11 41 41 3 -0.31 0.50 0.58 1.13 1.05 1.03 1.14 41 41 4 -0.39 0.60 0.71 1.15 1.04 1.07 1.13 41 41 5 -0.45 0.72 0.82 1.17 1.02 1.13 1.14 41 41 H ME(S) MAE(S) RMSE(S) RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) Nspf N History: Five Qtrs After Initial Release 1991:04-2007:01 1 -0.06 0.11 0.15 0.50 0.49 0.49 1.03 62 62 2 -0.17 0.36 0.43 0.89 0.82 0.83 1.03 62 62 3 -0.28 0.54 0.63 1.02 0.90 0.86 0.98 62 62 4 -0.35 0.65 0.76 1.04 0.86 0.83 0.93 62 62 5 -0.44 0.74 0.85 1.07 0.82 0.82 0.86 62 62 1991:04-1996:04 1 -0.04 0.11 0.13 0.37 0.38 0.38 0.83 21 21 2 -0.13 0.41 0.48 0.79 0.72 0.70 0.94 21 21 3 -0.21 0.62 0.72 0.91 0.78 0.73 0.85 21 21 4 -0.28 0.73 0.84 0.93 0.72 0.67 0.77 21 21 5 -0.41 0.78 0.91 0.95 0.65 0.62 0.67 21 21 1997:01-2007:01 1 -0.08 0.12 0.16 0.60 0.56 0.56 1.14 41 41 2 -0.20 0.34 0.40 0.99 0.93 1.00 1.11 41 41 3 -0.31 0.50 0.58 1.13 1.05 1.03 1.14 41 41 4 -0.39 0.60 0.71 1.15 1.04 1.07 1.13 41 41 5 -0.45 0.72 0.82 1.17 1.02 1.13 1.14 41 41 H ME(S) MAE(S) RMSE(S) RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) Nspf N History: Nine Qtrs After Initial Release 1991:04-2007:01 1 -0.06 0.11 0.15 0.50 0.49 0.49 1.03 62 62 2 -0.17 0.36 0.43 0.89 0.82 0.83 1.03 62 62 3 -0.28 0.54 0.63 1.02 0.90 0.86 0.98 62 62 4 -0.35 0.65 0.76 1.04 0.86 0.83 0.93 62 62 5 -0.44 0.74 0.85 1.07 0.82 0.82 0.86 62 62 1991:04-1996:04 1 -0.04 0.11 0.13 0.37 0.38 0.38 0.83 21 21 2 -0.13 0.41 0.48 0.79 0.72 0.70 0.94 21 21 3 -0.21 0.62 0.72 0.91 0.78 0.73 0.85 21 21 4 -0.28 0.73 0.84 0.93 0.72 0.67 0.77 21 21 5 -0.41 0.78 0.91 0.95 0.65 0.62 0.67 21 21 1997:01-2007:01 1 -0.08 0.12 0.16 0.60 0.56 0.56 1.14 41 41 2 -0.20 0.34 0.40 0.99 0.93 1.00 1.11 41 41 3 -0.31 0.50 0.58 1.13 1.05 1.03 1.14 41 41 4 -0.39 0.60 0.71 1.15 1.04 1.07 1.13 41 41 5 -0.45 0.72 0.82 1.17 1.02 1.13 1.14 41 41 H ME(S) MAE(S) RMSE(S) RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) Nspf N History: Latest Vintage 1991:04-2007:01 1 -0.06 0.11 0.15 0.50 0.49 0.49 1.03 62 62 2 -0.17 0.36 0.43 0.89 0.82 0.83 1.03 62 62 3 -0.28 0.54 0.63 1.02 0.90 0.86 0.98 62 62 4 -0.35 0.65 0.76 1.04 0.86 0.83 0.93 62 62 5 -0.44 0.74 0.85 1.07 0.82 0.82 0.86 62 62 1991:04-1996:04 1 -0.04 0.11 0.13 0.37 0.38 0.38 0.83 21 21 2 -0.13 0.41 0.48 0.79 0.72 0.70 0.94 21 21 3 -0.21 0.62 0.72 0.91 0.78 0.73 0.85 21 21 4 -0.28 0.73 0.84 0.93 0.72 0.67 0.77 21 21 5 -0.41 0.78 0.91 0.95 0.65 0.62 0.67 21 21 1997:01-2007:01 1 -0.08 0.12 0.16 0.60 0.56 0.56 1.14 41 41 2 -0.20 0.34 0.40 0.99 0.93 1.00 1.11 41 41 3 -0.31 0.50 0.58 1.13 1.05 1.03 1.14 41 41 4 -0.39 0.60 0.71 1.15 1.04 1.07 1.13 41 41 5 -0.45 0.72 0.82 1.17 1.02 1.13 1.14 41 41 Table 1 notes. (1) The forecast horizon is given by H, where H = 1 is the SPF forecast for the current quarter. (2) The headers ME(S), MAE(S), and RMSE(S) are mean error, mean absolute error, and root-mean-square error for the SPF. (3) The header RMSE(S/NC) is the ratio of the SPF RMSE to that of the no-change (NC) model. (4) The headers RMSE(S/IAR), RMSE(S/DAR) and RMSE(S/DARM) are the ratios of the SPF RMSE to the RMSE of the iterated and direct autoregressive models and the direct autoregressive model augmented with monthly observations, respectively. All models are estimated on a rolling window of 60 observations from the Phila Fed real-time data set. (5) The headers Nspf and N are the number of observations analyzed for the SPF and benchmark models. (6) When the variable forecast is a growth rate or an interest rate, it is expressed in annualized percentage points. When the variable forecast is the unemployment rate, it is expressed in percentage points. (7) Sample periods refer to the dates forecast, not the dates when the forecasts were made. Source: Tom Stark, Research Department, FRB Philadelphia. -------------------------------------------------------------------- Table 2. Recent SPF Forecasts - Dated at the Quarter Forecast -------------------------------------------------------------------- Variable: BOND (Moodys AAA Rate [QA,PPs]) By Forecast Step (1 to 5) Transformation: Level Last Updated: 09/01/2009 10:22 -------------------------------------------------------------------- Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2002:04 6.300 6.400 6.900 6.820 6.910 2003:01 6.200 6.200 6.600 7.000 6.930 2003:02 5.880 6.220 6.300 6.710 7.030 2003:03 5.700 6.000 6.260 6.400 6.800 2003:04 5.850 5.840 6.080 6.350 6.450 2004:01 5.600 5.900 6.000 6.200 6.450 2004:02 5.900 5.770 6.100 6.010 6.210 2004:03 5.921 6.110 5.920 6.300 6.000 2004:04 5.600 6.161 6.293 6.100 6.450 2005:01 5.500 5.825 6.390 6.400 6.300 2005:02 5.460 5.700 6.099 6.550 6.580 2005:03 5.279 5.700 5.840 6.288 6.735 2005:04 5.500 5.611 5.900 6.020 6.345 2006:01 5.500 5.900 5.844 6.100 6.240 2006:02 5.940 5.870 6.100 5.978 6.250 2006:03 5.990 6.074 5.950 6.216 6.007 2006:04 5.600 6.100 6.150 5.950 6.300 2007:01 5.500 5.699 6.240 6.200 6.065 2007:02 5.447 5.620 5.750 6.235 6.183 2007:03 5.700 5.525 5.700 5.800 6.209 2007:04 5.611 5.790 5.620 5.784 5.815 2008:01 5.220 5.690 5.900 5.700 5.850 2008:02 5.472 5.177 5.750 5.950 5.750 2008:03 5.700 5.445 5.300 5.800 5.970 2008:04 6.140 5.785 5.500 5.300 5.850 2009:01 5.130 6.000 5.775 5.563 5.415 2009:02 5.400 5.250 5.900 5.825 5.600 2009:03 5.500 5.330 5.280 5.840 5.935 2009:04 NA 5.500 5.390 5.290 5.817 2010:01 NA NA 5.578 5.310 5.440 2010:02 NA NA NA 5.599 5.350 2010:03 NA NA NA NA 5.588 Table 2 notes. (1) Each column gives the sequence of SPF projections for a given forecast step. The forecast steps range from one (the forecast for the quarter in which the survey was conducted) to four quarters in the future (step 5). (2) The dates listed in the rows are the dates forecast, not the dates when the forecasts were made, with the exception of the forecast at step one, for which the two dates coincide. Source: Tom Stark, Research Department, FRB Philadelphia. ------------------------------------------------------------------------------------ Table 3. Recent Benchmark Model 1 IAR Forecasts - Dated at the Quarter Forecast ------------------------------------------------------------------------------------ Variable: BOND (Moodys AAA Rate [QA,PPs]) By Forecast Step (1 to 5) Transformation: Level Lag Length for IAR(p): AIC Last Updated: 09/01/2009 10:22 ------------------------------------------------------------------------------------ Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2002:04 6.302 6.884 6.662 7.083 7.312 2003:01 6.326 6.343 6.950 6.752 7.106 2003:02 5.965 6.396 6.406 6.969 6.795 2003:03 5.110 5.995 6.466 6.472 6.968 2003:04 5.906 5.101 6.042 6.531 6.534 2004:01 5.701 6.046 5.164 6.091 6.590 2004:02 5.465 5.768 6.156 5.251 6.139 2004:03 6.153 5.541 5.837 6.248 5.343 2004:04 5.481 6.284 5.635 5.904 6.329 2005:01 5.592 5.586 6.375 5.729 5.967 2005:02 5.102 5.445 5.440 6.446 5.817 2005:03 5.211 5.140 5.461 5.456 6.506 2005:04 5.139 5.294 5.209 5.543 5.540 2006:01 5.521 5.206 5.368 5.267 5.505 2006:02 5.437 5.611 5.285 5.463 5.357 2006:03 6.094 5.508 5.691 5.335 5.485 2006:04 5.550 6.190 5.440 5.640 5.345 2007:01 5.368 5.583 6.249 5.430 5.599 2007:02 5.184 5.198 5.430 6.292 5.434 2007:03 5.704 5.214 5.231 5.483 6.327 2007:04 5.894 5.838 5.342 5.362 5.569 2008:01 5.523 5.948 5.900 5.378 5.401 2008:02 5.482 5.574 5.906 5.865 5.457 2008:03 5.621 5.505 5.636 5.853 5.836 2008:04 5.673 5.641 5.528 5.697 5.810 2009:01 5.854 5.693 5.659 5.549 5.753 2009:02 5.293 5.870 5.711 5.677 5.569 2009:03 5.529 5.313 5.886 5.728 5.694 2009:04 NA 5.543 5.331 5.900 5.745 2010:01 NA NA 5.557 5.349 5.915 2010:02 NA NA NA 5.570 5.366 2010:03 NA NA NA NA 5.582 Table 3 notes. (1) Each column gives the sequence of benchmark IAR projections for a given forecast step. The forecast steps range from one to five. The first step corresponds to the forecast that SPF panelists make for the quarter in which the survey is conducted. (2) The dates listed in the rows are the dates forecast, not the dates when the forecasts were made, with the exception of the forecast at step one, for which the two dates coincide. (3) The IAR benchmark model is estimated on a fixed 60-quarter rolling window. Its forecasts are computed with the indirect method. Estimation uses data from the Philadelphia Fed real-time data set. Source: Tom Stark, Research Department, FRB Philadelphia. --------------------------------------------------------------------------------------- Table 4. Recent Benchmark Model 2 No-Change Forecasts - Dated at the Quarter Forecast --------------------------------------------------------------------------------------- Variable: BOND (Moodys AAA Rate [QA,PPs]) By Forecast Step (1 to 5) Transformation: Level Last Updated: 09/01/2009 10:22 --------------------------------------------------------------------------------------- Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2002:04 6.350 6.713 6.623 6.923 7.107 2003:01 6.280 6.350 6.713 6.623 6.923 2003:02 6.003 6.280 6.350 6.713 6.623 2003:03 5.310 6.003 6.280 6.350 6.713 2003:04 5.697 5.310 6.003 6.280 6.350 2004:01 5.657 5.697 5.310 6.003 6.280 2004:02 5.457 5.657 5.697 5.310 6.003 2004:03 5.927 5.457 5.657 5.697 5.310 2004:04 5.643 5.927 5.457 5.657 5.697 2005:01 5.487 5.643 5.927 5.457 5.657 2005:02 5.320 5.487 5.643 5.927 5.457 2005:03 5.147 5.320 5.487 5.643 5.927 2005:04 5.093 5.147 5.320 5.487 5.643 2006:01 5.380 5.093 5.147 5.320 5.487 2006:02 5.390 5.380 5.093 5.147 5.320 2006:03 5.893 5.390 5.380 5.093 5.147 2006:04 5.680 5.893 5.390 5.380 5.093 2007:01 5.387 5.680 5.893 5.390 5.380 2007:02 5.363 5.387 5.680 5.893 5.390 2007:03 5.577 5.363 5.387 5.680 5.893 2007:04 5.753 5.577 5.363 5.387 5.680 2008:01 5.530 5.753 5.577 5.363 5.387 2008:02 5.457 5.530 5.753 5.577 5.363 2008:03 5.600 5.457 5.530 5.753 5.577 2008:04 5.653 5.600 5.457 5.530 5.753 2009:01 5.837 5.653 5.600 5.457 5.530 2009:02 5.273 5.837 5.653 5.600 5.457 2009:03 5.513 5.273 5.837 5.653 5.600 2009:04 NA 5.513 5.273 5.837 5.653 2010:01 NA NA 5.513 5.273 5.837 2010:02 NA NA NA 5.513 5.273 2010:03 NA NA NA NA 5.513 Table 4 notes. (1) Each column gives the sequence of benchmark no-change projections for a given forecast step. The forecast steps range from one to five. The first step corresponds to the forecast that SPF panelists make for the quarter in which the survey is conducted. (2) The dates listed in the rows are the dates forecast, not the dates when the forecasts were made, with the exception of the forecast at step one, for which the two dates coincide. (3) The projections use data from the Philadelphia Fed real-time data set. Source: Tom Stark, Research Department, FRB Philadelphia. ------------------------------------------------------------------------------------ Table 5. Recent Benchmark Model 3 DAR Forecasts - Dated at the Quarter Forecast ------------------------------------------------------------------------------------ Variable: BOND (Moodys AAA Rate [QA,PPs]) By Forecast Step (1 to 5) Transformation: Level Lag Length for DAR(p): AIC Last Updated: 09/01/2009 10:22 ------------------------------------------------------------------------------------ Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2002:04 6.302 6.877 6.612 7.147 7.401 2003:01 6.326 6.340 6.948 6.698 7.257 2003:02 5.965 6.423 6.473 7.012 6.798 2003:03 5.110 6.000 6.498 6.544 7.035 2003:04 5.906 5.275 6.093 6.622 6.709 2004:01 5.701 5.968 5.399 6.139 6.514 2004:02 5.465 5.807 6.114 5.688 6.386 2004:03 6.153 5.546 5.840 5.956 5.662 2004:04 5.481 6.198 5.656 5.882 5.988 2005:01 5.592 5.698 6.227 5.710 5.930 2005:02 5.102 5.460 5.770 6.116 5.748 2005:03 5.211 5.124 5.654 5.874 6.104 2005:04 5.139 5.279 5.483 5.728 5.902 2006:01 5.521 5.220 5.342 5.582 5.746 2006:02 5.437 5.585 5.290 5.419 5.603 2006:03 6.094 5.523 5.655 5.365 5.462 2006:04 5.550 6.022 5.446 5.597 5.400 2007:01 5.368 5.547 5.999 5.412 5.616 2007:02 5.184 5.222 5.382 5.830 5.403 2007:03 5.704 5.164 5.252 5.334 5.641 2007:04 5.894 5.810 5.319 5.384 5.613 2008:01 5.523 5.962 5.875 5.361 5.397 2008:02 5.482 5.624 5.908 5.824 5.710 2008:03 5.621 5.547 5.688 5.899 5.808 2008:04 5.673 5.666 5.617 5.739 5.914 2009:01 5.854 5.714 5.718 5.680 5.752 2009:02 5.293 5.883 5.752 5.770 5.693 2009:03 5.529 5.363 5.910 5.795 5.785 2009:04 NA 5.554 5.429 5.931 5.806 2010:01 NA NA 5.608 5.485 5.930 2010:02 NA NA NA 5.662 5.497 2010:03 NA NA NA NA 5.674 Table 5 notes. (1) Each column gives the sequence of benchmark DAR projections for a given forecast step. The forecast steps range from one to five. The first step corresponds to the forecast that SPF panelists make for the quarter in which the survey is conducted. (2) The dates listed in the rows are the dates forecast, not the dates when the forecasts were made, with the exception of the forecast at step one, for which the two dates coincide. (3) The DAR benchmark model is estimated on a fixed 60-quarter rolling window. Its forecasts are computed with the direct method. Estimation uses data from the Philadelphia Fed real-time data set. Source: Tom Stark, Research Department, FRB Philadelphia. ------------------------------------------------------------------------------------ Table 6. Recent Benchmark Model 4 DARM Forecasts - Dated at the Quarter Forecast ------------------------------------------------------------------------------------ Variable: BOND (Moodys AAA Rate [QA,PPs]) By Forecast Step (1 to 5) Transformation: Level Lag Length for DARM(p): AIC Last Updated: 09/01/2009 10:22 ------------------------------------------------------------------------------------ Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2002:04 6.483 6.636 6.771 6.718 7.271 2003:01 6.194 6.652 6.737 6.626 6.707 2003:02 5.710 6.316 6.805 6.811 6.983 2003:03 5.616 5.731 6.393 6.845 6.849 2003:04 5.762 5.785 5.905 6.480 6.913 2004:01 5.514 5.978 5.562 5.880 6.404 2004:02 5.891 5.580 6.076 6.195 6.136 2004:03 5.771 6.004 5.698 6.102 6.362 2004:04 5.469 5.897 5.962 5.739 5.942 2005:01 5.322 5.502 6.117 6.178 5.833 2005:02 5.290 5.386 5.596 6.211 6.202 2005:03 5.097 5.352 5.552 5.689 6.171 2005:04 5.442 5.153 5.444 5.657 5.832 2006:01 5.264 5.515 5.177 5.328 5.665 2006:02 5.946 5.363 5.577 5.177 5.323 2006:03 5.845 6.028 5.368 5.644 5.285 2006:04 5.400 5.917 6.064 5.298 5.563 2007:01 5.366 5.421 5.661 5.949 5.275 2007:02 5.443 5.198 5.297 5.528 5.763 2007:03 5.688 5.395 5.234 5.267 5.408 2007:04 5.627 5.832 5.468 5.340 5.528 2008:01 5.185 5.692 5.930 5.519 5.322 2008:02 5.581 5.283 5.799 5.782 5.768 2008:03 5.664 5.663 5.430 5.820 5.685 2008:04 6.479 5.726 5.774 5.445 5.857 2009:01 5.009 6.502 5.794 5.807 5.578 2009:02 5.362 5.032 6.358 5.786 5.758 2009:03 5.390 5.529 5.066 6.413 5.777 2009:04 NA 5.461 5.613 5.473 6.124 2010:01 NA NA 5.640 5.549 5.772 2010:02 NA NA NA 5.530 5.494 2010:03 NA NA NA NA 5.586 Table 6 notes. (1) Each column gives the sequence of benchmark DARM projections for a given forecast step. The forecast steps range from one to five. The first step corresponds to the forecast that SPF panelists make for the quarter in which the survey is conducted. (2) The dates listed in the rows are the dates forecast, not the dates when the forecasts were made, with the exception of the forecast at step one, for which the two dates coincide. (3) The DARM benchmark model is estimated on a fixed 60-quarter rolling window. Its forecasts are computed with the direct method and incorporate recent monthly values of the dependent variable. Estimation uses data from the Philadelphia Fed real-time data set. Source: Tom Stark, Research Department, FRB Philadelphia. ------------------------------------------------------------ Table 7. Recent Realizations (Various Measures) Source: Philadelphia Fed Real-Time Data Set ------------------------------------------------------------ Variable: BOND (Moodys AAA Rate [QA,PPs]) Transformation: Level Last Updated: 09/01/2009 10:22 1- Initial Release 2- One Qtr After Initial Release 3- Five Qtrs After Initial Release 4- Nine Qtrs After Initial Release 5- Latest Vintage ------------------------------------------------------------- Obs. Date (1) (2) (3) (4) (5) 2002:04 6.280 6.280 6.280 6.280 6.280 2003:01 6.003 6.003 6.003 6.003 6.003 2003:02 5.310 5.310 5.310 5.310 5.310 2003:03 5.697 5.697 5.697 5.697 5.697 2003:04 5.657 5.657 5.657 5.657 5.657 2004:01 5.457 5.457 5.457 5.457 5.457 2004:02 5.927 5.927 5.927 5.927 5.927 2004:03 5.643 5.643 5.643 5.643 5.643 2004:04 5.487 5.487 5.487 5.487 5.487 2005:01 5.320 5.320 5.320 5.320 5.320 2005:02 5.147 5.147 5.147 5.147 5.147 2005:03 5.093 5.093 5.093 5.093 5.093 2005:04 5.380 5.380 5.380 5.380 5.380 2006:01 5.390 5.390 5.390 5.390 5.390 2006:02 5.893 5.893 5.893 5.893 5.893 2006:03 5.680 5.680 5.680 5.680 5.680 2006:04 5.387 5.387 5.387 5.387 5.387 2007:01 5.363 5.363 5.363 5.363 5.363 2007:02 5.577 5.577 5.577 NA 5.577 2007:03 5.753 5.753 5.753 NA 5.753 2007:04 5.530 5.530 5.530 NA 5.530 2008:01 5.457 5.457 5.457 NA 5.457 2008:02 5.600 5.600 NA NA 5.600 2008:03 5.653 5.653 NA NA 5.653 2008:04 5.837 5.837 NA NA 5.837 2009:01 5.273 5.273 NA NA 5.273 2009:02 5.513 NA NA NA 5.513 2009:03 NA NA NA NA NA 2009:04 NA NA NA NA NA 2010:01 NA NA NA NA NA 2010:02 NA NA NA NA NA 2010:03 NA NA NA NA NA Table 7 notes. (1) Each column reports a sequence of realizations from the Philadelphia Fed real-time data set. (2) The date listed in each row is the observation date. (3) Moving across a particular row shows how the observation is revised in subsequent releases. Source: Tom Stark, Research Department, FRB Philadelphia.