What is meant by autocorrelation? Explain one of the remedial measures for the problem of heteroscedasticity

Autocorrelation:

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Autocorrelation, also known as serial correlation, occurs when the errors (residuals) in a time series or regression model are correlated with each other. In other words, the value of the error term in one period is related to the value of the error term in a previous period. Autocorrelation violates the assumption of independence of errors, which is a crucial assumption for classical linear regression.

This phenomenon is often encountered in time series data where observations are collected over time, and there may be patterns or trends that persist.

Remedial Measure for Heteroscedasticity:

Heteroscedasticity refers to the situation where the variance of the errors is not constant across all levels of the independent variable(s). One remedial measure for heteroscedasticity is using weighted least squares (WLS).

In WLS, the model is estimated by giving different weights to different observations based on their variances. Observations with higher variances are given lower weights, and observations with lower variances are given higher weights. This allows the model to be less influenced by observations with higher variances, thus addressing the issue of heteroscedasticity.

The weights are typically determined based on the squared residuals from an initial model. The procedure involves estimating the model, obtaining the residuals, calculating the squared residuals, and then using these squared residuals as weights in the weighted least squares estimation.

By down-weighting the influence of observations with larger variances, WLS provides more efficient and unbiased estimates in the presence of heteroscedasticity.