A link to a FRED graph of average Michigan survey forecast over next 12 months and of CPI and CPI core inflation over the past 12. Looks as if survey participants don't believe petroleum prices will continue to decline after a decline and, aside from that, the average forecast looks a lot like lagged CPI inflation (definitely not core). Not ograph but this wasn't true back in 1980-1 when inflation very high and average forecast lower (they actually did OK back then, we've gotten dumber).
See it looks a lot as if athe average Michigan survey forecast is the greater of lagged CPI inflation and lagged CPI core inflation. There is an anomalous very low average forecast right at the recession trough in 2001 and recent forecasts have been higher tha either lagged inflation rate.