Predicting Smoothed Returns and the Limits of Added Autocorrelation

Summary

The document considers whether forecasting smoothed returns is appropriate when raw financial returns have a low signal-to-noise ratio. It describes applying an exponentially weighted moving average to prices before calculating returns, or using returns over a longer rolling horizon. Both transformations can create autocorrelation that may make a simple autoregressive model appear more capable of predicting the resulting series.

The central caveat is that smoothed or overlapping-horizon returns are not the same target as raw returns and may even point in the opposite direction. Such forecasts can be relevant when the goal is to estimate trends, but their usefulness depends on matching the prediction target to the intended decision. The text raises this modeling concern but supplies no empirical results or answer establishing whether the approach works. Any assessment would need to account for the transformed target and test its relevance to actual trading outcomes.

Key ideas

• Smoothing prices before calculating returns can increase autocorrelation in the transformed series.
• Longer rolling return horizons can also create autocorrelation relative to daily returns.
• A model predicting smoothed returns is forecasting a different quantity from raw returns.
• The transformed target may suit trend estimation, but its relevance to trading must be evaluated separately.

Tags

# Predicting smoothed returns


# Predicting smoothed returns












Due to the extremly low ratio of signal to noise in financial data, predicting raw returns is very difficult.

If we smooth out the price time series, say by an EWMA, and then calculate returns on this smoothed timeseries, we can introduce higher autocorrelations. Then predicting these smoothed returns is a lot easier, even for a simple AR(p) model. Similarly, taking a return over a longer period (say rolling 5 days instead of 1 day) also introduces some autocorrelation not seen in 1 day returns.

Is there anything fundamentally wrong in predicting smoothed returns? Of course, the smoothed returns will never be the same as the raw returns, and many times will not even have the same sign. But if you are building a model to predict trends, is there an issue with using smoothed returns?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.