An innovation in a time-series model is the new random input at time , usually denoted , that cannot be predicted from earlier observations
in the model. Innovations are commonly assumed to have zero mean, constant covariance,
and no serial correlation. Stronger models
may assume that the innovations are independent.
Innovations are the one-step-ahead prediction errors generated by the model rather than arbitrary discrepancies between observed and fitted values.
, usually denoted 
, that cannot be predicted from earlier observations
in the model. Innovations are commonly assumed to have zero mean, constant covariance,
and no serial correlation. Stronger models
may assume that the innovations are independent.
