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Will AR(1) model exactly equals to MA(1) model? since both models use the previous one value for forecasting

Richard Hardy
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haozheng li
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  • Neural networks and regression can use exactly the same $X$ variables and will arrive at different predicitons for $y$. Your question is textbook material on an introductory level. To answer it, you can also look at the formulas defining the models and think if they can ever generate the same behavior. – Richard Hardy Feb 27 '21 at 10:17
  • @RichardHardy but that is only true if you do stochastic forward passes, isn’t it? – Carol Eisen Feb 27 '21 at 12:09
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    @CarolEisen, what are stochastic forward passes? – Richard Hardy Feb 27 '21 at 18:09
  • @RichardHardy a non-deterministic forward pass. For example, when using dropout or Bayes by Backprop, where weights are described by variational distributions instead of point estimates and each forward pass requires sampling from this distribution. – Carol Eisen Feb 27 '21 at 19:36
  • If I am not mistaken an AR(1) model is equivalent to an MA(infinity) and vice versa. So MA(1) != AR(1) (tbh my time series knowledge is a bit rusty but if u start googling this you should find an answer) – Carol Eisen Feb 27 '21 at 19:40
  • @CarolEisen, sorry, I do not see how this is relevant to the question. What I meant is the difference between regression and a neural network, not between multiple fits of a neural network if that is what you meant. But indeed, AR(1) $\neq$ MA(1), and this is textbook material, so the OP would benefit from reading it up first and returning with a more concrete question if the textbook explanation is unclear. – Richard Hardy Feb 27 '21 at 19:47

1 Answers1

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Welcome here!

AR(1) and MA(1) use different input values and will not give the same results.

AR(1) models $y_t = a_1 \cdot y_{t-1} + \epsilon_t$ indeed use a lagged variable of the outcome. This model can be estimated via OLS (biased but consistent) or maximum likelihood among others because the predictors are directly observed.

MA(1) models $y_t = \epsilon_t + \beta_1 \cdot \epsilon_{t-1}$ use unobserved error terms as input, not observed lagged variables. This model can therefore not be estimated via OLS. The estimation procedure is more complicated (recursively computed) as explained here.

Arne Jonas Warnke
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