This ppt describes the concept, causes and consequences of autocorrelation.

1. Autocorrelation
The Concept, Causes and Consequences
Shilpa Chaudhary
JDMC

2. Introduction
Autocorrelation occurs in time-series studies
when the errors associated with a given time
period carry over into future time periods.
It can occur in cross section also (Spatial).
The assumption of no auto or serial correlation
in the error term that underlies the CLRM will
be violated.
Autocorrelation implies i≠j0)( jiuuE

3. Patterns of autocorrelation
Topic Nine Serial Correlation
(a)-(d):
Some
pattern, so
AC
(E) No AC
Note: u or e is plotted
against t

4. Positive and negative autocorrelation
Positive AC: Eg
T Et et-1
1 2
2 3 2
3 2 3
5 0 2
6 -2 0
Correlation=0.8 (+ve)
Negative AC: Eg
T Et et-1
1 3
2 2 3
3 0 2
5 -2 0
6 4 -2
correlation=-0.29 (-ve)

5. Causes of Autocorrelation
1. Inertia - Macroeconomics data often exhibit
business cycles.
2. Model Specification Error- eg. Exclusion of a
variable
 True model:
 Estimated model:
 Estimating the second equation implies
Autocorrelation could arise due to incorrect Functional
Form eg. If we fit linear model instead of log-linear
form.
ttttt uXXXY  4433221 
tttt vXXY  33221 
ttt uXv  44

6. Causes of Autocorrelation
3. Cobweb Phenomenon
 In agricultural market, the supply reacts to
price with a lag of one time period because
supply decisions take time to implement. This
is known as the cobweb phenomenon.
 Eg. Farmers’ decision to plant crops is
influenced by last year’s prices.
 Now disturbances may not be random.

7. Causes of Autocorrelation
4. Data Manipulation
• data ‘massaging’ can lead to patterns in error term. eg
by taking a moving average of observations, the
errors will no longer be independent of one another.
• If we use first difference model, the error term
exhibits autocorrelation.
Original model
Model at time period t-1
First difference model
ttt uXY  21 
11211 
 ttt uXY 
ttt vXY  2

8. Consequences of Using OLS Disregarding Autocorrelation
 OLS estimators are still linear and unbiased
 But they are not efficient. They do not have minimum
variance.
 The usual formula to compute the error variance (RSS/d.f) is
a biased estimator of true σ2. In some cases, likely to
underestimate the latter.
 The estimated variances of OLS estimators are biased.
Sometimes the variance/ standard errors are underestimated,
hence inflating t-values.
 Therefore, the usual t and F tests of significance are no
longer reliable and if applied, are likely to give misleading
conclusions about the statistical significance of the estimated
regression coefficients.
 The R-squared so computed is also unreliable.