Moment Convergence of Nonlinear Least Squares Estimates with Applications to Time-series Forecasting

• Activity Number: 141
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
• Sponsor: General Methodology
• Author(s): Ching-Kang Ing*+
• Companies: Institute of Statistical Science, Academia Sinica
• Keywords: Nonlinear least squares estimate ; Nonlinear Stochastic regression model ; Prediction ; Moment convergence

Abstract

The problem of estimating unknown parameters in nonlinear stochastic regression models has attracted a lot of attention during the past three decades. In situations where the design vector is nonrandom, Jennrich (1969) gave the first rigorous proof of the strong consistency and central limit theorem (CLT) of the nonlinear least squares estimate (LSE). Wu (1981) subsequently obtained the same result under much weaker assumptions. Lai (1994) further gave an analog of Wu's strong consistency theorem and CLT for the case of random designs. While a more complete understanding of limiting behaviors of the nonlinear LSE is gained from these previous efforts, recently, the requirements for moment convergence results of the same estimate have surfaced due to dealing with prediction problems in time-series models. However, moment properties of the nonlinear LSE have seldom been discussed in the literature. This motivated our study. This work provides the first moment convergence results of the nonlinear LSE. These results are general and can be applied to prediction problems in various time-series models (e.g., ARMA and ARFIMA).