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I am trying to use the discrete Kalman filter for forecasting and I wonder what is commonly considered as the optimal way of determining the measurement noise covariance constants (Q and R) for a given time series? Do you recommend some approaches based on your research/experience?

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I recently blogged about this very topic.

Essentially, there are 3 ways to estimate Q & R.

  1. approximate
    • calculate variate estimate of error in a controlled environment
    • if z doesn't change, calculate variance estimate of z
    • if z does change, calculate variance of regression estimate of z
  2. guess
    • use some constant multiplied by the identity matrix
    • higher the constant, higher the noise
  3. MLE
    • pykalman's em
    • unfortunately, non-convex problem => local optima

Check out the rest of my post here

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