Autocorrelation

 

AUTO CORRELATION

Consider a linear regression model:

One of the assumptions of classical linear regression model the disturbance term observations are random and independent.

Now if this assumption is violated and the disturbance term observations in a regression model of different variables are correlated;

It means that there is some sort of linear dependencies. This phenomenon is called auto correlation or sometimes is called serial correlation.

Autocorrelation refers to the degree of linear relationship between the disturbance term values of the same series of observations ordered in time (time series data) or space (cross sectional data).

Examples:

1.      If a market is "up" today, it is more likely to be up tomorrow as well if the autocorrelation of returns is strongly positive.

2.      The preceding month’s expenditure has an influence on the current monthly data on spending by households.

Types of Autocorrelations

1. Positive Autocorrelation: When a positive (or negative) residual tends to follow a positive (or negative) residual or when 

i.                    2. Negative Autocorrelation: When a positive (or negative) residual tends to follow a negative (or positive) residual or when 

Mean, Variance and Covariance of AR (1) Scheme

The complete form of AR (1) scheme as under:

Positive first-order correlated data are represented as points in a smooth snake-like curve. If the points are connected, they produce a zigzag pattern with negative first-order correlation.

• Read More: Consequence and sources of autocorrelation
• Read More: Detection of autocorrelation
• Read More: Stochastic Regression