假設Xt 是一個p 維度的自回歸模型，而他們的隨機項則滿足穩定分布的條件。
我們的目的是透過訊息量準則選擇p，不同於傳統方差的方法，我們這邊選擇用絕對值得方法來選取^p，最後我們證明當隨機項滿足他的穩定分布的係數α介於1到2之間的時候，我們的估計值^p會強收斂到真實的p值。

Suppose that Xt is a p-th order autoregressive process whose innovation follows a stable distribution. Our purpose is to choose p via an information criterion. Instead of the conventional least squares estimate, our estimate, ^p, of p is based on the least absolute
deviation. We prove that ^p is strongly consistent when the innovation is stable, with index 1 < α < 2.

Contents
摘要i
Abstract ii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .. . . .1
2 Background Knowledge . .. . . . . . . . . . . . . . . . .. .. . . .2
2.1 Stable distribution . . . .. . . . . . . . . . . . . . . . . . . 2
2.2 LAD estimate . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Theoretical results. . . . . . . . . . . . . . . . . . . . . . . . 4
4 Simulation . . . . . . . . . . . . . . . . . . . . . .. . . .. . . 9
5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . .. . .21

References
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