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In a time series with OLS regression curve Y-hat (rolling linear regression), and with n=20, what can I say about this transformation? This formula is similar to a differential dY/dt minus an integral of a data series. enter image description here

The first term is the n-th residual of the OLS model. The second term is closely related to the SSE or MSE functions. However, I have summed the raw residuals without squaring so this is basically a term that follows the trend in the residuals.

  • What is the variance of each term? (1)
  • Can I use SSE or MSE to find (1)?
  • Does anybody recognize this kind of data transform? Related literature or topics? (3)

P.S. The "1/4" in the second term is really just 5/n for my formula.

Thanks!

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  • $\begingroup$ In what context did you find this transformation (where did it show up)? Could you maybe provide us with some more information about its relevancy or something else? $\endgroup$ Commented May 16, 2024 at 20:53
  • $\begingroup$ It's related to standard error estimation in rolling regression. This formula is used to analyze momentum in futures, options, and stock market data. $\endgroup$ Commented May 17, 2024 at 13:02

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