Question

1: Explain the term ‘autoregression’ in a time series regression context.

2. Explain the term ‘autocorrelation’ and the problems it creates when using OLS regression in time series data.

Answer 1

1) Autoregression- Autoregression is a time series model that uses observations from previous time steps as input to a regression equation to predict the value at the next time step.

It is a very simple idea that can result in accurate forecasts on a range of time series problems. Model can be expressed as:

X(t) = b0 + b1*X(t-1) + b2*X(t-2)

2) Autocorrelation- One common way for the "independence" condition in a multiple linear regression model to fail is when the sample data have been collected over time and the regression model fails to effectively capture any time trends. In such a circumstance, the random errors in the model are often positively correlated over time, so that each random error is more likely to be similar to the previous random error that it would be if the random errors were independent of one another. This phenomenon is known as autocorrelation (or serial correlation) and can sometimes be detected by plotting the model residuals versus time.

Problems- In this regression model, the response variable in the previous time period has become the predictor and the errors have our usual assumptions(errors are independentally and identically distributed) about errors in a simple linear regression model. Therefore, OLS estimators obtained in presence of autocorrelation, are not est linear unbiased estimators.Their variances become high and these are no more efficient.