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 in context of time series is a kind of model or equation to represent a time series where the current value of the time series depends on the value from the previous steps (could be as many steps as required by the model)

An example for the same could be given as:
yt = ayt-1 + b

In the above equaiton, we can see that the current value yt depends on just the previous step value: yt-1

2) Autocorrelation in case of regression or OLS method happen when the residuals in the data are not independent of each other ( which is one of the assumption required for the OLD model ). This can happen in a time series regression like a stock price where of course the stock price on a particular day would depende on the historical stock prices.