Autocorrelation occurs when errors in a time series model are correlated across time periods, violating the assumption of independent errors. This can be caused by inertia in the data, omitted variables, incorrect functional form, or data manipulation. Consequences of ignoring autocorrelation in OLS models include inefficient estimators, biased error variances, and unreliable t-tests, F-tests, and R-squared values. Autocorrelation can be identified through patterns in the error terms and estimated using measures like sample 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.