 # Moving average time series models

I’m at a bit of a loss as to the status of MA models in the time-series reading. It isn’t explicitly mentioned in any of the LOS but does have several pages dedicated to it in the CFA readings and is included in the end-of-chapter summary. How the the Schweser notes cover it? Secondly, I’m rather confused by the model as it’s presented (pages 387-388 of book 1). I understand the concept of a q period-moving average but if I’d been asked to suggest a model I’d have written: x[t] = b0 + (1/q)*x[t-1] + … (1/q)*x[t-q] + error[t] instead the formula suggested is based on the previous error terms: x[t] = b0 + z[t-1]*error[t-1] + z[t-2]*error[t-2]+ … + z[t-q]*error[t-q] + error[t] Can anyone explain why this is? The one example they present for an MA model is the monthly returns on the S&P500. By showing that none of the autoregressions for any period >1 lags are significantly different from 0 they conclude that an AR(x) model can’t be used for x >=1. For the same reason, it can’t be an MA(x) model for x >=1. So they go on to conclude that an MA(0) model is appropriate where x[t] = b0 + error[t]. Isn’t this basically what an AR(0) model would be? What’s the point in bringing up MA() models if the only example you show is 0th-order?

Please excuse the bump but … any ideas?

riot Wrote: ------------------------------------------------------- > I’m at a bit of a loss as to the status of MA > models in the time-series reading. It isn’t > explicitly mentioned in any of the LOS but does > have several pages dedicated to it in the CFA > readings and is included in the end-of-chapter > summary. How the the Schweser notes cover it? > > Secondly, I’m rather confused by the model as it’s > presented (pages 387-388 of book 1). I understand > the concept of a q period-moving average but if > I’d been asked to suggest a model I’d have > written: > > x = b0 + (1/q)*x + … (1/q)*x + error > This is an AR model (or at least before the copy it was). > instead the formula suggested is based on the > previous error terms: > > x = b0 + z*error + z*error+ … + z*error + error > > Can anyone explain why this is? > This is an MA model. They are just different animals. > The one example they present for an MA model is > the monthly returns on the S&P500. By showing that > none of the autoregressions for any period >1 lags > are significantly different from 0 they conclude > that an AR(x) model can’t be used for x >=1. For > the same reason, it can’t be an MA(x) model for x > >=1. So they go on to conclude that an MA(0) model > is appropriate where x = b0 + error. Isn’t this > basically what an AR(0) model would be? An AR(0) model is the same as an MA(0) model is the same as having a normal distribution with mean b0 (as long as errors are normal). >What’s the > point in bringing up MA() models if the only > example you show is 0th-order? No clue.