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ma or Ar
When someone talks about MA or AR errors what exactly do they mean? I can understand the maths but I can understand the intuition behind it. I mean if a time series has AR errors then what kind of properties shoulsd that series demonstrate compared to one that has MA error terms?
ma or Ar
I guess that the key place to look for differences in the properties of MA and AR processes is in the autocorrelation function of the process in question. Taking first order ARs and MAs for simplicity, the former will give you an autocorrelation function that is exponentially decaying - the correlation between observations k time-periods apart is equal to the parameter in the AR(1) model to the power k. For an MA(1) process, all autocorrelations aside from the first are zero. What does this mean? It means that the effects of shocks to AR processes are felt over a relatively long period with the impact of the shock declining towards zero while the effects of a shock to an MA(1) processes are felt for one for one period (subsequent to that when the shock actually hits) only. Thus, if you like, the processes have very different "memory" characteristics. More generally, in the kth order case, the AR(k) process will still have an autocorrelation function that decays in some exponential fashion, while an MA(k) will have an autocorrelation function that's zero after lag k. Again, the memory characteristics of the two processes are very different. Hope this helps,richg.
ma or Ar
If you want to visualize the graph,there is a "Gretl" project out there in www.sourceforge.net you could try. It takes an input file of data , and plots the ACF/PACF functions for different lags. May be you could try different combinations of AR(p) and MA(q) process generated in VBA, and see the effect in the ACF/PACF plots.Hope it helps,asd
ma or Ar
Player,I have attached a VBA program I used for trying to understand the AR(p) and MA(q) processes, by simulating different combinations of AR and MA in a DGP , and running the algorithm to see the effect on AR and MA coeffecients and their average/variance by changing length of path and no. of trials.Please correct me if I have done something wrong.Hope it helps.Regards,asd
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Last edited by asd on October 7th, 2003, 10:00 pm, edited 1 time in total.
ma or Ar
i understand what an ar and ma processes are but what i dont understand is what an ar and ma ERROR processes are . For example if y(t) = q*y(t-1) + v(t)this is an ar(1) processbut what do you mean when your errro term is also arHow can an error term be an ar process?egv(t) = q*v(t-1)
ma or Ar
Take a regression equation: y_t = B*x_t + v_t and then introduce dependence into the v_t. If you specify v_t = rho*v_t-1 + e_t then you've got AR(1) errors and if you specify v_t = e_t + theta*e_t-1 then you've got MA(1) errors (where e_t is white noise). Diagnose the existence of these kinds of dependence in your errors by looking at the autocorrelation function of the regression residuals.Am I still missing the point?richg.
ma or Ar
I understand the maths but I cant see why it should be the case.i.e if you ignore the maths why would an error in the past affect an error now (ar processes). Thats what i'm not clear about. IE can you explain without maths why a series would have past ERROR terms ??
ma or Ar
A possible example is that maybe your regression model is mis-specified. Assume that in your regression specification (the y_t =B*x_t + v_t bit of the model) you've omitted to include a real explanatory variable on the RHS, let's call it z_t, which deserves to be there. Moreover, let's assume that this variable has some time-series structure, AR or MA. Then, your regression residuals are likely to look as if they have AR or MA structure because they in some sense contain the omitted variable z_t.richg.