Simulation of a stationary autoregression: A characterization of the normal distribution |
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Institution: | Department of Statistics and Modelling Science, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK;Nanotechnology Institute, Babol Noshirvani University of Technology, Shariati Ave., Babol, 47148-71167, Iran;Universidad Autónoma de Yucatán, Mérida, Yucatán, Mexico |
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Abstract: | Simulating a stationary AR(p), Xt = ∑pi=1αiXt−i + Zt, when the innovations {Zt} are assumed to be i.i.d. is straightforward. Starting the process in the stationary state, however, requires generation of (X1,X2,…,Xp) from the stationary p-dimensional distribution. When Zt is normal this may be achieved by generating Xi as a linear function of X1,X2,…,Xi−1 and an independent normal variate for i = 2,3,…, p. It is shown that the ability to initialize a stationary AR(p) in this way characterizes the normal distribution. |
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