Facing problem with Math of Harmonic Analysis

[DANZY]

Few days ago I read one old book: Economic Cycles: There Law and Cause By Henry Ludwell Moore (freely available on the internet). Moore in his book used Harmonic Analysis (Fourier Series) to ascertain the dominant cycle in Ohio Valley rainfall data. Moore uses 72 years (1839-1910) of Ohio valley rainfall data to predict the future trend of rainfall in that region. Moore shares rainfall data and formula for calculating coefficients. Then he shares final values after calculation and plots a graph of those values.

Moore writes that his results are based on invention of Joseph Fourier, but the perfection of Fourier's method is possible due to work of Professor Arthur Schuster. After searching about Arthur Schuster I found he is well known for Periodogram Analysis. Then, I started reading about Periodogram Analysis, but because of my lack of knowledge of higher mathematics I am unable to find the right way forward and thus decided to ask for help.

Moore calculated coefficient values for 3 to 36 cycle lengths. After applying the formula I am getting right values for cycles which completely divide 72, such as 3, 4, 6, 8, 9, 12, 18, 24 and 36. For all other cycles, with an exception of 5, I am getting wrong values.

I am attaching the excel sheet with all the relevant data. Formula is calculated in the sheet. I am also attaching the ebook 'Economic Cycles: There Law and Cause By Henry Ludwell Moore'. The rainfall data and periodogram values are given in page 32 and 33 of the book. Chapter 2 of the book (page 6 to 36) deals with calculation process. If someone who is good in math or have an understanding of this method can be kind enough to assist me in this, I would be truly grateful. I don't need to calculate exact values, but even if close values are calculated that's enough.

 

[tomokan]

Few days ago I read one old book: Economic Cycles: There Law and Cause By Henry Ludwell Moore (freely available on the internet). Moore in his book used Harmonic Analysis (Fourier Series) to ascertain the dominant cycle in Ohio Valley rainfall data. Moore uses 72 years (1839-1910) of Ohio valley rainfall data to predict the future trend of rainfall in that region. Moore shares rainfall data and formula for calculating coefficients. Then he shares final values after calculation and plots a graph of those values.

Moore writes that his results are based on invention of Joseph Fourier, but the perfection of Fourier's method is possible due to work of Professor Arthur Schuster. After searching about Arthur Schuster I found he is well known for Periodogram Analysis. Then, I started reading about Periodogram Analysis, but because of my lack of knowledge of higher mathematics I am unable to find the right way forward and thus decided to ask for help.

Moore calculated coefficient values for 3 to 36 cycle lengths. After applying the formula I am getting right values for cycles which completely divide 72, such as 3, 4, 6, 8, 9, 12, 18, 24 and 36. For all other cycles, with an exception of 5, I am getting wrong values.

I am attaching the excel sheet with all the relevant data. Formula is calculated in the sheet. I am also attaching the ebook 'Economic Cycles: There Law and Cause By Henry Ludwell Moore'. The rainfall data and periodogram values are given in page 32 and 33 of the book. Chapter 2 of the book (page 6 to 36) deals with calculation process. If someone who is good in math or have an understanding of this method can be kind enough to assist me in this, I would be truly grateful. I don't need to calculate exact values, but even if close values are calculated that's enough.

Very informative! Thanks!

 

[ashaab]

Few days ago I read one old book: Economic Cycles: There Law and Cause By Henry Ludwell Moore (freely available on the internet). Moore in his book used Harmonic Analysis (Fourier Series) to ascertain the dominant cycle in Ohio Valley rainfall data. Moore uses 72 years (1839-1910) of Ohio valley rainfall data to predict the future trend of rainfall in that region. Moore shares rainfall data and formula for calculating coefficients. Then he shares final values after calculation and plots a graph of those values.

Moore writes that his results are based on invention of Joseph Fourier, but the perfection of Fourier's method is possible due to work of Professor Arthur Schuster. After searching about Arthur Schuster I found he is well known for Periodogram Analysis. Then, I started reading about Periodogram Analysis, but because of my lack of knowledge of higher mathematics I am unable to find the right way forward and thus decided to ask for help.

Moore calculated coefficient values for 3 to 36 cycle lengths. After applying the formula I am getting right values for cycles which completely divide 72, such as 3, 4, 6, 8, 9, 12, 18, 24 and 36. For all other cycles, with an exception of 5, I am getting wrong values.

I am attaching the excel sheet with all the relevant data. Formula is calculated in the sheet. I am also attaching the ebook 'Economic Cycles: There Law and Cause By Henry Ludwell Moore'. The rainfall data and periodogram values are given in page 32 and 33 of the book. Chapter 2 of the book (page 6 to 36) deals with calculation process. If someone who is good in math or have an understanding of this method can be kind enough to assist me in this, I would be truly grateful. I don't need to calculate exact values, but even if close values are calculated that's enough.

I donot find any excel sheet or the relevant data. I have some knowledge in this respect please share the Excel sheet so that we can continue out discussion in this respect.