Quant: First differencing

CFA Level II
#1

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.

#2

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

#3

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

#4

And doing that means?

#5

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

#6

ONE MORE - ARCH also uses first differencing

#7

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

#8

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

#9

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).

#10

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

#11

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.

#12

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

#13

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

#14

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.

#15

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