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Why are residuals usually autocorrelated in time-series data? Could it stem from the autocorrelation of the response variable? Is the reason that in some cases the differencing (i.e., the differences between adjacent values of the response variable) is used?

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    $\begingroup$ Autocorrelation of residuals is a property simultaneously of the data and of the method used to model the data. As such, I would be interested in a more refined statement of your initial assumption: just what kinds of data and what forms of analysis do you have in mind when you assert that residuals are "usually" autocorrelated? $\endgroup$ – whuber Mar 4 '13 at 23:14
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Residuals can be autocorrelated due to a number of factors. Possible causes are:

  1. insufficient ARIMA structure,
  2. omitted lags of one or more of the user-specified causal variables,
  3. omitted deterministic structure such as Pulses, Level Shifts, Seasonal Pulses and or Local Time Trends,
  4. untreated changes in the parameters over time,
  5. untreated changes in the error variance attributable to dependence on the value of the observed series,
    OR due to deterministic change points in time,
    OR due to a true stochastic variance.
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