# What is the difference between Random Walk & Unit root

Is my understanding is correct related to the difference between Random Walk & Unit root?

The image is not clear on my head I’m confused!!! Any assitant

Q1: Random walk is a special case of AR1, where b0=0 & b1=1. Therefore, MRL=0/(1-1)=0 undefine. A stock that follows a random walk has no mean reversion level, so you can’t predict which direction it is likely to trend in the future. Is that right???.

Random walk with a drift: b0=1 If a time series is a random walk wit a drift, the next predication for it’s next value is last value.Is that right???. By definition, all random walks have a unit root. when AR1 model b0=1 we call it Unit root. Therefore, MRL=1/(1-1)=0 undefine.

Example: A stock that follows a random walk with unit root, so the predication for it’s next value is last value???

Q2? The first difference for random walk is Yt=change in Xt

Using first difference make the time series coverance stationary with finite MRL=0/1-0=0 = finite??? What the difference between:

MRL=0/(1-1)=0 undefine MRL=0/1-0=0 = finite

What make them differ???

Q3?

Is the following is right?

Unit root b0=1 it could be random walk when b1=1?? Q4?

Why stock that follows a random walk is defined as having a unit root.

It may be b1=0 not 1???

Let

Xt = b0 + b1Xt−1 + εt

If b1 = 1, the model has a unit root, and the mean-reverting level is undefined.

If b1 = 1 and b0 = 0, the model is a random walk.

If b1 = 1 and b0 ≠ 0, the model is a random walk with drift.

Therefore:

• If the model has a unit root
• It is a random walk if b0 = 0
• It is a random walk with drift if b0 ≠ 0
• If the model is a random walk, it has a unit root
• If the model is a random walk with drift, it has a unit root
2 Likes

Correct.

The first has a denominator of zero, so it is undefined.

The second has a denominator of one, so it is defined, and 0/1 = 0.

A unit root is not defined as b0 = 1; a unit root is defined as b1 = 1.

Because b1 = 1.

Thanks a lot S2000magician

My pleasure.

My master S2000magician

I summarize what I got from U in the following link;

https://www.dropbox.com/sh/0c6ht68g902sghk/Eoz8zgIpW5#/ again thanks a lot.

Again, my pleasure.

In your summary, I’d encourage you to put parentheses around the denominators – 0/(1-1), 1/(1-1), and so on – to make it absolutely clear what you intend.