The first-order autoregressive model AR(1) has the form

Rt=0+1Rt-1+ut

Where Rt denotes the continuously compounded return on an asset at time t and ut is the error term at time t.

In the AR(1) model, how do you test mean aversion and reversion in asset returns using the value of 1?

The following represents R linear regression output from estimating the AR(1) model for S&P 500 index using monthly continuously compounded return data over the 5-year period September 2015 September 2021.

Using the estimated results, how do you interpret the estimate of each coefficient and R-squared?

Using the estimation results, what can you say about the market efficiency?

If the this month's return on the S&P 500 index is 5% (0.05), what will be the next month's expected returns predicted by the AR(1) model?