Time series Residual

Foal

New Member
#1
The residual concept in regression is clear to me.
But, when looking a time series, I was a bit confused:

"Actually, fitted values are often not true forecasts because any parameters involved in the forecasting method are estimated using all available observations in the time series, including future observations. When the estimate of involves observations after timet, the fitted values are not true forecasts. On the other hand, naïve or seasonal naïve forecasts do not involve any parameters, and so fitted values are true forecasts in such cases."
Quote from Forecasting: principles and practice – Rob J Hyndman, George Athanasopoulos

When we make a time series forecast, we estimate each point in the future, there is no better fit line as in regression. Then why fitted values are not forecast?

Tank you in advance!
 
#2
Because a "forecast" is not supposed to use all the data, only the past data. If you have GDP for years 1980-2017, you are allowed to use only years 1980-2000 to predict the GDP for year 2001. On the other hand, any model attempting to explain the overall dynamics will use the whole sample. And this model will imply some fitted values. In particular, the fitted value for 2001 will use years 2001 - 2017 as well.