Consider a sequence of random variables which obeys a first order autoregressive model with unknown parameter alpha. Under suitable assumptions on the error structure of the model, the limiting distribution of the normalized least squares estimator of alpha is discussed. The choice of the normalizing constant depends on whether alpha is less than one, equals one, or is greater than one in absolute value. In particular, the limiting distribution is normal provided that the absolute value of alpha is less than one, but is a function of Brownian motion whenever the absolute value of alpha equals one. Some general remarks are made whenever the sequence of random variables is a first order moving average process.
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Master of Science (M.S.)
College of Sciences
Mathematical Science; Industrial Mathematics
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic
Wade, Kelly, "Autoregressive Models" (2012). Electronic Theses and Dissertations. 2322.