Why does first differencing correct autocorrelation?

Question

If we have an autocorrelated variable in the multiple regression model, why does taking first difference help?

Answer 1

I don't know the nature of the autocorrelation in your application. However, taking differences does not, in general, mitigate autocorrelation.

Here is an example with a simple Markov chain:

set.seed(618)
m = 1000;  x = numeric(m);  x[1] = 0
for (i in 2:m) 
  {
  if (x[i-1] == 0) x[i] = rbinom(1,1,.9)
  else             x[i] = rbinom(1,1,.2)
  }
table(x)
x
  0   1 
458 542 

x[1:16]
 [1] 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1
diff(x)[1:15]
 [1]  1  0 -1  1 -1  1 -1  1 -1  1 -1  1 -1  1  0

par(mfrow=c(1,3))
 plot(x[1:30], type="b", pch=19)  # first 30 steps
 acf(x)
 acf(diff(x))
par(mfrow=c(1,1))