Nadaraya-Watson Estimator [LuxAlgo]

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The following tool smooths the price data using the Nadaraya-Watson estimator, a simple Kernel regression method. We make use of the Gaussian kernel as a weighting function.

Kernel smoothing allows the estimating of underlying trends in the price and has found certain applications in stock prices pattern detection.

Note that results are subject to repainting, this tool is meant for descriptive analysis, see the Usage section.

1. Settings

  • Bandwidth: controls the bandwidth of the Gaussian kernel, with higher values returning smoother results.
  • Src: Input source of the kernel regression.

    2. Usage

    Non-causal smoothing methods have found low support from technical analysts because they tended to repaint, yet they can provide powerful insights such as underlying trends in the price and how far the price deviates from them. They can also make drawing certain patterns easier and can help see underlying structures in the price more clearly.

    Using higher bandwidth values allows estimating longer-term trends in the price.

    Triangular labels highlight points where the direction of the estimator change. This allows for the identification of tops and bottoms in the underlying trend which can be compared to the actual price tops and bottoms.

    Note that multiple labels can appear in real-time, which highlights real-time changes in direction of the estimator. The most recent label on a series of labels is the first ones to appear. This can eventually be useful for the real-time predictive application of the estimator. However, it is not a usage we particularly recommend.

    3. Details

    The Nadaraya-Watson estimator can be described as a series of weighted averages using a specific normalized kernel as a weighting function. For each point of the estimator at time t, the peak of the kernel is located at time t, as such the highest weights are attributed to values neighboring the price located at time t.

    A lower bandwidth value would contribute toward a more important weighting of the price at a precise point and would as such less smooth results. In the case where our bandwidth is so small that the resulting kernel is just an impulse, we would get the raw price back.

    However, when the bandwidth is sufficiently large, prices would be weighted similarly, thus resulting in a result closer to the price mean.

    It can be interesting to note that due to the nature of the estimator and its weighting procedure, real-time results would not deviate drastically for points in the estimator near the center of the calculation window.
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