What is the main difference between an AR model and an MA model?Answer choicesSelect only one optionREVISITAn MA model uses past observations to predict the current observation, while an AR model uses past errors.An AR model does not use past observations or past errors to predict the current observation.An AR model uses past observations to predict the current observation, while an MA model uses past errors.An MA model does not use past observations or past errors to predict the current observation.

If you were to model a financial variable a lot of memory (autocorrelation never zero for any lags), as a time series, how would you choose between an AR(p) and MA(q) process? And which p or q ?

If you were to model a financial variable zero memory (autocorrelation zero at all lags), as a time series, how would you choose between an AR(p) and MA(q) process? And which p or q ?

AR(1) is equivalent to MA(1) when the autoregressive parameter is equal to 1.Group of answer choicesTrueFalse

Consider two time series, {𝑥𝑡}𝑡=1𝑇 and {𝑦𝑡}𝑡=1𝑇, one generated using AR(1) and the other using MA(1), as follows:𝑥𝑡=𝛼+𝛽𝑥𝑡−1+𝜀𝑡, and𝑦𝑡=𝜇+𝜀𝑡+𝜃𝜀𝑡−1.Suppose 𝛽=𝜃=0.5.Based on the provided information, we can claim that:Group of answer choicesNone of the presented answers are correct.The first order autocorrelation of the series following the presented AR model is larger than the first order autocorreation of the series following the presented MA model.The autocorrelation functions of the two models are identical for lags greater than one.The second order autocorrelation of the series following the presented AR model is equal to zeroThe two step-ahead forecast of the series following the presented AR model is equal to the unconditional mean of the series.

A time series modeled using an AR model is assumed to be generated as a linear function of its past values, plus:business insightsa random noise/errora target mean/median