# AR model on SMA(k)

If I were to regress Yt+1 on the simple average of Yt, Yt-1, ..., Yt-k, would I have results similar to a AR(k) model?

More specifically, is there any literature on the characteristics of this breed of models (e.g. momentum in finance), and how do they compare to the AR(k)/MA(k) counterpart?

• I don't think so as "the k simple averages" is an assumption about the implicit memory structure and as such would be quite similar to each other. – IrishStat Jul 30 at 10:54
• What does "SMA" mean to you? Also, $Y_t$ to $Y_{t-k}$ contains $k+1$ entries - do you really wish to compare that to an $AR(k)$ rather than an $AR(k+1)$ model? – Christoph Hanck Jul 31 at 14:16
• @christoph-hanck SMA is the simple moving average. And yeah, you're right, I should be comparing with an $AR(k+1)$ model. My question is motivated from noticing a lot of smoothing in finance⁠: e.g. using a rolling moving average and/or normalization of some variable as a signal⁠. I was wondering if there is any literature on a time series regression on such smoothed variables, or how should I test the significance of these variables (other than running a backtest). – matt Jul 31 at 15:52
• What you're suggesting is simply an AR model where the coefficients are restricted to be the same for every lag. – Chris Haug Aug 1 at 14:20