Premium
Bounds for the least squares extrapolation in non‐linear AR(1) processes
Author(s) -
Andĕl Jir̆í
Publication year - 2001
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/1099-131x(200101)20:1<79::aid-for757>3.0.co;2-y
Subject(s) - extrapolation , mathematics , least squares function approximation , generalized least squares , non linear least squares , linear least squares , white noise , function (biology) , autoregressive model , linear model , statistics , explained sum of squares , estimator , evolutionary biology , biology
It is proved that formula for least squares extrapolation in stationary non‐linear AR(1) process is valid also for non‐stationary non‐linear AR(1) processes. This formula depends on the distribution of the corresponding white noise. If the non‐linear function used in the model is non‐decreasing and concave, upper and lower bounds are derived for least squares extrapolation such that the bounds depend only on the expectation of the white noise. It is shown in an example that the derived bounds in some cases give a good approximation to the least squares extrapolation. Copyright © 2001 John Wiley & Sons, Ltd.