Lecture 9 Autocorrelation

ECM1000 Research Methods in
Finance
Lecture 9
Autocorrelation

1

Outline
•
•
•
•

Introduction
Consequences of Autocorrelated Disturbances
Detecting Autocorrelation
Remedy

References:
Gujrati, Ch. 12

Introduction
Imagine that we are fitting the regression equation to a set of economic variables observed through time:

yt     xt1  ........   xtk  ut
Then it is usual to assume that the disturbance ut represents the net effect of everything not accounted for by the systematic part of the regression. Now imagine that, instead of accumulating over time, the effects of these variables will tend to cancel each other in any period. Then their overall effect might have a small constant expected value. The inclusion of the intercept term allows us to assume that E (ut ) 0
; for any nonzero net effect of the subsidiary variables will be absorbed by  .

Introduction
Economic variables evolve over time and they are strongly correlated with each other. If the disturbance term is indeed compounded from such variables, then we should expect that it too will follow a slowly-evolving trend. The assumptions of the classical regression model that disturbance terms are independently and identically distributed random variables are no more tenable. In such cases -

E (ut u s ) 0
We experience Autocorrelation

for

t s

Causes
1.
2.
3.
4.
5.
6.

Inertia
Specification bias – excluded variable
Specification bias – incorrect functional forms
Lags in adjustment to shocks
Cobweb phenomena
Data manipulation

Common Causes
• Inertia
• Miss-specification and/or Wrong functional form
• Example 1, cost function We estimate MC= α + β output + u
• True model, however, is MC = α + β1 output + β2 output2 +v
– Pattern to residuals
• Example 2, current supply depends on previous periods price
– St = β1 + β2Pt-1 + u
• But we estimate St = β1 + β2Pt + v
– The effect is negative serial correlation
• Most economic time-series exhibit trends over time
– That means X3t is most likely