# Week4 ![](https://i.imgur.com/SILwmCo.png) ![](https://i.imgur.com/Kx4wHKw.png) ![](https://i.imgur.com/vQ9PBxp.png) ![](https://i.imgur.com/u1oBcCO.png) ![](https://i.imgur.com/r3E8ez1.png) Random Walk很像AR Q:所以AR一樣是不平穩的嗎?! ------以下模擬-------phi 給0.4 ![](https://i.imgur.com/W3mYMYW.png) **Lag 2-3後就很平穩!!!** ------以下模擬-------phi 但phi 給1 ![](https://i.imgur.com/D67sfk1.png) **變異數無快速下降** ------以下模擬-------AR(2) ![](https://i.imgur.com/BMLUvvf.png) **有收斂** ##### 結論 |phi|<1 才穩! ![](https://i.imgur.com/UBB3v0y.png) 第二段 ![](https://i.imgur.com/BE5kYjy.png) ![](https://i.imgur.com/yUKsiaf.png) 證明 ![](https://i.imgur.com/GpTAfqq.jpg) 證明平均數 ![](https://i.imgur.com/ZZauWgd.png) 證明變異數 ![](https://i.imgur.com/x16GZ48.png) Autocovariance ![](https://i.imgur.com/ssCjZI4.png) Autocorrelation ![](https://i.imgur.com/Pii06kU.png) AR(1)證明 ![](https://i.imgur.com/T6qVKsS.png) ![](https://i.imgur.com/4vvZ85g.png) 結論 ![](https://i.imgur.com/C4BguYB.png) Yule-Walker-Equations https://d3c33hcgiwev3.cloudfront.net/_abd6986bc2f9f05be40002e2ed403dec_Yule-Walker-Equations-2.pdf?Expires=1585785600&Signature=V5SjnAXzSVUJbwy6Uv7hZmaVmoZ1oAAuPixdq8rtb90S2XkXTVxXXdoGM8MHz9aEd1cDMObhsl57t4iMgT2apJ8dhF9xJNKoq53ks31kdxWMA3aM0ZQH6sXRH28u1-rcKXhXJCDhV4PSHj-7rLt2PgWpSj7ukt1pGGxUUB2wijU_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A