Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences

✍ Scribed by Sidney Yakowitz; László Györfi; John Kieffer; Gusztáv Morvai

• Book ID: 102602046
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 145 KB
• Volume: 71
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1999.1825

✦ Synopsis

Let [(X i , Y i )] be a stationary ergodic time series with (X, Y) values in the product space R d R. This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance) algorithm for inferring m(x)=E[Y 0 | X 0 =x] under the presumption that m(x) is uniformly Lipschitz continuous. Auto-regression, or forecasting, is an important special case, and as such our work extends the literature of nonparametric, nonlinear forecasting by circumventing customary mixing assumptions. The work is motivated by a time series model in stochastic finance and by perspectives of its contribution to the issues of universal time series estimation.