Introduction
Climate of a place or a wider area (a vineyard, a valley, a continent,
the whole planet) derives froma variety of astronomical or geophysical causes
(table 1) often interacting each other in a, also complex, way giving place,
e.g., to well characterized positive and negative feedbacks.
In table 1 we denoted with an asterisk factors subjected to cycles over
a very wide range of periods (hours to millions years).
As anexample, Sun presents 11yr activity cycles and longer cycles(Suess, Eddy, Hallstatt,
etc.) e Ocean circulation shows cycles like AMOC (Atlantic Meridional
Overturning Circulation) that then plays a role on the surface temperature
of the Atlantic Ocean by forcing typical cycles known as AMO (Atlantic
Multidecadal Oscillation).
The consciousness of the exixtence of climte cycles has a long hystory.
We can quote, e.g., the Saserna, roman treaters (writers) whose work has been lost
but are quoted by Columella, argued the climate of their epoch had become
milder than in the old times, so that olive trees and vineyards can live well where it would
been impossible before.
In the same way the idea of cyclical cycles, that incuded also a deluge
as in the biblic narrative, is widely spread in many cultures (precolombians
peoples, australian blackfellows, ecc.). They mantained in trouble our
progenitors along many millenia.
In the first half of the XIX century Joseph Fourier, during his
studies on heat propagation, realized that analyses waer much more simple if
a function was represented as the sum of simple trigonometric functions with
adequate parameters. Also, the researches by Fourier are near to climatology
because the terrestrial atmosphere is an heat machine whose motions depend
on the need to equilibrate the differences due the unequal subdivision of
heat on the Planet's surface ^{1}.
Again, from the XIX century, due to geomorphological work lead between
1800 and 1900 and summarized by Louis Agassiz the idea of the presence of glacial cycles
takes place, what gives rise to modern climate studies about climate cycles
converging to the theory by Milutin Milankovich about the astronomical
causes of glacial eras proven in the following by Cesare Emiliani (1955) with his studies on ocean floor
cores.
Briefly said, what Fourier, Agassiz, Milankovich and Emiliani give us
has all neede to understand the spectral analisys and its usefulness.
Actual cycle study depends on instrumental data (temperature, precipitation, global solar radiation etc.). We outline that the presence of periodicity in independent series (like speleothemes, tree rings growth, grape harvest date) is an important reinforce to their reality. In applications, it will be important to link period analisys with (also hystorical) documents or narrative (e.g. legends); it follows may be of importance to link the astronomical cycles at periods of 2000 years (Bray or Hallstatt cycles) and 1000 years (Eddy's cycle) (Scafetta et al., 2016) with key periods in the Holocene like:
Astronomical factors weighting on the amount of energy at the planet's surface.

geophysical factors that modulate the effects of astronomical factors

(*) submitted to cycles over a very large range of time scales (days to millions years).
the large variety of periods force someone to select a group of spectral scycles
belonging to, ofen unknown, precise causes.
Her we used time series covering about 5 million years and selected
cycles of some hundreds of thousands years.
Data Analysis
At about the end of August 2019, we have had the availability of a paper
by Kent et al., 2018, where the empirical evidence for the stability of
the 405kiloyear JupiterVenus eccentricity cycle over at hundreds of milions
of year (at least 215 Myr) was presented. We never had notice of such a spectral maximum before
of this paper, so used the De Boer et al.(2014) dataset
We decided to separate deboer2014.txt into 8 datasets of 7000 data each (the last one of 4000 data). In such a way we had something resembling a wavelets ensamble which allowed to derive spectra (MEM spectra: they are at constant step) of different and adjacent time sections, covering 700 kyr (kilo years) each one.
At the same time we computed the LombScargle periodogram (hereafter
Lomb) of the whole dataset, deriving both ~400 Kyr and ~1 Myr spectral maxima
as shown in figure 2
Fig.2: Lomb periodogram, from the
CRAN R suite, of the full deboer2014.txt series. The green lines define here
and in figure 3 the ensemble of secondary maxima between 0.4 and 1 Myr.
Dashed line is the 99% confidence level.
We also continued with the MEM spectrum, computing the two halfdataset (i.e.
26000 data points each) spectra, as shown in figure 3.
Fig.3: MEM spectra of the two
halfdataset sections of deboer2014.txt. The green lines define here
and in figure 2 the ensemble of secondary maxima between 0.4 and 1 Myr.
The comparison between the above spectra shows that the main ~0.4 and ~1 Myr maxima remain at about the same period with a skyrocket variation of the power during the second half section (730/103 or 7X and 230/11 or 21X); also the peak at 0.24 Myr (the leftmost one in figure 2) becomes 7 times higher (50/7) during the more recent two millions years than during the first section. The other visible peaks changed their frequency (period).
Green lines in both figure 2 and 3 define a group of secondary maxima: to be noted the 0.74 Kyr maximum (0.68 in the upper frame of figure 3) clearly visible in the Lomb spectrum of figure 2 and that confirm that the analysis of the whole dataset (figure 2) is strongly dominated by the 2.nd (more recent) section of the dataset because the 0.74 maximum clearly emerges above the little "forest" of maxima.
In order to verify within a better accuracy the variation of frequency along the time sequence, we used the 8 sections defined above to compute the MEM spectrum. The time sequence is listed in Table1.
Sec  Start Kyr  End Kyr  Comments 

1  5300.0  4600.1  7000 values 
2  4600.0  3900.1  
3  3900.0  3200.1  min power 
4  3200.0  2500.1  
5  2500.0  1800.1  
6  1800.0  1100.1  max power 
7  1100.0  400.1  
8  400.0  0.1  4000 values 
A summary of the results is in figure 4
Fig.4: The MEM spectrum of the 8
sequential and adjacent sections defined by color and, in one case, by line
shape. Here only 400 Kyr and nearby maxima have been selected. The bottom
plot is an enlargement in power (yaxis) of the top one.
Analysis of the ~0.41 Kyr spectral maximum
We can derive from figure 4 the suggestion that the power of spectral maxima
evolve along the sections (i.e. with time) and a more precise list of peak's
power confirm, as in figure 5, this hypothesis:
Fig.5: Time evolution of the ~0.4 Myr
spectral maximum power from the 8sections series. The blue line is the fitting parabola of the first 6
data.
The power variation of the 0.4 Kyr peak has nothing to do with casuality
but it seems to follow a rising law (the blue line is the fitting parabola)
through section 6 and then a drop not too much different from the corresponding
rise. So, we can
suppose that, at the end of the period 1.81.1 Myr (section 6), something
happened, so that the power of the most important cycle in the 200700 Kyr
time lapse, begun to drop.
We cannot know what happened before section 1 (i.e. before 5.3 Myr) but
perhaps it could show a cyclic behavior with a 5.7 Myr period (46001100
from table 1).
Fig.6: Time evolution of the ~0.4 Myr
spectral maximum power from the 7sections, 2subsections each one, series.
red lineanddot accounts for the 1.st subsection, blue lineanddot
accounts for the 2.st subsection of each section. dotdashed lines are the
respective parabolic fits.
The characteristic shape of figure 5, relative to the 8 sections, holds
again for the 14 subsections,
with the data of subsections 1 appearing shifted backward by one section.
We cannot explain such a behaviour, only note, as in figure 7, that a
positive shift of 1 section changes notably the comparisons in figure 6
Fig.6: Time evolution of the ~0.4
Myr spectral maximum power from the 7sections, 2subsections each one,
series when the section of subsections 1 becomes "section+1".
Nothing of what has been found in the analysis of the power of the main peak of the actual series appears to be casual. It seems the result of an (unknown) evolution of external or internal forcings, spanning over millions of years.
Milankovic Cycles
The δ^{18}O benthic by De Boer et al. (2014), while seems
very good for 0.41 Myr (and more) spectral peaks, poses the problem that
the 100, 41, 26 Kyr Milankovic cycles (the orbital cycles of eccentricity,
obliquity and precession) cannot be derived from this series as e.g. it
appears in figure 3.
We can suppose the actual spectral maxima are too weak to be identified
in the above plots, so try their "emersion" by a x1000 amplification
but, as it can be seen in figure 7, a daunting result in obtained: no
orbital maximum in the spectra, at all.
Fig.7: Trying to identify the
Milankovic cycles by a x1000 amplification: in the range 97104 Kyr 6 peaks
(out of 8 series) can b be identified, but nothing at all at 40 and, mainly,
at 26 Kyr.
Fig.8: MEM Spectrum of Page800
δ^{18}O benthic 0 to 800 Kyr BP (Ka is used in place of Kyr BP). The bottom plot outlines the periods of
Milankovic cycles. This figure has been already published elsewhere; here it has been
slightly revised. To be noted, as a mirror of figure 7, the absence of the
400 Kyr peak.
The data De Boer et al., 2014 used is the stacked dataset LR04 Benthic by
Lisiecki and Raymo (2005) at variable step, to which a model has been applied
in order to derive a dataset at 100 yr step. So we dowloaded the Lisiecki
& Raymo's series and computed the Lomb and wavelet spectrum. The
following figures 9 and 10 show that the spectra are the same and exclude
some kind of procedural error.
Fig.9: LOMB spectrum of the Lisiecki
& Raymo (2005) dataset LR04 Stack. Bottom frame is a 0200 Kyr enlargement
of the above total. Dotdash green lines are the 95%, white noise,
confidence level
Fig.10: Wavelet spectrum of the LR04
series computed by PAST. Due to the log2 vertical scale, the figure has been
labelled with the corresponding periods in Kyr. The xaxis has been also
labelled in Kyr BP.
The last dataset also confirms that the 400 Kyr peak has low power and this is confirmed in both LOMB an wavelets
initial and derived data, and plots, are available at the support site 
References