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I am building a factor model to estimate future equity returns. I'd like to include an autoregressive residual term in this model. I'd like to have yesterday's error (the difference between yesterday's predicted return and actual return) be included in the regression as an independent variable. What type of autoregressive model is this called? I've searched through various time series econometrics texts and have not found this particular model described.

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This type of model is called an ARIMAX or ARX. The "X" stands for exogenous inputs or explanatory inputs.

Here is a good reference:

https://robjhyndman.com/hyndsight/arimax/

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  • $\begingroup$ As the other answer said, you need an MA(1) as the error term in the model, not as the model itself. So, for example: $Y_t = factor model + \epsilon_{t} - \alpha *\epsilon_{t-1}$. See Harvey's latest text for good discussions of these types of models. $\endgroup$ – mark leeds Sep 10 '18 at 13:46
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This is a MA(1) model. if you keep the lagged time-series observation as well as the lagged residual, it would be an ARMA(1, 1) model. Basically, p lagged observations and q lagged residuals will form ARMA(p, q) model.

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