# Panel regression with moving averages

Suppose I have a panel fixed effects regression of the form

$$Y_{it} = + \beta X_{it} + \alpha_i + \alpha_t + u_{it}$$

where Y is the outcome, X is a set of controls, ai and at constants for each panel group and time period, and uit the error term.

The complication is that both Y and X are data presented as rolling averages of 7 time periods within each panel, which introduces serial correlation in the error term (I think). Do you know what approaches can be done to account for this?

• Could you perhaps circumvent the problem by backing up the raw values from the rolling averages and modeling them directly? – Richard Hardy Feb 8 at 9:58
• Not really. Because of the nature of the data it makes sense to model averages rather than single day data points. – Papayapap Feb 8 at 10:10
• Well, you know better but just maybe you could model the raw values and then based on that model make inference on averages. But your question is an interesting one in general, regardless of the particular case of application. – Richard Hardy Feb 8 at 10:38
• Yes, I saw there is some methods using FEGLS with AR(1) process but not sure if this applies to a 7-period autocorrelation? – Papayapap Feb 10 at 9:03
• Then perhaps use an AR(7) process instead? – Richard Hardy Feb 10 at 9:26