# Quant: First differencing

To get this right once and for all. When and why do we use first differencing? Some background that makes me never forget would certainly help.

I think its when we have a random walk or unit root.

A random walk is a AR time series with a unit root. So you first difference the model.

And doing that means?

Instead of regression actual data (e.g., sales), you regress the changes in sales over time. Do not understand how this removes unit root. Not a stat major

ONE MORE - ARCH also uses first differencing

I don’t think first differencing will fix ARCH errors. You would need to use generalized least squares.

ops yea, I got that mixed up. Its Generalized Least Squares.

The unit root is removed because changes in sales have a constant mean, independent of any time shift (they are random or stochastic) whereas the underlying data in the case of sales usually exhibit a trend (not random or stochastic).

To test for the Unit Root you use the Dickey Fuller test right? (X(1) - X(t-1)) = b0 + b1(Xt-1) + e ?

mcpass, a series is integrated of order I(d) if the series has to be differenced d times before it becomes a stationary process. To have the final say: xt ~ I(d). the upper subplot describes a random walk, if you look at the subplot you see that the data is stationary and fluctuates around a constant mean… http://img102.imageshack.us/my.php?image=clipboard01ia3.jpg edit- stationary data is easier to model even tough you lose valuable information.

afjunkie, yes, you use the augmented dickey & fuller test for that…

afjunkie, that formula should be Xt-Xt-1=B0+G1(Xt-1)+et where G1= (B1-1)

Keep in mind that first-differencing only allows you to determine if the model is in fact a random walk. It does nothing to help you actually model it. MargaHills above got it right. If the process is a random walk, changes from one period to the next will have a stationary mean ( zero ), and a finite variance. If we then regress this first-differenced equation on the independent variables, and find that our intercept and slope coefficients do not differ significantly from zero, we know that we have a random walk.

Why can’t CFA just give us a quant question, like the one on the practice exam A random walk is equal to having a unit root and not be covarience stationary?