Autocorrelation's Sources & Consequences

•  Read: Detection of Autocorrelation

Auto correlation's Sources 

1.      I.         Interconnected Economic Variables

Econometric models are based on economic variables; sometimes, many economic variables are interconnected, and this connection introduces auto correlation.

e.g., GNP and employment are moving in the same direction, on the other hand, GNP and un employment moves in the opposite direction.

2.      Exclusion of predictor variable(s)

When predictor variables are excluded from the model, auto correlation is introduced to the system.

Consider the following corrected regression model:

3.      Cobweb Phenomenon

The supply of various agricultural goods shows the so-called cobweb phenomenon. Many agricultural goods' supply levels in period t are influenced by their prices in period (t - 1) prior. This is due to the fact that the price of the product in the period before has an impact on the decision to grow a crop in period t.

As a result, the given equation is defined as:

According to this supply model, farmers will decide to produce more in the period t if the price in the period (t - 1) is higher. Price in period t will be lower than price in period t-1 as a result of greater supply in period t. As a result, the farmer will produce less in period (t + 1) due to the reduced price in period t.

4.      Lagged Relationship

The model includes auto correlation since the lagged values of the dependent variable are included as an independent variable.

For instance, in order to evaluate how taste and habits affect consumption in period t, period (t-1) consumption Ct-1 is used as an explanatory variable at time t.

The source of the consumption model is:

Ct = α + β1 Yt + β2 Ct-1 + ut

$$

Yt : income in period t.

The impact of habits and preferences on current consumption will be reflected in the error term as a result of the inclusion of the variable  Ct-1 in the model mentioned above, and introduce auto correlation.

5.      Manipulation of Data

The data manipulation introduces auto correlation in the system.

Consider we have a time series regression model at time t.

$$

Yt = β0 + β1 Xt + εt

The model will hold at time (t -1).

Yt-1 = β0 + β1 Xt-1 + εt-1

Yt - Yt-1 =  β1 (Xt - Xt-1) + εt - εt-1

ΔYt  = β1 ΔXt + νt

This equation is known as the first difference and dynamic regression model. The previous equation is known as the level form.The error term in the first equation is not auto correlated but, in the difference, form model the error term will be correlated.

Consequences of Auto correlation

 

Consider the SLRM

1.                    The OLS estimates are unbiased estimate of parameter in the presence of auto correlation.

2.                    If the disturbance term is are auto correlated then the variance of OLS estimator will be underestimating the true variance.

The OLS estimator is given by:

If there is positive auto correlation, the variance of OLS estimator will be under estimated

3.                    The OLS method provides underestimate of the true variance. The t test and F test provide a misleading result.

4.                  In the presence of auto-correlation, the prediction based on O L S method will be less efficient than the prediction based on other methods.