Error Statistics for the Survey of Professional Forecasters for Unemployment Rate [QA, PPs] Release Date: 11/18/2011 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. Tables 1A-1B report 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 periods shown in Table 1A. 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. Tables 1A-1B report four such comparisons. They show 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. Table 1A reports the root-mean-square-error ratios using as many observations as possible for each model. The number of observations can differ from model to model. We first compute the RMSE for each model. We then construct the ratio. Table 1B reports RMSE ratios after we adjust the samples to include only the observations common to both models in the pair. Accordingly, the ratios reported in Table 1B may differ slightly from those of Table 1A, depending on the availability of sufficient real-time observations for estimating the benchmark models or for computing the errors of the SPF or benchmark forecasts. Table 1B also reports three two-sided p-values for each ratio. The p-values, corrected for the presence of heteroskedasticity and serial correlation in the time series of differences in squared forecast errors, are those for the test of equality of mean-square error between the SPF and the benchmark. The p-values are those for: (1) The Diebold-Mariano statistic (July 1995, Journal of Business and Economic Statistics), using a uniform lag window with the truncation lag set to the forecast horizon minus unity. When the uniform lag window produces a nonpositive standard error, the Bartlett window is used. (2) The Harvey-Leybourne-Newbold correction (1997, International Journal of Forecasting) to the Diebold-Mariano statistic. (3) The Diebold-Mariano statistic, using a Bartlett lag window with the truncation lag increased four quarters beyond that of (1) and (2). 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. In Tables 1A - 1B, 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 1A 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 Tables 1A - 1B. Any 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. They 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 postdates by one month the vintage that SPF panelists would have had at their disposal when they formed their projections. 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 in the vintage dated 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 squared root-mean-square error. The latter is estimated over the aforementioned sample, using the measure of history listed in the footnote. --------------------------------------------------------------------------------------- Table 1A. Forecast Error Summary Statistics for SPF Variable: UNEMP (Unemployment 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: 11/18/2011 16:35 --------------------------------------------------------------------------------------- H ME(S) MAE(S) RMSE(S) RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) Nspf N History: Initial Release 1985:01-2009:02 1 -0.03 0.10 0.13 0.44 0.55 0.55 0.91 98 98 2 -0.05 0.23 0.31 0.60 0.71 0.70 0.82 98 98 3 -0.03 0.34 0.47 0.69 0.72 0.72 0.81 98 98 4 -0.01 0.45 0.65 0.79 0.78 0.80 0.86 98 98 5 -0.01 0.55 0.77 0.81 0.78 0.81 0.83 98 98 1985:01-1996:04 1 -0.04 0.12 0.14 0.64 0.66 0.66 0.97 48 48 2 -0.09 0.23 0.28 0.75 0.73 0.73 0.87 48 48 3 -0.10 0.33 0.39 0.76 0.71 0.71 0.77 48 48 4 -0.10 0.39 0.49 0.76 0.69 0.70 0.76 48 48 5 -0.10 0.49 0.59 0.74 0.68 0.71 0.74 48 48 1997:01-2009:02 1 -0.01 0.09 0.12 0.34 0.47 0.47 0.85 50 50 2 -0.00 0.22 0.33 0.54 0.69 0.69 0.80 50 50 3 0.04 0.35 0.53 0.66 0.72 0.73 0.83 50 50 4 0.07 0.51 0.77 0.80 0.83 0.85 0.91 50 50 5 0.08 0.61 0.90 0.85 0.84 0.86 0.88 50 50 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 1985:01-2009:02 1 -0.02 0.10 0.13 0.44 0.56 0.56 0.90 98 98 2 -0.04 0.23 0.31 0.60 0.71 0.70 0.82 98 98 3 -0.03 0.34 0.47 0.69 0.72 0.72 0.81 98 98 4 -0.01 0.45 0.65 0.79 0.78 0.80 0.85 98 98 5 -0.01 0.55 0.77 0.81 0.78 0.81 0.84 98 98 1985:01-1996:04 1 -0.04 0.12 0.14 0.63 0.67 0.67 0.95 48 48 2 -0.09 0.23 0.28 0.74 0.73 0.73 0.87 48 48 3 -0.10 0.33 0.39 0.76 0.71 0.71 0.77 48 48 4 -0.10 0.39 0.49 0.75 0.69 0.70 0.76 48 48 5 -0.10 0.49 0.59 0.74 0.68 0.71 0.74 48 48 1997:01-2009:02 1 -0.00 0.09 0.12 0.35 0.48 0.48 0.85 50 50 2 0.00 0.22 0.33 0.54 0.69 0.69 0.80 50 50 3 0.04 0.35 0.54 0.66 0.72 0.73 0.83 50 50 4 0.08 0.51 0.77 0.80 0.83 0.85 0.91 50 50 5 0.08 0.61 0.91 0.85 0.84 0.86 0.88 50 50 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 1985:01-2009:02 1 -0.02 0.11 0.13 0.44 0.56 0.56 0.86 98 98 2 -0.04 0.23 0.31 0.60 0.71 0.70 0.82 98 98 3 -0.03 0.34 0.47 0.69 0.72 0.73 0.81 98 98 4 -0.01 0.45 0.65 0.79 0.78 0.80 0.85 98 98 5 -0.01 0.55 0.77 0.81 0.78 0.81 0.83 98 98 1985:01-1996:04 1 -0.04 0.11 0.13 0.64 0.66 0.66 0.89 48 48 2 -0.09 0.22 0.27 0.74 0.72 0.72 0.85 48 48 3 -0.10 0.32 0.38 0.75 0.70 0.70 0.76 48 48 4 -0.10 0.38 0.48 0.75 0.68 0.69 0.74 48 48 5 -0.10 0.47 0.57 0.73 0.66 0.70 0.73 48 48 1997:01-2009:02 1 -0.00 0.10 0.13 0.36 0.50 0.50 0.84 50 50 2 0.01 0.23 0.35 0.55 0.70 0.69 0.80 50 50 3 0.04 0.36 0.55 0.67 0.73 0.74 0.83 50 50 4 0.08 0.52 0.78 0.80 0.83 0.85 0.91 50 50 5 0.09 0.62 0.92 0.85 0.84 0.87 0.88 50 50 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 1985:01-2009:02 1 -0.02 0.10 0.13 0.43 0.55 0.55 0.86 98 98 2 -0.04 0.23 0.31 0.60 0.71 0.70 0.82 98 98 3 -0.03 0.34 0.48 0.69 0.72 0.73 0.81 98 98 4 -0.01 0.45 0.65 0.79 0.78 0.80 0.86 98 98 5 -0.01 0.55 0.77 0.81 0.78 0.81 0.83 98 98 1985:01-1996:04 1 -0.04 0.11 0.13 0.63 0.65 0.65 0.89 48 48 2 -0.09 0.22 0.27 0.74 0.73 0.73 0.85 48 48 3 -0.10 0.32 0.38 0.76 0.70 0.71 0.78 48 48 4 -0.10 0.38 0.48 0.75 0.68 0.70 0.75 48 48 5 -0.10 0.47 0.57 0.73 0.67 0.70 0.73 48 48 1997:01-2009:02 1 -0.01 0.09 0.12 0.35 0.49 0.49 0.83 50 50 2 -0.00 0.23 0.34 0.55 0.69 0.69 0.80 50 50 3 0.04 0.36 0.55 0.66 0.73 0.74 0.83 50 50 4 0.07 0.52 0.78 0.80 0.83 0.85 0.91 50 50 5 0.08 0.62 0.92 0.85 0.84 0.87 0.88 50 50 H ME(S) MAE(S) RMSE(S) RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) Nspf N History: Latest Vintage 1985:01-2009:02 1 -0.01 0.11 0.14 0.45 0.59 0.59 0.87 98 98 2 -0.03 0.23 0.32 0.61 0.72 0.71 0.84 98 98 3 -0.02 0.35 0.48 0.69 0.73 0.74 0.82 98 98 4 0.00 0.46 0.66 0.79 0.79 0.81 0.87 98 98 5 0.01 0.56 0.78 0.81 0.80 0.82 0.85 98 98 1985:01-1996:04 1 -0.01 0.12 0.15 0.64 0.71 0.71 0.91 48 48 2 -0.06 0.24 0.29 0.74 0.76 0.76 0.90 48 48 3 -0.07 0.33 0.41 0.76 0.74 0.75 0.81 48 48 4 -0.07 0.40 0.51 0.76 0.72 0.74 0.79 48 48 5 -0.07 0.50 0.61 0.74 0.71 0.74 0.78 48 48 1997:01-2009:02 1 -0.01 0.09 0.13 0.35 0.49 0.49 0.81 50 50 2 -0.00 0.22 0.34 0.54 0.69 0.69 0.80 50 50 3 0.04 0.36 0.55 0.66 0.73 0.74 0.83 50 50 4 0.07 0.52 0.78 0.81 0.83 0.85 0.91 50 50 5 0.08 0.62 0.92 0.85 0.84 0.87 0.88 50 50 Notes for Table 1A. (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 Philadelphia 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 1B. Ratios of Root-Mean-Square Errors for SPF Variable: UNEMP (Unemployment Rate [QA, PPs]) Alternative P-Values in Parentheses ---------------------------------------------------------------------------------------------- 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: 11/18/2011 16:35 ---------------------------------------------------------------------------------------------- History: Initial Release 1985:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.436 0.549 0.549 0.909 98 98 98 98 (0.002) (0.000) (0.000) (0.192) (0.002) (0.000) (0.000) (0.197) (0.043) (0.000) (0.000) (0.146) 2 0.603 0.707 0.704 0.822 98 98 98 98 (0.069) (0.000) (0.004) (0.002) (0.076) (0.001) (0.006) (0.003) (0.081) (0.001) (0.007) (0.005) 3 0.687 0.718 0.723 0.807 98 98 98 98 (0.068) (0.002) (0.005) (0.008) (0.078) (0.004) (0.007) (0.011) (0.056) (0.002) (0.003) (0.005) 4 0.789 0.777 0.798 0.855 98 98 98 98 (0.029) (0.000) (0.002) (0.001) (0.038) (0.001) (0.003) (0.002) (0.016) (0.000) (0.001) (0.002) 5 0.811 0.779 0.808 0.834 98 98 98 98 (0.008) (0.001) (0.007) (0.007) (0.014) (0.003) (0.012) (0.012) (0.003) (0.000) (0.004) (0.007) History: Initial Release 1985:01-1996:04 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.635 0.658 0.658 0.965 48 48 48 48 (0.001) (0.000) (0.000) (0.760) (0.002) (0.001) (0.001) (0.764) (0.006) (0.000) (0.000) (0.725) 2 0.747 0.729 0.732 0.867 48 48 48 48 (0.092) (0.000) (0.000) (0.180) (0.109) (0.000) (0.000) (0.200) (0.070) (0.000) (0.000) (0.133) 3 0.761 0.708 0.714 0.771 48 48 48 48 (0.112) (0.001) (0.001) (0.001) (0.138) (0.003) (0.004) (0.003) (0.060) (0.002) (0.003) (0.003) 4 0.756 0.685 0.704 0.758 48 48 48 48 (0.038) (0.023) (0.036) (0.016) (0.060) (0.040) (0.058) (0.030) (0.009) (0.017) (0.032) (0.019) 5 0.740 0.678 0.709 0.744 48 48 48 48 (0.005) (0.052) (0.102) (0.071) (0.014) (0.084) (0.145) (0.108) (0.001) (0.032) (0.076) (0.064) History: Initial Release 1997:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.336 0.466 0.466 0.849 50 50 50 50 (0.009) (0.000) (0.000) (0.047) (0.013) (0.000) (0.000) (0.055) (0.094) (0.001) (0.001) (0.031) 2 0.542 0.693 0.687 0.795 50 50 50 50 (0.124) (0.016) (0.053) (0.002) (0.142) (0.023) (0.066) (0.004) (0.143) (0.026) (0.068) (0.014) 3 0.657 0.723 0.728 0.827 50 50 50 50 (0.136) (0.038) (0.055) (0.105) (0.163) (0.055) (0.075) (0.130) (0.120) (0.028) (0.042) (0.084) 4 0.803 0.826 0.847 0.905 50 50 50 50 (0.125) (0.004) (0.014) (0.030) (0.159) (0.011) (0.027) (0.048) (0.095) (0.005) (0.015) (0.035) 5 0.847 0.835 0.862 0.882 50 50 50 50 (0.110) (0.001) (0.005) (0.032) (0.152) (0.006) (0.013) (0.057) (0.077) (0.001) (0.002) (0.033) History: One Qtr After Initial Release 1985:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.439 0.557 0.557 0.902 98 98 98 98 (0.002) (0.000) (0.000) (0.151) (0.002) (0.000) (0.000) (0.156) (0.044) (0.000) (0.000) (0.110) 2 0.603 0.707 0.705 0.823 98 98 98 98 (0.065) (0.000) (0.004) (0.002) (0.072) (0.001) (0.006) (0.003) (0.079) (0.001) (0.007) (0.005) 3 0.686 0.718 0.724 0.807 98 98 98 98 (0.066) (0.002) (0.005) (0.008) (0.076) (0.004) (0.007) (0.011) (0.054) (0.002) (0.003) (0.006) 4 0.788 0.778 0.799 0.855 98 98 98 98 (0.029) (0.000) (0.001) (0.001) (0.038) (0.001) (0.003) (0.002) (0.016) (0.000) (0.001) (0.002) 5 0.811 0.780 0.809 0.836 98 98 98 98 (0.008) (0.001) (0.007) (0.008) (0.013) (0.002) (0.012) (0.012) (0.003) (0.000) (0.004) (0.007) History: One Qtr After Initial Release 1985:01-1996:04 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.631 0.665 0.665 0.950 48 48 48 48 (0.001) (0.000) (0.000) (0.672) (0.002) (0.001) (0.001) (0.677) (0.006) (0.000) (0.000) (0.621) 2 0.743 0.728 0.732 0.868 48 48 48 48 (0.087) (0.000) (0.000) (0.186) (0.104) (0.000) (0.000) (0.207) (0.067) (0.000) (0.000) (0.138) 3 0.757 0.707 0.713 0.771 48 48 48 48 (0.111) (0.001) (0.001) (0.001) (0.137) (0.002) (0.003) (0.004) (0.060) (0.002) (0.002) (0.003) 4 0.753 0.686 0.705 0.756 48 48 48 48 (0.039) (0.021) (0.034) (0.014) (0.061) (0.038) (0.055) (0.027) (0.010) (0.015) (0.030) (0.017) 5 0.738 0.677 0.709 0.744 48 48 48 48 (0.005) (0.049) (0.100) (0.071) (0.014) (0.081) (0.142) (0.108) (0.001) (0.030) (0.074) (0.064) History: One Qtr After Initial Release 1997:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.348 0.481 0.481 0.855 50 50 50 50 (0.008) (0.000) (0.000) (0.038) (0.011) (0.000) (0.000) (0.046) (0.092) (0.002) (0.002) (0.032) 2 0.544 0.694 0.688 0.797 50 50 50 50 (0.120) (0.015) (0.050) (0.002) (0.138) (0.023) (0.063) (0.004) (0.140) (0.026) (0.067) (0.014) 3 0.657 0.724 0.729 0.828 50 50 50 50 (0.133) (0.037) (0.054) (0.104) (0.160) (0.053) (0.073) (0.129) (0.117) (0.027) (0.042) (0.085) 4 0.802 0.826 0.848 0.905 50 50 50 50 (0.123) (0.004) (0.014) (0.027) (0.158) (0.011) (0.027) (0.045) (0.093) (0.005) (0.015) (0.033) 5 0.847 0.836 0.863 0.883 50 50 50 50 (0.108) (0.001) (0.005) (0.033) (0.150) (0.005) (0.013) (0.059) (0.075) (0.001) (0.002) (0.034) History: Five Qtrs After Initial Release 1985:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.441 0.561 0.561 0.862 98 98 98 98 (0.002) (0.000) (0.000) (0.042) (0.003) (0.000) (0.000) (0.046) (0.057) (0.000) (0.000) (0.026) 2 0.603 0.707 0.704 0.821 98 98 98 98 (0.069) (0.001) (0.005) (0.002) (0.076) (0.001) (0.007) (0.002) (0.083) (0.001) (0.008) (0.005) 3 0.689 0.721 0.726 0.809 98 98 98 98 (0.069) (0.003) (0.005) (0.009) (0.079) (0.004) (0.008) (0.012) (0.057) (0.002) (0.003) (0.006) 4 0.788 0.778 0.798 0.855 98 98 98 98 (0.029) (0.000) (0.001) (0.001) (0.038) (0.001) (0.002) (0.002) (0.016) (0.000) (0.001) (0.002) 5 0.810 0.779 0.808 0.833 98 98 98 98 (0.008) (0.001) (0.006) (0.006) (0.013) (0.002) (0.010) (0.010) (0.003) (0.000) (0.003) (0.005) History: Five Qtrs After Initial Release 1985:01-1996:04 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.645 0.663 0.663 0.892 48 48 48 48 (0.002) (0.000) (0.000) (0.380) (0.003) (0.001) (0.001) (0.390) (0.010) (0.000) (0.000) (0.297) 2 0.736 0.721 0.723 0.853 48 48 48 48 (0.077) (0.000) (0.000) (0.145) (0.093) (0.000) (0.000) (0.164) (0.059) (0.000) (0.000) (0.097) 3 0.752 0.696 0.702 0.764 48 48 48 48 (0.097) (0.001) (0.001) (0.001) (0.123) (0.002) (0.003) (0.004) (0.050) (0.002) (0.002) (0.003) 4 0.746 0.676 0.695 0.744 48 48 48 48 (0.034) (0.020) (0.031) (0.011) (0.056) (0.036) (0.051) (0.023) (0.009) (0.014) (0.027) (0.014) 5 0.728 0.664 0.696 0.731 48 48 48 48 (0.004) (0.042) (0.086) (0.060) (0.013) (0.071) (0.127) (0.094) (0.000) (0.025) (0.063) (0.054) History: Five Qtrs After Initial Release 1997:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.357 0.495 0.495 0.835 50 50 50 50 (0.009) (0.000) (0.000) (0.012) (0.013) (0.000) (0.000) (0.016) (0.103) (0.003) (0.003) (0.019) 2 0.552 0.699 0.694 0.804 50 50 50 50 (0.121) (0.016) (0.050) (0.003) (0.139) (0.023) (0.064) (0.005) (0.140) (0.026) (0.065) (0.017) 3 0.665 0.733 0.738 0.832 50 50 50 50 (0.137) (0.041) (0.059) (0.105) (0.164) (0.058) (0.079) (0.130) (0.120) (0.030) (0.046) (0.085) 4 0.805 0.827 0.848 0.908 50 50 50 50 (0.123) (0.005) (0.014) (0.030) (0.157) (0.011) (0.027) (0.050) (0.093) (0.005) (0.014) (0.037) 5 0.848 0.840 0.866 0.883 50 50 50 50 (0.109) (0.001) (0.005) (0.033) (0.151) (0.005) (0.013) (0.058) (0.076) (0.000) (0.002) (0.033) History: Nine Qtrs After Initial Release 1985:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.432 0.553 0.553 0.859 98 98 98 98 (0.003) (0.000) (0.000) (0.033) (0.004) (0.000) (0.000) (0.037) (0.058) (0.000) (0.000) (0.019) 2 0.600 0.706 0.703 0.820 98 98 98 98 (0.071) (0.001) (0.006) (0.002) (0.078) (0.001) (0.008) (0.003) (0.083) (0.002) (0.009) (0.006) 3 0.691 0.722 0.728 0.813 98 98 98 98 (0.070) (0.003) (0.005) (0.010) (0.081) (0.004) (0.008) (0.014) (0.058) (0.002) (0.004) (0.007) 4 0.790 0.779 0.799 0.858 98 98 98 98 (0.030) (0.000) (0.001) (0.001) (0.039) (0.001) (0.003) (0.003) (0.017) (0.000) (0.001) (0.002) 5 0.811 0.782 0.810 0.834 98 98 98 98 (0.009) (0.001) (0.006) (0.007) (0.014) (0.002) (0.010) (0.011) (0.003) (0.000) (0.003) (0.006) History: Nine Qtrs After Initial Release 1985:01-1996:04 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.630 0.645 0.645 0.891 48 48 48 48 (0.002) (0.000) (0.000) (0.340) (0.004) (0.000) (0.000) (0.350) (0.011) (0.000) (0.000) (0.257) 2 0.738 0.728 0.729 0.848 48 48 48 48 (0.088) (0.000) (0.000) (0.138) (0.105) (0.000) (0.000) (0.157) (0.065) (0.000) (0.000) (0.083) 3 0.760 0.702 0.709 0.778 48 48 48 48 (0.099) (0.001) (0.001) (0.003) (0.125) (0.002) (0.004) (0.008) (0.049) (0.002) (0.002) (0.006) 4 0.752 0.681 0.700 0.751 48 48 48 48 (0.034) (0.022) (0.036) (0.015) (0.055) (0.040) (0.058) (0.029) (0.008) (0.017) (0.033) (0.018) 5 0.731 0.671 0.700 0.734 48 48 48 48 (0.004) (0.048) (0.093) (0.062) (0.013) (0.080) (0.134) (0.098) (0.000) (0.030) (0.069) (0.058) History: Nine Qtrs After Initial Release 1997:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.345 0.488 0.488 0.829 50 50 50 50 (0.011) (0.000) (0.000) (0.013) (0.015) (0.000) (0.000) (0.017) (0.109) (0.003) (0.003) (0.016) 2 0.547 0.694 0.688 0.804 50 50 50 50 (0.123) (0.017) (0.052) (0.004) (0.142) (0.025) (0.065) (0.007) (0.141) (0.027) (0.066) (0.022) 3 0.665 0.732 0.737 0.830 50 50 50 50 (0.137) (0.041) (0.059) (0.101) (0.164) (0.058) (0.079) (0.125) (0.121) (0.030) (0.046) (0.081) 4 0.805 0.827 0.847 0.910 50 50 50 50 (0.123) (0.005) (0.014) (0.037) (0.158) (0.011) (0.027) (0.058) (0.093) (0.005) (0.014) (0.043) 5 0.849 0.840 0.867 0.883 50 50 50 50 (0.111) (0.001) (0.004) (0.034) (0.153) (0.005) (0.012) (0.060) (0.077) (0.000) (0.002) (0.033) History: Latest Vintage 1985:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.451 0.587 0.587 0.867 98 98 98 98 (0.002) (0.000) (0.000) (0.025) (0.003) (0.000) (0.000) (0.028) (0.054) (0.000) (0.000) (0.022) 2 0.605 0.717 0.714 0.838 98 98 98 98 (0.066) (0.001) (0.007) (0.006) (0.074) (0.002) (0.009) (0.008) (0.079) (0.002) (0.010) (0.014) 3 0.695 0.734 0.741 0.825 98 98 98 98 (0.068) (0.004) (0.008) (0.016) (0.078) (0.006) (0.011) (0.021) (0.056) (0.003) (0.006) (0.011) 4 0.791 0.790 0.811 0.870 98 98 98 98 (0.029) (0.001) (0.003) (0.004) (0.038) (0.002) (0.005) (0.007) (0.016) (0.001) (0.003) (0.006) 5 0.814 0.796 0.824 0.847 98 98 98 98 (0.009) (0.003) (0.013) (0.016) (0.014) (0.005) (0.020) (0.023) (0.003) (0.001) (0.008) (0.014) History: Latest Vintage 1985:01-1996:04 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.642 0.712 0.712 0.914 48 48 48 48 (0.003) (0.001) (0.001) (0.364) (0.005) (0.002) (0.002) (0.373) (0.034) (0.000) (0.000) (0.346) 2 0.741 0.757 0.760 0.905 48 48 48 48 (0.098) (0.000) (0.000) (0.349) (0.116) (0.001) (0.001) (0.369) (0.088) (0.001) (0.001) (0.269) 3 0.763 0.737 0.747 0.812 48 48 48 48 (0.119) (0.004) (0.006) (0.011) (0.147) (0.008) (0.013) (0.020) (0.068) (0.009) (0.011) (0.018) 4 0.757 0.716 0.736 0.788 48 48 48 48 (0.045) (0.045) (0.069) (0.046) (0.070) (0.069) (0.098) (0.071) (0.013) (0.037) (0.066) (0.054) 5 0.744 0.712 0.743 0.777 48 48 48 48 (0.007) (0.088) (0.158) (0.133) (0.018) (0.129) (0.207) (0.180) (0.001) (0.062) (0.128) (0.124) History: Latest Vintage 1997:01-2009:02 H RMSE(S/NC) RMSE(S/IAR) RMSE(S/DAR) RMSE(S/DARM) N1 N2 N3 N4 1 0.349 0.492 0.492 0.815 50 50 50 50 (0.012) (0.000) (0.000) (0.006) (0.016) (0.000) (0.000) (0.009) (0.114) (0.002) (0.002) (0.005) 2 0.545 0.692 0.686 0.799 50 50 50 50 (0.125) (0.018) (0.053) (0.003) (0.144) (0.026) (0.066) (0.006) (0.143) (0.028) (0.067) (0.020) 3 0.665 0.732 0.737 0.832 50 50 50 50 (0.140) (0.042) (0.060) (0.107) (0.167) (0.059) (0.080) (0.132) (0.123) (0.031) (0.046) (0.087) 4 0.806 0.828 0.848 0.911 50 50 50 50 (0.127) (0.005) (0.016) (0.037) (0.162) (0.012) (0.029) (0.059) (0.097) (0.006) (0.015) (0.044) 5 0.850 0.841 0.867 0.883 50 50 50 50 (0.115) (0.001) (0.004) (0.036) (0.158) (0.005) (0.013) (0.062) (0.081) (0.000) (0.002) (0.035) Notes for Table 1B. (1) The forecast horizon is given by H, where H = 1 is the SPF forecast for the current quarter. (2) The headers RMSE(S/NC), RMSE(S/IAR), RMSE(S/DAR), and RMSE(S/DARM) are the ratios of the SPF root-mean-square error to that of the benchmark models: No-change (NC), indirect autoregression (IAR), direct autoregession (DAR), and direct autoregression augmented with monthly information (DARM). These statistics may differ slightly from those reported in Table 1A because they incorporate only those observations common to both the SPF and the benchmark model. The previous statistics make use of all available observations for each model. (3) All models are estimated on a rolling window of 60 observations from the Philadelphia Fed real-time data set. (4) A set of three two-sided p-values (in parentheses) accompanies each statistic. These are the p-values for the test of the equality of mean-square-error. The first is for the Diebold-Mariano (1995, JBES) statistic, using a uniform lag window with the trunction lag set to the forecast horizon minus one. (The tables report the p-values using a Bartlett window when the uniform window produces a negative standard error.) The second is for the Harvey-Leybourne-Newbold (1997, IJF) correction to the Diebold-Mariano statistic. The third is for the Diebold-Mariano statistic, using a Bartlett lag window with the truncation lag increased four quarters. (5) The headers N1, N2, N3, and N4 show the number of observations used in constructing each ratio of root-mean-square errors. (6) 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: UNEMP (Unemployment Rate [QA, PPs]) By Forecast Step (1 to 5) Transformation: Level Last Updated: 11/18/2011 16:35 -------------------------------------------------------------------- Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2005:01 5.300 5.308 5.383 5.400 5.400 2005:02 5.200 5.200 5.283 5.283 5.300 2005:03 5.000 5.200 5.200 5.200 5.200 2005:04 5.000 5.000 5.100 5.113 5.200 2006:01 4.800 5.000 4.912 5.100 5.100 2006:02 4.700 4.800 4.900 4.900 5.100 2006:03 4.700 4.700 4.800 4.900 4.900 2006:04 4.533 4.800 4.790 4.809 5.000 2007:01 4.600 4.700 4.800 4.800 4.900 2007:02 4.574 4.700 4.800 4.890 4.822 2007:03 4.600 4.649 4.700 4.800 4.900 2007:04 4.700 4.700 4.700 4.800 4.900 2008:01 5.000 4.800 4.700 4.800 4.800 2008:02 5.133 5.100 4.900 4.700 4.800 2008:03 5.700 5.400 5.200 4.960 4.707 2008:04 6.600 5.800 5.500 5.240 5.000 2009:01 7.800 7.000 6.000 5.500 5.200 2009:02 9.100 8.300 7.400 6.000 5.500 2009:03 9.602 9.561 8.710 7.600 6.047 2009:04 10.167 9.900 9.800 8.900 7.700 2010:01 9.900 10.200 9.947 9.800 8.950 2010:02 9.800 9.926 10.100 9.845 9.700 2010:03 9.600 9.600 9.818 9.978 9.600 2010:04 9.600 9.600 9.500 9.667 9.800 2011:01 9.280 9.516 9.400 9.300 9.400 2011:02 8.867 9.200 9.400 9.300 9.129 2011:03 9.100 8.677 9.000 9.244 9.000 2011:04 9.006 8.961 8.500 8.800 9.005 2012:01 NA 8.933 8.800 8.400 8.700 2012:02 NA NA 8.892 8.700 8.200 2012:03 NA NA NA 8.795 8.566 2012:04 NA NA NA NA 8.700 Notes for Table 2. (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: UNEMP (Unemployment Rate [QA, PPs]) By Forecast Step (1 to 5) Transformation: Level Lag Length for IAR(p): AIC Last Updated: 11/18/2011 16:35 ------------------------------------------------------------------------------------ Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2005:01 5.410 5.298 5.465 5.206 5.422 2005:02 5.202 5.405 5.265 5.450 5.181 2005:03 5.003 5.151 5.403 5.249 5.444 2005:04 4.932 4.944 5.131 5.408 5.249 2006:01 4.902 4.896 4.921 5.129 5.416 2006:02 4.653 4.888 4.884 4.923 5.142 2006:03 4.566 4.593 4.890 4.891 4.944 2006:04 4.722 4.537 4.571 4.903 4.912 2007:01 4.416 4.765 4.533 4.571 4.924 2007:02 4.478 4.369 4.804 4.547 4.587 2007:03 4.536 4.506 4.367 4.845 4.574 2007:04 4.694 4.572 4.535 4.383 4.884 2008:01 4.928 4.761 4.615 4.575 4.415 2008:02 5.003 4.996 4.808 4.656 4.617 2008:03 5.474 5.051 5.042 4.847 4.696 2008:04 6.298 5.609 5.081 5.071 4.877 2009:01 7.439 6.541 5.655 5.098 5.089 2009:02 9.058 7.885 6.647 5.668 5.107 2009:03 10.485 10.040 8.163 6.663 5.643 2009:04 9.920 11.688 10.882 8.292 6.602 2010:01 10.135 9.901 12.859 11.591 8.280 2010:02 9.174 10.040 9.652 13.974 12.123 2010:03 9.190 8.309 9.736 9.180 15.014 2010:04 9.249 8.582 7.228 9.258 8.525 2011:01 9.602 8.794 7.739 5.984 8.633 2011:02 8.252 9.541 8.222 6.787 4.677 2011:03 8.766 7.463 9.410 7.567 5.745 2011:04 9.064 8.569 6.656 9.244 6.860 2012:01 NA 8.954 8.235 5.845 9.044 2012:02 NA NA 8.800 7.907 5.073 2012:03 NA NA NA 8.606 7.543 2012:04 NA NA NA NA 8.387 Notes for Table 3. (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: UNEMP (Unemployment Rate [QA, PPs]) By Forecast Step (1 to 5) Transformation: Level Last Updated: 11/18/2011 16:35 --------------------------------------------------------------------------------------- Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2005:01 5.433 5.433 5.600 5.633 5.867 2005:02 5.267 5.433 5.433 5.600 5.633 2005:03 5.100 5.267 5.433 5.433 5.600 2005:04 5.000 5.100 5.267 5.433 5.433 2006:01 4.933 5.000 5.100 5.267 5.433 2006:02 4.733 4.933 5.000 5.100 5.267 2006:03 4.633 4.733 4.933 5.000 5.100 2006:04 4.700 4.633 4.733 4.933 5.000 2007:01 4.467 4.700 4.633 4.733 4.933 2007:02 4.500 4.467 4.700 4.633 4.733 2007:03 4.500 4.500 4.467 4.700 4.633 2007:04 4.633 4.500 4.500 4.467 4.700 2008:01 4.833 4.633 4.500 4.500 4.467 2008:02 4.933 4.833 4.633 4.500 4.500 2008:03 5.333 4.933 4.833 4.633 4.500 2008:04 5.967 5.333 4.933 4.833 4.633 2009:01 6.867 5.967 5.333 4.933 4.833 2009:02 8.067 6.867 5.967 5.333 4.933 2009:03 9.267 8.067 6.867 5.967 5.333 2009:04 9.633 9.267 8.067 6.867 5.967 2010:01 10.033 9.633 9.267 8.067 6.867 2010:02 9.700 10.033 9.633 9.267 8.067 2010:03 9.700 9.700 10.033 9.633 9.267 2010:04 9.567 9.700 9.700 10.033 9.633 2011:01 9.633 9.567 9.700 9.700 10.033 2011:02 8.900 9.633 9.567 9.700 9.700 2011:03 9.100 8.900 9.633 9.567 9.700 2011:04 9.100 9.100 8.900 9.633 9.567 2012:01 NA 9.100 9.100 8.900 9.633 2012:02 NA NA 9.100 9.100 8.900 2012:03 NA NA NA 9.100 9.100 2012:04 NA NA NA NA 9.100 Notes for Table 4. (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: UNEMP (Unemployment Rate [QA, PPs]) By Forecast Step (1 to 5) Transformation: Level Lag Length for DAR(p): AIC Last Updated: 11/18/2011 16:35 ------------------------------------------------------------------------------------ Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2005:01 5.410 5.284 5.560 5.143 5.598 2005:02 5.202 5.286 5.184 5.268 5.053 2005:03 5.003 5.084 5.248 5.092 5.253 2005:04 4.932 4.922 5.042 5.289 5.171 2006:01 4.902 4.905 4.905 5.080 5.333 2006:02 4.653 4.892 4.898 4.926 5.105 2006:03 4.566 4.602 4.911 4.899 4.891 2006:04 4.722 4.528 4.569 4.948 4.905 2007:01 4.416 4.749 4.514 4.598 4.984 2007:02 4.478 4.406 4.781 4.524 4.661 2007:03 4.536 4.488 4.401 4.817 4.568 2007:04 4.694 4.579 4.519 4.464 4.898 2008:01 4.928 4.756 4.612 4.507 4.532 2008:02 5.003 5.006 4.819 4.680 4.516 2008:03 5.474 5.066 5.054 4.875 4.754 2008:04 6.298 5.585 5.100 5.110 4.928 2009:01 7.439 6.455 5.657 5.127 5.174 2009:02 9.058 7.725 6.534 5.626 5.238 2009:03 10.485 9.665 7.656 6.397 5.635 2009:04 9.920 11.508 9.592 7.540 6.333 2010:01 10.135 10.515 11.659 9.041 7.392 2010:02 9.174 9.929 10.645 10.989 8.728 2010:03 9.190 8.570 10.015 10.140 10.050 2010:04 9.249 8.571 7.598 9.808 9.338 2011:01 9.602 8.725 8.000 7.530 9.156 2011:02 8.252 9.211 7.964 7.580 6.972 2011:03 8.766 6.984 9.004 6.957 6.585 2011:04 9.064 8.252 6.792 8.134 6.210 2012:01 NA 8.941 8.940 6.027 6.511 2012:02 NA NA 8.536 8.663 4.677 2012:03 NA NA NA 8.293 8.221 2012:04 NA NA NA NA 7.909 Notes for Table 5. (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: UNEMP (Unemployment Rate [QA, PPs]) By Forecast Step (1 to 5) Transformation: Level Lag Length for DARM(p): AIC Last Updated: 11/18/2011 16:35 ------------------------------------------------------------------------------------ Qtr Forecast Step 1 Step 2 Step 3 Step 4 Step 5 2005:01 5.169 5.396 5.338 5.388 5.147 2005:02 5.158 4.994 5.294 5.229 5.095 2005:03 4.949 5.082 4.912 5.259 5.219 2005:04 5.034 4.872 5.016 4.835 5.331 2006:01 4.686 4.949 4.848 5.069 4.833 2006:02 4.689 4.635 4.918 4.866 5.225 2006:03 4.789 4.655 4.518 4.849 4.870 2006:04 4.368 4.817 4.557 4.461 4.784 2007:01 4.597 4.368 4.841 4.611 4.622 2007:02 4.467 4.632 4.388 4.928 4.800 2007:03 4.607 4.493 4.553 4.310 4.969 2007:04 4.735 4.666 4.558 4.611 4.389 2008:01 4.983 4.783 4.778 4.711 4.679 2008:02 5.067 5.011 4.846 4.852 4.574 2008:03 5.685 5.075 5.002 4.939 4.907 2008:04 6.529 5.815 5.071 5.067 4.932 2009:01 7.776 6.704 5.933 5.112 5.047 2009:02 9.222 8.266 6.876 5.969 5.006 2009:03 9.533 10.072 8.344 6.933 6.102 2009:04 10.356 10.316 10.301 8.259 7.017 2010:01 9.639 10.387 10.462 9.583 8.015 2010:02 9.723 9.375 10.742 9.701 9.307 2010:03 9.322 9.071 8.699 10.467 8.528 2010:04 9.499 8.836 8.731 8.204 9.475 2011:01 8.813 9.088 7.960 7.997 7.558 2011:02 8.772 8.291 8.409 7.299 7.453 2011:03 9.138 7.453 6.849 7.572 6.298 2011:04 8.976 9.029 6.771 6.549 6.776 2012:01 NA 8.831 8.236 7.221 5.146 2012:02 NA NA 8.541 8.538 6.059 2012:03 NA NA NA 8.074 8.133 2012:04 NA NA NA NA 7.982 Notes for Table 6. (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: UNEMP (Unemployment Rate [QA, PPs]) Transformation: Level Last Updated: 11/18/2011 16:35 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) 2005:01 5.267 5.267 5.233 5.267 5.300 2005:02 5.100 5.100 5.067 5.067 5.100 2005:03 5.000 5.000 5.000 5.000 4.967 2005:04 4.933 4.933 4.967 4.933 4.967 2006:01 4.733 4.733 4.733 4.700 4.733 2006:02 4.633 4.633 4.633 4.667 4.633 2006:03 4.700 4.700 4.633 4.633 4.633 2006:04 4.467 4.467 4.433 4.433 4.433 2007:01 4.500 4.500 4.500 4.500 4.500 2007:02 4.500 4.500 4.533 4.533 4.500 2007:03 4.633 4.700 4.700 4.633 4.667 2007:04 4.833 4.833 4.800 4.800 4.800 2008:01 4.933 4.933 4.933 4.967 4.967 2008:02 5.333 5.333 5.367 5.300 5.300 2008:03 5.967 6.067 6.033 6.033 6.033 2008:04 6.867 6.867 6.967 6.900 6.900 2009:01 8.067 8.067 8.167 8.200 8.200 2009:02 9.267 9.267 9.267 9.267 9.267 2009:03 9.633 9.633 9.667 NA 9.667 2009:04 10.033 10.033 9.967 NA 9.967 2010:01 9.700 9.700 9.700 NA 9.700 2010:02 9.700 9.700 9.633 NA 9.633 2010:03 9.567 9.567 NA NA 9.567 2010:04 9.633 9.633 NA NA 9.633 2011:01 8.900 8.900 NA NA 8.900 2011:02 9.100 9.100 NA NA 9.100 2011:03 9.100 NA NA NA 9.100 2011:04 NA NA NA NA NA 2012:01 NA NA NA NA NA 2012:02 NA NA NA NA NA 2012:03 NA NA NA NA NA 2012:04 NA NA NA NA NA Notes for Table 7. (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.