Choosing Statistical Comparisons for Transformed Financial Series

Summary

The document poses a question about how to assess whether two financial series are similar when one series has been created from the other using an orthogonal transformation. It does not specify what similarity should mean, and asks whether comparing summary measures such as mean, variance, skewness, kurtosis, and correlation would be sufficient to support a reliable conclusion.

No answer or analysis is included, so the document does not recommend a test, define a similarity criterion, or present empirical evidence. Its useful point is the framing: similarity needs a clear definition, and agreement in selected summary statistics alone may not establish that two series behave alike. Any assessment would also depend on the research purpose and data properties, but those issues remain open in the text.

Key ideas

• The document asks how to compare a financial series with a version formed by an orthogonal transformation.
• It raises mean, variance, skewness, kurtosis, and correlation as possible descriptive comparisons.
• It leaves the meaning of similarity undefined and does not provide a recommended statistical test.
• Matching selected summary statistics alone is not presented as proof that two series are similar.

Tags

# Statistical methods to compare two financial series data


# Statistical methods to compare two financial series data












I have two financial series data, `x` and `x'`, where `x'` was formed form `x` using the orthogonal transformation as explained in Orthogonalized Equity Risk Premia and Systematic Risk Decomposition.

I was just wondering what statistical methods exist to see if `x` and `x'` are "similar" to each other. As of now, I do not have precise definition of "similar", but I can think of comparing simple summary statistics such as mean, variance, skewness, kurtosis, and correlation coefficient between `x` and `x'`. What statistical methods exist to safely conclude that `x` and `x'` are similar to each other?

Thank you very much in advance for your help!

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