Smoothed functional canonical correlation analysis of humidity and temperature data

What is it about?

This paper focuses on smoothed functional canonical correlation analysis (SFCCA) to investigate the relationships and changes in large, seasonal and long-term data sets. The aim of this study is to introduce a guideline for SFCCA for functional data and to give some insights on the fine tuning of the methodology for long-term periodical data. The guidelines are applied on temperature and humidity data for 11 years between 2000 and 2010 and the results are interpreted. Seasonal changes or periodical shifts are visually studied by yearly comparisons. The effects of the ‘number of basis functions’ and the ‘selection of smoothing parameter’ on the general variability structure and on correlations between the curves are examined. It is concluded that the number of time points (knots), number of basis functions and the time span of evaluation (monthly, daily, etc.) should all be chosen harmoniously. It is found that changing the smoothing parameter does not have a significant effect on the structure of curves and correlations. The number of basis functions is found to be the main effector on both individual and correlation weight functions.

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Photo by Igor Kasalovic on Unsplash

Photo by Igor Kasalovic on Unsplash

Why is it important?

The main aim of this study is to provide a guideline for smoothed FCCA while dealing with large, seasonal and long-term data sets with an application on humidity and temperature data. There are many studies that use seasonal and meteorological data in order to develop methodology on FDA. However, investigations were mostly carried out on the basis of the whole time span of the data. We also searched for and reported the optimal values for the number of basis functions (K) and smoothing parameters. Another aim of the study is to uncover highly correlated relationships between temperature and humidity by nvestigating individual functions and the correlations between the two curve sets of temperature and humidity and compare effects of land forms and climates on this relationship. We also investigated whetherthere are seasonal changes or periodical shifts in terms of temperature and humidity for 11 years between 2000 and 2010 .

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