Consider the time series model yt = βyt-1 + g(yt–2,…,yt–p) for t ≥ p + 1, Here β is an unknown parameter to be estimated, g(·) is an unknown function in Rp–1, etare i.i.d. random errors with Ee1= 0 and Ee12<∞, and et are independent of ys for all s = 1,2,…, p and t ≥ p + 1. Based on a kernel estimate ğτ(·) of g(·) and the model yt = βyt–1+ ğτ(yt–2,…, yt–p)+e1we investigate the asymptotic normality of the least squares estimate β̂τof β and an estimate σ̂τ2 of σ2, and obtain the law of the iterated logarithm for β̂τ and σ̂τ2.
- Asymptotic property
- Kernel estimation
- Partly Linear Autoregressive model