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My residuals are autocorrelated. Will this be a problem if I want to use the time series to do forecasting?

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  • $\begingroup$ Thank you ! Actually I should have mentioned that I try to do forecasting by multiple regression model and not ARMA model. $\endgroup$ – Dim Dec 25 '15 at 19:04
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If your residuals are autocorrelated then this means that there are systematic movements in your time series which your ARMA model has failed to capture. In that sense, forecasts are a risky affair. I know that parsimonious models are usually preferred by researchers but one has to at least make sure that the residuals are white noise in order to have a valid model, even if this means that the AR or MA order have to be increased by a bit.

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  • $\begingroup$ You seem to ignore the tradeoff between bias and variance. If you develop a model that does very good in sample (for example, judging by residual properties) you may have overfit such that the out-of-sample performance will be poor. An optimal forecasting model will normally not look excellent in sample. Thus I would not strive to achieve white noise residuals in this case. Better look at AIC or BIC, or similar penalized measures. $\endgroup$ – Richard Hardy Dec 25 '15 at 19:54
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    $\begingroup$ @RichardHardy Whiteness of the residuals is hardly a stringent requirement. In fact, it is a bare minimum and does not impose any kind of overfitting most of the time. In any case the answer is not appropriate since the OP has now stated that he is working with a simple regression model, not an ARMA. $\endgroup$ – JohnK Dec 25 '15 at 19:59
  • $\begingroup$ I disagree that it does not lead to overfitting most of the time. Non-overfitting would be a special case which may not be encountered frequently in practice. There are sound theoretical arguments in textbooks and research papers. There are also examples showing that underfit models may perform better in forecasting than actual models (which are estimated, not given) precisely because estimating the true models increases variance a lot but reduces bias only a little. And if your answer is besides the point, why don't you edit it? $\endgroup$ – Richard Hardy Dec 25 '15 at 20:05
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    $\begingroup$ @RichardHardy I adhere to the Box and Jenkins approach, which advises us to validate the model before using it for forecasts. Their approach is known to lead to parsimonious models with high predictive accuracy. If you like a reference, you can check for instance chapter 2 of Applied Econometric Time Series by W.Enders. $\endgroup$ – JohnK Dec 25 '15 at 20:11
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Auto-correlation is not a problem for forecasting, so long as you take it into account. Ideally, you should add an allowance for auto-correlated error terms into your underlying model (whatever that is), and re-fit, to get simultaneous estimates of all your model parameters, including the estimated auto-correlation in error terms. Your forecast method should then incorporate the estimated auto-correlation.

If you have positive auto-correlation then your forecasts will predict higher values following outcomes that were higher than expected, and lower values following outcomes that were lower than expected. Contrarily, if you have negative auto-correlation, then your forecasts will predict lower values following outcomes that were higher than expected, and higher values following outcomes that were lower than expected.

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