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I am working on a forecasting model for the stock price using nonlinear autoregressive network with exogenous inputs (NARX) with MATLAB software. I have achieved good performance and good results in the neural network model. For denoising, the variables (time series data) I have used SMA (simple moving average) for both input and target variables. Am I allowed to use the moving average for smoothing the output variable? Is it a big problem or challenge for interpreting my findings when I have used the data smoothing technique for my target (output) variable? Is it possible to interpret my result?
My skepticism is more about the mathematical and computational aspect of the theorem. Could I have reached unrealistic and high-error results due to output manipulation?

Richard Hardy
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Armin Saatian
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    Please copy-edit your question to use complete sentences, so that it's easier to understand your intention and give a helpful answer. – Arya McCarthy Jun 03 '22 at 22:18
  • Thank you for editing it—it helps! Now, thinking about your business case, what would it mean if you were able to predict this manipulated variable well? How would that help you to make decisions about the actual problem (e.g. buy/don't buy)? – Arya McCarthy Jun 03 '22 at 22:58
  • My skepticism is more about the mathematical and computational aspects of the theorem. Could I have come up with unrealistic, high-error results due to output manipulation? – Armin Saatian Jun 03 '22 at 23:06

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The original target variable (a stock price) is most likely unpredictable as it is roughly a random walk (RW) – unless you have some weird stock, that is. By using moving-average smoothing on it, you are introducing predictability. The predictability is entirely an artefact of smoothing.* Thus, if you find that you are able to predict your smoothed target variable, you should not conclude that you are able to predict the underlying stock price. It is also not obvious for me why you would be interested in predicting a smoothed variable rather than the actual one.

*You can check that by simulating a random walk and then smoothing it. Look at the autocorrelation function (ACF) of the increments of the original RW and the smoothed RW. You will see the former shows no predictability while the latter shows some (perhaps even considerable) predictability, depending on exactly what kind of moving average you have used for smoothing.

Richard Hardy
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