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I'm trying to make a multivariate time series forecast using endogenous variables. My features show a lot of spikes (noise), and as I was researching some steps to handle it, I found moving average smoothing to be an option.

But I have a question. If we use MA to smooth out the noise and build a time series model, then its forecast will also be a smoothed out result (without noise and spikes), right? But in ideal conditions, I would like too see some uncertainties in the forecast in order to be conservative in my results. Can someone help me understand what is the right approach to this?

Richard Hardy
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1 Answers1

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Any forecasting method (actually: any statistical model) will try to separate forecastable signal from unforecastable noise, and then only forecast the signal, because the noise is by definition unforecastable. Thus, spikes should in principle not be a problem that needs to be addressed specifically. There is a reason why standard forecasting pipelines usually do not include a smoothing step by default: Resources/books for project on forecasting models

One exception are spikes that your model believes could be signal. For instance, if you have a short history (so your seasonal signal is hard to detect), then your model might erroneously believe that a spike last summer is part of a seasonal pattern. Which, after all, it might well be. So it is often useful to include domain knowledge, or model entire groups of time series together, e.g., by modeling seasonality on an aggregate level.

But in ideal conditions, I would like too see some uncertainties in the forecast in order to be conservative in my results.

See above: you want to forecast the signal, not the noise. And yes, that may well mean that the best forecast is a flat line, even if - perhaps especially if - your history is noisy. Uncertainty in the forecast should be captured through quantile forecasts or full predictive densities.

Stephan Kolassa
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