# Estimate an AR(1) model from returns [closed]

I am studying share price log returns and AR(1) model. I downloaded data from $FTSE100$ and I used the Adj.close column to find the Ln returns:

Now I am trying to understand how can I estimate an AR(1) model using this information.

I understand the AR(1) model. I did a couple of example in excel, but I do not understand how the ln returns are related to that.

AR(1) is given by:

$X_t=\phi+\alpha*X_{t-1}+\epsilon$

I assume that I need to find values for $\phi$ and $\alpha$ to try to fit the AR(1) model but I am confused.

Can anyone help me on this?

Thanks.

## closed as off-topic by LocalVolatility, Helin, Neeraj, lehalle, Bob Jansen♦Dec 3 '17 at 11:48

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• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – LocalVolatility, Helin, Neeraj, lehalle, Bob Jansen
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You're on the right track. The time series you're trying to fit is the one formed by the returns $X_t = \ln (P_{t}/P_{t-1})$, where $P_t$ the tabulated price.
Once you calculate the returns just use a linear fit to estimate $\alpha$, $\phi$ and you're set. Probably you want to check $|\alpha|$ as well, it tells you something about the stationarity of the series