Ri (2005), the logarithm of the conditional variance of the error term in equation (2) follows a randomwalk process (in unreported results, we found that treating log-volatility as an AR(1) process with a coefficient of 0.9 slightly reduced the forecast accuracy). In a VAR context, studies such as Clark (2011), Carriero et al. (2012) and D’Agostino et al. (2013) have found that this type of stochastic volatility formulation improves the accuracy of both point and density forecasts. The specification of the regressor Sch66336MedChemExpress Lonafarnib vector Xm,t in the BMF and BMFSV models is partly a function of the way that we sample the monthly variables. For each monthly variable, we first transform it at the monthly frequency as necessary to achieve stationarity. At the quarterly frequency, for each monthly variable, we then define three different variables, by sampling the monthly series separately for each month of the quarter. Exactly what variables are included in Xm,t depends on when in the quarter the forecast is formed. We consider four timings for forecasting period t GDP growth: forecasting at the end of the first week of month 1 of quarter t (m = 1), at the end of the first week of month 2 of quarter t (m = 2), at the end of the first week of month 3 (m = 3) and at the end of the first week of month 1 of quarter t + 1 (m = 4). These points in time are chosen to correspond to the usual timing of the publication of employment data: employment data for month s are normally published at the end of the first week of month s + 1. At each of the four forecast origins that we consider, for each quarter t, the regressor set Xm,t is specified to include the subset of variables that are available for t (details are given in Section 3.2). At these points in time, the availability of other indicators also varies. As a consequence, the model specification changes in each month of the quarter, reflecting and accommodating the ragged edge of the data, in line with a direct GSK2256098MedChemExpress GSK2256098 approach to forecasting. We stress that this approach does not involve bridge methods. Bridge methods require forecasting monthly observations of monthly variables for any months of quarter t for which data are not yet available. We do not use such forecasts. Rather, on the right-hand side of the regression model we put only the actual monthly observations that are available for the quarter, in the form of different quarterly variables associated with the different months of the quarter. 3.2. Indicators used We report below results for both `large’ and `small’ versions of the BMF and BMFSV models. The large version includes a broad set of 12 monthly indicators: payroll employment (logchange); industrial production (log-change); real retail sales (log-change); housing starts (logarithmic); the ISM index (overall) for manufacturing; the ISM index for supplier delivery times; the ISM index for orders; average weekly hours of production and supervisory workers (logchange); new claims for unemployment insurance; stock prices as measured by the Standard and Poor’s 500 index (log-change); the 10-year Treasury bond yield; the 3-month Treasury bill rate. The small version uses just the first five indicators of the 12-variable set, which might be considered primary contemporaneous indicators of economic activity. In the results that are reported in this paper, in the model we include only values of these variables for the current quarter t (the quarter for which GDP growth is being forecast). However, our general.Ri (2005), the logarithm of the conditional variance of the error term in equation (2) follows a randomwalk process (in unreported results, we found that treating log-volatility as an AR(1) process with a coefficient of 0.9 slightly reduced the forecast accuracy). In a VAR context, studies such as Clark (2011), Carriero et al. (2012) and D’Agostino et al. (2013) have found that this type of stochastic volatility formulation improves the accuracy of both point and density forecasts. The specification of the regressor vector Xm,t in the BMF and BMFSV models is partly a function of the way that we sample the monthly variables. For each monthly variable, we first transform it at the monthly frequency as necessary to achieve stationarity. At the quarterly frequency, for each monthly variable, we then define three different variables, by sampling the monthly series separately for each month of the quarter. Exactly what variables are included in Xm,t depends on when in the quarter the forecast is formed. We consider four timings for forecasting period t GDP growth: forecasting at the end of the first week of month 1 of quarter t (m = 1), at the end of the first week of month 2 of quarter t (m = 2), at the end of the first week of month 3 (m = 3) and at the end of the first week of month 1 of quarter t + 1 (m = 4). These points in time are chosen to correspond to the usual timing of the publication of employment data: employment data for month s are normally published at the end of the first week of month s + 1. At each of the four forecast origins that we consider, for each quarter t, the regressor set Xm,t is specified to include the subset of variables that are available for t (details are given in Section 3.2). At these points in time, the availability of other indicators also varies. As a consequence, the model specification changes in each month of the quarter, reflecting and accommodating the ragged edge of the data, in line with a direct approach to forecasting. We stress that this approach does not involve bridge methods. Bridge methods require forecasting monthly observations of monthly variables for any months of quarter t for which data are not yet available. We do not use such forecasts. Rather, on the right-hand side of the regression model we put only the actual monthly observations that are available for the quarter, in the form of different quarterly variables associated with the different months of the quarter. 3.2. Indicators used We report below results for both `large’ and `small’ versions of the BMF and BMFSV models. The large version includes a broad set of 12 monthly indicators: payroll employment (logchange); industrial production (log-change); real retail sales (log-change); housing starts (logarithmic); the ISM index (overall) for manufacturing; the ISM index for supplier delivery times; the ISM index for orders; average weekly hours of production and supervisory workers (logchange); new claims for unemployment insurance; stock prices as measured by the Standard and Poor’s 500 index (log-change); the 10-year Treasury bond yield; the 3-month Treasury bill rate. The small version uses just the first five indicators of the 12-variable set, which might be considered primary contemporaneous indicators of economic activity. In the results that are reported in this paper, in the model we include only values of these variables for the current quarter t (the quarter for which GDP growth is being forecast). However, our general.