Random Walk and Auto-Regressive Model

Random Walk Hypothesis

Burton Malkiel said a random walk is a process of change where each change is independent of the previous change and totally unforecastable. He referred to Stock Market prices as a random walk. And, he said you should just hold a diversified portfolio. In his book, he mentioned that there is no such thing as efficient markets.

Random Walk: Xt = Xt-1 + Ɛt

Auto-Regressive Model

A statistical model is autoregressive if it predicts future values based on past values. For example, an autoregressive model might seek to predict a stock’s future prices based on its past performance.

Karl Pearson presented this idea. He said the prices of a stock are influenced by its past performance. He also explained the mechanism of a bubble in the stock market. He said it’s as if an elastic is tied to a pole, if you stretch that elastic a lot ( increase in a share price by manifold) it will come back to the pole( Like an elastic).

Xt=100+ρ(Xt-1 -100) +Ɛt

In this, 100 represents the lamp post(Starting Point)

Xt = The position at time ‘t’

Xt-1–100 is how far is he from the lamp post

Here, ρ represents the elasticity that how far can a stock price go.

If ρ=1, it’s as good as if a random walk.