EXAMPLE 13.33 Forecasting PMI

Consider forecasting August 2014 PMI using an exponential smoothing model with . The PMI series ended on . This means that the forecasting of August 2014 is forecasting period 56:

We need the forecasted value to finish our calculation. However, to calculate , we will need the forecasted value of ! In fact, this pattern continues, and we need to calculate all past forecasts before we can calculate . We calculate the first few forecasts here and leave the remaining calculations for software. Taking to be , the calculations begin as follows:

Software continues our calculations to arrive at a forecast for of 55.248. We use this value to complete our forecast calculation for :