Input-Output time series model

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For an input and output model, I heard two techniques to model it.

1. If differencing needed, both output and input series need to be differenced first.

2. With input and output represented in the model, the ARIMA model was used for the residual part ( differencing for the residuals if needed).

The second approach more sounds like the time series regression with correlated errors, isn't it?

In R, in the function of "arima", if arima(xreg = X), the input is presented here, which approach the "arima" function used to model the input and output model??

Also which function or package in R can be used to model the distributed lag models or transfer function by examining the cross-correlation and prewhitening the input series??

Thank you very much.

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关键词：Time Series Series output model Input time Series model