ALMOST SURE PROPERTIES OF WEIGHTED VECTORIAL
MARTINGALES TRANSFORMS WITH APPLICATIONS TO PREDICTION
FOR LINEAR REGRESSION MODELS
Abstract: We establish new almost sure properties for powers of weighted martingale
transforms. It allows us to deduce useful asymptotic results for cumulative prediction
and estimation errors associated with linear regression models. We also provide
two examples of applications on the linear and functional autoregressive models.
2000 AMS Mathematics Subject Classification: 62J12, 62H12, 60G25, 60G42.
Key words and phrases: Linear regression models; martingales transforms; least squares
estimators; cumulative prediction and estimation errors.