Simulation of a stationary autoregression: A characterization of the normal distribution

✍ Scribed by Eddie McKenzie

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 257 KB
• Volume: 63
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00022-0

✦ Synopsis

Simulating a stationary AR(p), Xt -~'t ~Xt ~ +Z, when the innovations {Z,} are assumed to be i.i.d, is straightforward. Starting the process in the stationary state, however, requires generation of (X1,X~ ..... Xp) from the stationary p-dimensional distribution. When Zt is normal this may be achieved by generating X~ as a linear function of X1,X2 .... ,X~.__ t 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.