Asymptotic Distribution of an Estimator of the Boundary Parameter of an Unstable Process

Moments of the Limiting Distribution for the Boundary Case in the First Order Autoregressive Process

“…The case of the AR(1) process with p = 1 was studied widely, see Rao (1978) and Dickey and Fuller (1979). The interest was mostly genera ted by applications in economics.…”

On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)

“…The model (1.1) is a particular case of unstable autoregressive processes AR(p) which have been studied by many authors due to their applications in automatic control, identification and in modeling economic and financial time series (we refer the reader to Anderson [2], Ahtola and Tiao [1], Dickey and Fuller [5], Chan and Wei [4], Greenwood and Shiryaev [8], Greenwood and Wefelmeyer [9], Jeganathan [11,12], Rao [16] for details and further references).…”

On the bias of the least squares estimator for the first order autoregressive process

“…In the stable case, i.e., lal < 1, with Sa(T)= [T/(1-a2)] 1/2, ~ is standard normal (Anderson (1959(Anderson ( , 1971). In the unstable case, i.e., lal --1, with Sa(T) = 2Ta, ~is the distribution of (W 2-1)/(f01W2ds) where {Ws;0<s< 1} is astandard Brownian motion (Rao (1966(Rao ( , 1978). Finally, in the explosive case, i.e., lal > 1, with Sa(T) = lalr(a 2 -1) -1, ~2~is Cauchy (White (1958(White ( , 1959 and Rio (1961Rio ( , 1966).…”