This analysis establishes eigenvalue bounds in pentadiagonal matrices from the Hodrick-Prescott filter, suggesting implications for macroeconometric applications.
This study establishes lower and upper bounds for the eigenvalues of a symmetric pentadiagonal matrix arising in the Hodrick-Prescott (HP) filter, a widely used method for trend extraction in macroeconometrics. The derivation relies on the Cauchy interlacing theorem. Based on the results, we further derive bounds for the eigenvalues of the smoother matrix of the HP filter. Additionally, we present several related findings that complement our main results.
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Hiroshi Yamada (2025) studied this question.
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