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 ?
Question
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 ?
Solution
If you are modeling a financial variable with zero memory (autocorrelation zero at all lags), you would likely choose an MA(q) process over an AR(p) process. This is because an MA process is a model of a time series based on the idea that the error terms (the differences between the observed and predicted values) have an impact on the observed values. This is a reasonable assumption for a financial variable with zero memory, as it suggests that the current value is a function of the current and past shock, but not of past values.
In contrast, an AR(p) process models the value of a time series as a function of past values. This would not be appropriate for a financial variable with zero memory, as it assumes that past values have an impact on the current value.
As for choosing the order q of the MA process, you would typically use a method such as the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) to choose the best order. These methods balance the goodness-of-fit of the model with the complexity of the model (i.e., the number of parameters). You would choose the order that minimizes the AIC or BIC.
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