%0 Journal Article
%T Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter
%A Andrew Bartlett
%A William McCormick
%J Applied Mathematics
%P 2133-2147
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.312A294
%X <span>Consider a first-order autoregressive processes <img width=\"89\" height=\"23\" style=\"width:67px;height:12px;\" alt=\"\" src=\"Edit_dbeb66d2-f808-4eb1-b17d-07191f214c4b.bmp\" /><span></span>, where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint</span><span> </span><i><span>¦È</span></i><span>. We propose estimates for the autocorrelation parameter </span><i><span style=\"font-family:Symbol;\"><span>f</span></span></i><span> and the unknown location parameter</span><span> </span><i><span>¦È</span></i><i><span> </span></i><span>by taking the ratio of two sample values chosen with respect to an extreme value criteria for </span><i><span style=\"font-family:Symbol;\"><span>f</span></span></i><span> and by taking the minimum of <img width=\"77\" height=\"32\" style=\"width:76px;height:18px;\" alt=\"\" src=\"Edit_119f2b31-096d-4233-a0ae-4c508dd922c5.bmp\" /><span></span><span> </span>over the observed series, where <img width=\"26\" height=\"10\" style=\"width:14px;height:16px;\" alt=\"\" src=\"Edit_ede40942-f1ed-424e-9632-3ba6d7ba7f10.bmp\" /><span></span><span> </span>represents our estimate for </span><i><span style=\"font-family:Symbol;\"><span>f</span></span></i><span>. The joint limit distribution of the proposed estimators is derived using point process techniques. A simulation study is provided to examine the small sample size behavior of these estimates.</span>
%K Nonnegative Time Series
%K Autoregressive Processes
%K Extreme Value Estimator
%K Regular Variation
%K Point Processes
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=26075