A law of large numbers and central limit theorem for the logarithm of an autoregressive process with a stationary driving sequence

F.C. Shu

Statistics & Probability Letters, 2009, vol. 79, issue 9, 1141-1145

Abstract: Let be a stationary and ergodic sequence in . Consider the autoregressive process defined by, R0([xi],[eta],[nu])=[eta]0 and Rn([xi],[eta],[nu])=[xi]nRn-1([xi],[eta],[nu])+[eta]n[nu]n[dot operator]...[dot operator][nu]1,n>=1. We give conditions under which exists a.s. and at the same time, . We also generalize a Central Limit Theorem of Szekely for this process.

Date: 2009
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