LO 3.3.2.A

Learning Objective: Describe a random walk model and an autoregressive model.

Review:

• Random walk model is defined by

        where

        𝜇 is the drift of the process

        {𝜀t}  are identically distributed variables with mean zero and variance 𝜎2

        The variance of the random process is Var(Yt) = t∙𝜎2

• Autoregressive model (AR)

Random walk models cannot be used for all financial time series. Interest rates, for instance, are influenced by complicated political factors that make them difficult to describe mathematically. The Autoregressive models can fill this gap.

A general Autoregressive model of order p (AR-p) is defined by

where

        𝜇  is the drift of the process

        𝛼₁ , 𝛼₂ ,...,𝛼ₚ are the parameters of the model

{𝜀t} are identically distributed variables with mean zero and variance 𝜎2