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.
