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Lecture 9 Autocorrelation

 Essay regarding Lecture 9 Autocorrelation

ECM1000 Research Strategies in

Finance

Lecture 9

Autocorrelation

1

Outline

Advantages

Consequences of Autocorrelated Disturbances

Detecting Autocorrelation

Remedy

Referrals:

Gujrati, Ch. 12

Introduction

Imagine that our company is fitting the regression equation to a set of economic factors observed through time:

yt     xt1 ........   xtk  ut Then it is normal to imagine the interference ut represents the net a result of everything certainly not accounted for by the systematic portion of the regression.

At this point imagine that, instead of accumulating with time, the effects of these variables will certainly tend to end each other in any period. Then simply their total effect might have a small regular expected worth. The add-on of the intercept term allows us to assume that At the (ut ) 0; for almost any non-zero net effect of the subsidiary factors will be assimilated by .

Introduction

Financial variables progress over time and they are strongly

correlated with each other. In the event the disturbance term is indeed exponentially boosted from such variables, after that we should anticipate that it as well will follow a slowly-evolving craze. The presumptions of the time-honored regression model that disruption terms happen to be

independently and identically sent out random variables are no more tenable. In such instances -

Elizabeth (ut u s ) 0

We experience Autocorrelation

for

big t s

Causes

1 .

installment payments on your

3.

four.

5.

6th.

Inertia

Specs bias – excluded varying

Specification prejudice – completely wrong functional forms

Lags in adjustment to shocks

Cobweb phenomena

Data manipulation

Common Causes

• Inertia

• Miss-specification and/or Wrong practical form

• Example one particular, cost function We calculate MC= α + β output & u • True model, however , can be MC = α & β1 result + β2 output2 +v – Design to residuals

• Example 2, current supply is determined by previous intervals price – St sama dengan β1 + β2Pt-1 & u

• But we estimate Street = β1 + β2Pt + versus

– The effect is adverse serial relationship

• The majority of economic time-series exhibit trends over time

– That means X3t is most likely to depend on X3t-1, X3t-2, …etc • Which will lead to apparent relationship between ut and ut-1, ut6,

….

2

Consequences: Biased H. E.

• Recall estimator for β2

Cov ( X, Con )

b2 

Va ( Times )

• The correct formula for the variance if errors are AR is:

 e2

Var (b2 ) 

[1  a couple of 

a couple of

 xt

x back button

x

big t

t you

2

big t

 2

2

x x

x

t

t 2

a couple of

t

... ]

• Basically

• Var(b2)AR = Var(b2) + further more elements

– Further element

• Confident if ρ > 0

• Bad if ρ < 0

• In the event AR can be not made up, then difference of the agent will be underestimated by the sum of the ‘further element'

7

Consequences

In other words, if autocorrelation is present in the error

term •OLS estimators remain neutral

•But, OLS estimators happen to be inefficient since we

can find an alternative impartial estimator with

smaller variance

– Estimator is no longer " Best”, so its " LUE”

•In addition, the conventional errors are estimated

wrongly

– Might not trust testing of significance

8

Effects

Effects on Tests of Hypotheses and Forecasting:

– If there is positive autocorrelation the OLS

estimation leads to underestimation of guidelines

s. elizabeth. and t-values will be prejudiced upwards;

– With positive autocorrelation the OLS requirements will

cause underestimation of the variance of error

terms and Ur 2 will probably be exaggerated;

– Thus F- tests is likewise invalid;

– Forecasts depending on OLS evaluation will be

neutral. But predictions are bad with much larger

variances

Uncovering Autocorrelation

Visual method

There are many ways to look at the commissions:

• period sequence plan can be created

• alternatively we can plot the standardized residuals

against time; standardised residuals are simply the

residuals divided by the standard mistake of the regression.

If the actual and normal plot reveals a design, then the

mistakes may not be randomly.

•� we could also story the error...

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