# 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.

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

• In column H you have the returns, create a new column I with the previous day's return (for example in I4 have the formula =H3). Then do a linear regression with these two columns (H: dependent, I: independent variable). Nov 16 '17 at 23:37
• are you suggesting to do a regression using excel of the returns and lagged returns? and then find the intercept and slope values? Nov 24 '17 at 13:39
• @user290335 Yes Nov 24 '17 at 13:42
• when I do the regression I should only include in the X values the log returns starting from: H4 until the end and to Y values the lagged returns from I4 to the end right? Nov 24 '17 at 13:46
• @user290335 correct Nov 24 '17 at 14:03