Fisher's Identity

Fisher's identity is useful to use in maximum-likelihood parameter estimation problems. In this post, I give its proof. The main reference is Douc, Moulines, Stoffer; Nonlinear time series theory, methods and applications.

Batch MLE for the GARCH(1,1) model

Introduction

In this post, we derive the batch MLE procedure for the GARCH model in a more principled way than the last GARCH post. The derivation presented here is simple and concise.