Autocorrelation- Concept, Causes and Consequences

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
32 3
5 0 2
6-2 0
Correlation=0.8 (+ve)
Negative AC: Eg
T Et et-1
1 3
2 2 3
30 2
5 -2 0
64 -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
Formeg. If we fit linear model instead of log-linear
form.ttttt uXXXY 
4433221  tttt vXXY 
33221  ttt uXv 
44

6. Causes of Autocorrelation
3.CobwebPhenomenon
Inagriculturalmarket,thesupplyreactsto
pricewithalagofonetimeperiodbecause
supplydecisionstaketimetoimplement.This
isknownasthecobwebphenomenon.
Eg.Farmers’decisiontoplantcropsis
influencedbylastyear’sprices.
Nowdisturbancesmaynotberandom.

7. Causes of Autocorrelation
4.DataManipulation
•data‘massaging’canleadtopatternsinerrorterm.eg
bytakingamovingaverageofobservations,the
errorswillnolongerbeindependentofoneanother.
•Ifweusefirstdifferencemodel,theerrorterm
exhibitsautocorrelation.
Originalmodel
Modelattimeperiodt-1
Firstdifferencemodelttt uXY 
21 11211 

ttt uXY  ttt vXY 
2

8. Consequences of Using OLS Disregarding Autocorrelation
OLSestimatorsarestilllinearandunbiased
Buttheyarenotefficient.Theydonothaveminimum
variance.
Theusualformulatocomputetheerrorvariance(RSS/d.f)is
abiasedestimatoroftrueσ2.Insomecases,likelyto
underestimatethelatter.
TheestimatedvariancesofOLSestimatorsarebiased.
Sometimesthevariance/standarderrorsareunderestimated,
henceinflatingt-values.
Therefore,theusualtandFtestsofsignificanceareno
longerreliableandifapplied,arelikelytogivemisleading
conclusionsaboutthestatisticalsignificanceoftheestimated
regressioncoefficients.
TheR-squaredsocomputedisalsounreliable.