Reply on Comment on "High resolution coherence analysis between planetary and climate oscillations" by S. Holm

TL;DR

This paper defends the validity of a coherence analysis method against claims of irreproducibility, clarifying methodological differences and providing data and code for accurate replication of results.

Contribution

It clarifies the correct application of MSC-CCA, distinguishes it from other methods, and provides resources to ensure reproducibility of the original analysis.

Findings

MSC-CCA is stable and reliable under specific conditions.

Holm used a different algorithm, leading to irreproducibility.

The original results are confirmed at 95% significance.

Abstract

Holm (ASR, 2018) claims that Scafetta (ASR 57, 2121-2135, 2016) is "irreproducible" because I would have left "undocumented" the values of two parameters (a reduced-rank index p and a regularization term) that he claimed to be requested in the Magnitude Squared Coherence Canonical Correlation Analysis (MSC-CCA). Yet, my analysis did not require such two parameters. In fact: 1) using the MSC-CCA reduced-rank option neither changes the result nor was needed since Scafetta (2016) statistically evaluated the significance of the coherence spectral peaks; 2) the analysis algorithm neither contains nor needed the regularization term. Herein, I show that Holm could not replicate Scafetta (2016) because he used different analysis algorithms. In fact, although Holm claimed to be using MSC-CCA, for his figures 2-4 he used a MatLab code labeled "gcs_cca_1D.m" (see paragraph 2 of his Section 3), which Holm also modified, that implements a different methodology known as the Generalized Coherence Spectrum using the Canonical Correlation Analysis (GCS-CCA). This code is herein demonstrated to be unreliable under specific statistical circumstances such as those required to replicate Scafetta (2016). On the contrary, the MSC-CCA method is stable and reliable. Moreover, Holm could not replicate my result also in his figure 5 because there he used the basic Welch MSC algorithm by erroneously equating it to MSC-CCA. Herein I clarify step-by-step how to proceed with the correct analysis, and I fully confirm the 95% significance of my results. I add data and codes to easily replicate my results.