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Author

*The author of this computation has been verified*

R Software Module

rwasp_spectrum.wasp

Title produced by software

Spectral Analysis

Date of computation

Tue, 20 Dec 2016 21:52:54 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/20/t1482267220x2fbcloj48w4fj4.htm/, Retrieved Sat, 27 Apr 2024 18:09:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301806, Retrieved Sat, 27 Apr 2024 18:09:17 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Spectral Analysis] [cummulatief3] [2016-12-20 20:52:54] [2d1dd91c3b5ba64567b1d6b2c9fe9017] [Current]

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Dataseries X:

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Histogram

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301806&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301806&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301806&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	12
Degree of non-seasonal differencing (d)	2
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0083 (120)	2.05274281983111e+86
0.0167 (60)	4.7459238218753e+86
0.025 (40)	1.78527871103957e+85
0.0333 (30)	1.42444387526476e+86
0.0417 (24)	9.24723436280015e+86
0.05 (20)	1.08336026112975e+87
0.0583 (17.1429)	9.4144780332323e+86
0.0667 (15)	3.07696481312707e+87
0.075 (13.3333)	7.51278446901656e+86
0.0833 (12)	1.16670093401346e+87
0.0917 (10.9091)	4.01722597331179e+87
0.1 (10)	1.39389629802737e+87
0.1083 (9.2308)	2.37340819728174e+87
0.1167 (8.5714)	4.61677475779849e+87
0.125 (8)	7.12696780704853e+87
0.1333 (7.5)	7.07305273243939e+87
0.1417 (7.0588)	3.19762880820776e+87
0.15 (6.6667)	2.18830116883184e+87
0.1583 (6.3158)	1.44426862777247e+87
0.1667 (6)	1.21306309177086e+87
0.175 (5.7143)	1.35827046420271e+87
0.1833 (5.4545)	4.52446427551716e+87
0.1917 (5.2174)	9.4367353962757e+87
0.2 (5)	9.26974481824026e+87
0.2083 (4.8)	3.08868056339063e+87
0.2167 (4.6154)	2.74506717109612e+86
0.225 (4.4444)	3.54651143187359e+86
0.2333 (4.2857)	2.08926069503838e+87
0.2417 (4.1379)	2.64108980140375e+87
0.25 (4)	4.39857399520591e+87
0.2583 (3.871)	7.46339997936155e+87
0.2667 (3.75)	7.47172279209331e+87
0.275 (3.6364)	4.52436123714543e+87
0.2833 (3.5294)	1.14828102881739e+86
0.2917 (3.4286)	1.82147694109642e+86
0.3 (3.3333)	5.06835351213419e+87
0.3083 (3.2432)	1.35329928766425e+88
0.3167 (3.1579)	1.98333213026721e+88
0.325 (3.0769)	4.44925812950219e+88
0.3333 (3)	2.34987357161607e+88
0.3417 (2.9268)	2.39175401797051e+88
0.35 (2.8571)	2.68305268190224e+88
0.3583 (2.7907)	9.50441776702161e+87
0.3667 (2.7273)	1.82652891021259e+88
0.375 (2.6667)	6.13001305290465e+87
0.3833 (2.6087)	1.16881260566606e+88
0.3917 (2.5532)	9.21084252020378e+87
0.4 (2.5)	2.74784940305526e+87
0.4083 (2.449)	2.97682990367597e+87
0.4167 (2.4)	1.55363353805455e+88
0.425 (2.3529)	7.03345502618645e+87
0.4333 (2.3077)	1.78640270075151e+88
0.4417 (2.2642)	2.88388511444933e+87
0.45 (2.2222)	5.63475431016872e+86
0.4583 (2.1818)	4.94739518017185e+87
0.4667 (2.1429)	3.13052112591529e+87
0.475 (2.1053)	6.93360287175015e+87
0.4833 (2.069)	6.87062670803971e+87
0.4917 (2.0339)	2.95974261891254e+88
0.5 (2)	5.69679428236446e+87

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 12 \tabularnewline
Degree of non-seasonal differencing (d) & 2 \tabularnewline
Degree of seasonal differencing (D) & 0 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0083 (120) & 2.05274281983111e+86 \tabularnewline
0.0167 (60) & 4.7459238218753e+86 \tabularnewline
0.025 (40) & 1.78527871103957e+85 \tabularnewline
0.0333 (30) & 1.42444387526476e+86 \tabularnewline
0.0417 (24) & 9.24723436280015e+86 \tabularnewline
0.05 (20) & 1.08336026112975e+87 \tabularnewline
0.0583 (17.1429) & 9.4144780332323e+86 \tabularnewline
0.0667 (15) & 3.07696481312707e+87 \tabularnewline
0.075 (13.3333) & 7.51278446901656e+86 \tabularnewline
0.0833 (12) & 1.16670093401346e+87 \tabularnewline
0.0917 (10.9091) & 4.01722597331179e+87 \tabularnewline
0.1 (10) & 1.39389629802737e+87 \tabularnewline
0.1083 (9.2308) & 2.37340819728174e+87 \tabularnewline
0.1167 (8.5714) & 4.61677475779849e+87 \tabularnewline
0.125 (8) & 7.12696780704853e+87 \tabularnewline
0.1333 (7.5) & 7.07305273243939e+87 \tabularnewline
0.1417 (7.0588) & 3.19762880820776e+87 \tabularnewline
0.15 (6.6667) & 2.18830116883184e+87 \tabularnewline
0.1583 (6.3158) & 1.44426862777247e+87 \tabularnewline
0.1667 (6) & 1.21306309177086e+87 \tabularnewline
0.175 (5.7143) & 1.35827046420271e+87 \tabularnewline
0.1833 (5.4545) & 4.52446427551716e+87 \tabularnewline
0.1917 (5.2174) & 9.4367353962757e+87 \tabularnewline
0.2 (5) & 9.26974481824026e+87 \tabularnewline
0.2083 (4.8) & 3.08868056339063e+87 \tabularnewline
0.2167 (4.6154) & 2.74506717109612e+86 \tabularnewline
0.225 (4.4444) & 3.54651143187359e+86 \tabularnewline
0.2333 (4.2857) & 2.08926069503838e+87 \tabularnewline
0.2417 (4.1379) & 2.64108980140375e+87 \tabularnewline
0.25 (4) & 4.39857399520591e+87 \tabularnewline
0.2583 (3.871) & 7.46339997936155e+87 \tabularnewline
0.2667 (3.75) & 7.47172279209331e+87 \tabularnewline
0.275 (3.6364) & 4.52436123714543e+87 \tabularnewline
0.2833 (3.5294) & 1.14828102881739e+86 \tabularnewline
0.2917 (3.4286) & 1.82147694109642e+86 \tabularnewline
0.3 (3.3333) & 5.06835351213419e+87 \tabularnewline
0.3083 (3.2432) & 1.35329928766425e+88 \tabularnewline
0.3167 (3.1579) & 1.98333213026721e+88 \tabularnewline
0.325 (3.0769) & 4.44925812950219e+88 \tabularnewline
0.3333 (3) & 2.34987357161607e+88 \tabularnewline
0.3417 (2.9268) & 2.39175401797051e+88 \tabularnewline
0.35 (2.8571) & 2.68305268190224e+88 \tabularnewline
0.3583 (2.7907) & 9.50441776702161e+87 \tabularnewline
0.3667 (2.7273) & 1.82652891021259e+88 \tabularnewline
0.375 (2.6667) & 6.13001305290465e+87 \tabularnewline
0.3833 (2.6087) & 1.16881260566606e+88 \tabularnewline
0.3917 (2.5532) & 9.21084252020378e+87 \tabularnewline
0.4 (2.5) & 2.74784940305526e+87 \tabularnewline
0.4083 (2.449) & 2.97682990367597e+87 \tabularnewline
0.4167 (2.4) & 1.55363353805455e+88 \tabularnewline
0.425 (2.3529) & 7.03345502618645e+87 \tabularnewline
0.4333 (2.3077) & 1.78640270075151e+88 \tabularnewline
0.4417 (2.2642) & 2.88388511444933e+87 \tabularnewline
0.45 (2.2222) & 5.63475431016872e+86 \tabularnewline
0.4583 (2.1818) & 4.94739518017185e+87 \tabularnewline
0.4667 (2.1429) & 3.13052112591529e+87 \tabularnewline
0.475 (2.1053) & 6.93360287175015e+87 \tabularnewline
0.4833 (2.069) & 6.87062670803971e+87 \tabularnewline
0.4917 (2.0339) & 2.95974261891254e+88 \tabularnewline
0.5 (2) & 5.69679428236446e+87 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301806&T=1

[TABLE]
[ROW][C]Raw Periodogram[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]Box-Cox transformation parameter (lambda)[/C][C]12[/C][/ROW]
[ROW][C]Degree of non-seasonal differencing (d)[/C][C]2[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D)[/C][C]0[/C][/ROW]
[ROW][C]Seasonal Period (s)[/C][C]12[/C][/ROW]
[ROW][C]Frequency (Period)[/C][C]Spectrum[/C][/ROW]
[ROW][C]0.0083 (120)[/C][C]2.05274281983111e+86[/C][/ROW]
[ROW][C]0.0167 (60)[/C][C]4.7459238218753e+86[/C][/ROW]
[ROW][C]0.025 (40)[/C][C]1.78527871103957e+85[/C][/ROW]
[ROW][C]0.0333 (30)[/C][C]1.42444387526476e+86[/C][/ROW]
[ROW][C]0.0417 (24)[/C][C]9.24723436280015e+86[/C][/ROW]
[ROW][C]0.05 (20)[/C][C]1.08336026112975e+87[/C][/ROW]
[ROW][C]0.0583 (17.1429)[/C][C]9.4144780332323e+86[/C][/ROW]
[ROW][C]0.0667 (15)[/C][C]3.07696481312707e+87[/C][/ROW]
[ROW][C]0.075 (13.3333)[/C][C]7.51278446901656e+86[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]1.16670093401346e+87[/C][/ROW]
[ROW][C]0.0917 (10.9091)[/C][C]4.01722597331179e+87[/C][/ROW]
[ROW][C]0.1 (10)[/C][C]1.39389629802737e+87[/C][/ROW]
[ROW][C]0.1083 (9.2308)[/C][C]2.37340819728174e+87[/C][/ROW]
[ROW][C]0.1167 (8.5714)[/C][C]4.61677475779849e+87[/C][/ROW]
[ROW][C]0.125 (8)[/C][C]7.12696780704853e+87[/C][/ROW]
[ROW][C]0.1333 (7.5)[/C][C]7.07305273243939e+87[/C][/ROW]
[ROW][C]0.1417 (7.0588)[/C][C]3.19762880820776e+87[/C][/ROW]
[ROW][C]0.15 (6.6667)[/C][C]2.18830116883184e+87[/C][/ROW]
[ROW][C]0.1583 (6.3158)[/C][C]1.44426862777247e+87[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]1.21306309177086e+87[/C][/ROW]
[ROW][C]0.175 (5.7143)[/C][C]1.35827046420271e+87[/C][/ROW]
[ROW][C]0.1833 (5.4545)[/C][C]4.52446427551716e+87[/C][/ROW]
[ROW][C]0.1917 (5.2174)[/C][C]9.4367353962757e+87[/C][/ROW]
[ROW][C]0.2 (5)[/C][C]9.26974481824026e+87[/C][/ROW]
[ROW][C]0.2083 (4.8)[/C][C]3.08868056339063e+87[/C][/ROW]
[ROW][C]0.2167 (4.6154)[/C][C]2.74506717109612e+86[/C][/ROW]
[ROW][C]0.225 (4.4444)[/C][C]3.54651143187359e+86[/C][/ROW]
[ROW][C]0.2333 (4.2857)[/C][C]2.08926069503838e+87[/C][/ROW]
[ROW][C]0.2417 (4.1379)[/C][C]2.64108980140375e+87[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]4.39857399520591e+87[/C][/ROW]
[ROW][C]0.2583 (3.871)[/C][C]7.46339997936155e+87[/C][/ROW]
[ROW][C]0.2667 (3.75)[/C][C]7.47172279209331e+87[/C][/ROW]
[ROW][C]0.275 (3.6364)[/C][C]4.52436123714543e+87[/C][/ROW]
[ROW][C]0.2833 (3.5294)[/C][C]1.14828102881739e+86[/C][/ROW]
[ROW][C]0.2917 (3.4286)[/C][C]1.82147694109642e+86[/C][/ROW]
[ROW][C]0.3 (3.3333)[/C][C]5.06835351213419e+87[/C][/ROW]
[ROW][C]0.3083 (3.2432)[/C][C]1.35329928766425e+88[/C][/ROW]
[ROW][C]0.3167 (3.1579)[/C][C]1.98333213026721e+88[/C][/ROW]
[ROW][C]0.325 (3.0769)[/C][C]4.44925812950219e+88[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]2.34987357161607e+88[/C][/ROW]
[ROW][C]0.3417 (2.9268)[/C][C]2.39175401797051e+88[/C][/ROW]
[ROW][C]0.35 (2.8571)[/C][C]2.68305268190224e+88[/C][/ROW]
[ROW][C]0.3583 (2.7907)[/C][C]9.50441776702161e+87[/C][/ROW]
[ROW][C]0.3667 (2.7273)[/C][C]1.82652891021259e+88[/C][/ROW]
[ROW][C]0.375 (2.6667)[/C][C]6.13001305290465e+87[/C][/ROW]
[ROW][C]0.3833 (2.6087)[/C][C]1.16881260566606e+88[/C][/ROW]
[ROW][C]0.3917 (2.5532)[/C][C]9.21084252020378e+87[/C][/ROW]
[ROW][C]0.4 (2.5)[/C][C]2.74784940305526e+87[/C][/ROW]
[ROW][C]0.4083 (2.449)[/C][C]2.97682990367597e+87[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]1.55363353805455e+88[/C][/ROW]
[ROW][C]0.425 (2.3529)[/C][C]7.03345502618645e+87[/C][/ROW]
[ROW][C]0.4333 (2.3077)[/C][C]1.78640270075151e+88[/C][/ROW]
[ROW][C]0.4417 (2.2642)[/C][C]2.88388511444933e+87[/C][/ROW]
[ROW][C]0.45 (2.2222)[/C][C]5.63475431016872e+86[/C][/ROW]
[ROW][C]0.4583 (2.1818)[/C][C]4.94739518017185e+87[/C][/ROW]
[ROW][C]0.4667 (2.1429)[/C][C]3.13052112591529e+87[/C][/ROW]
[ROW][C]0.475 (2.1053)[/C][C]6.93360287175015e+87[/C][/ROW]
[ROW][C]0.4833 (2.069)[/C][C]6.87062670803971e+87[/C][/ROW]
[ROW][C]0.4917 (2.0339)[/C][C]2.95974261891254e+88[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]5.69679428236446e+87[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301806&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301806&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Raw Periodogram
Parameter	Value
Box-Cox transformation parameter (lambda)	12
Degree of non-seasonal differencing (d)	2
Degree of seasonal differencing (D)	0
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0083 (120)	2.05274281983111e+86
0.0167 (60)	4.7459238218753e+86
0.025 (40)	1.78527871103957e+85
0.0333 (30)	1.42444387526476e+86
0.0417 (24)	9.24723436280015e+86
0.05 (20)	1.08336026112975e+87
0.0583 (17.1429)	9.4144780332323e+86
0.0667 (15)	3.07696481312707e+87
0.075 (13.3333)	7.51278446901656e+86
0.0833 (12)	1.16670093401346e+87
0.0917 (10.9091)	4.01722597331179e+87
0.1 (10)	1.39389629802737e+87
0.1083 (9.2308)	2.37340819728174e+87
0.1167 (8.5714)	4.61677475779849e+87
0.125 (8)	7.12696780704853e+87
0.1333 (7.5)	7.07305273243939e+87
0.1417 (7.0588)	3.19762880820776e+87
0.15 (6.6667)	2.18830116883184e+87
0.1583 (6.3158)	1.44426862777247e+87
0.1667 (6)	1.21306309177086e+87
0.175 (5.7143)	1.35827046420271e+87
0.1833 (5.4545)	4.52446427551716e+87
0.1917 (5.2174)	9.4367353962757e+87
0.2 (5)	9.26974481824026e+87
0.2083 (4.8)	3.08868056339063e+87
0.2167 (4.6154)	2.74506717109612e+86
0.225 (4.4444)	3.54651143187359e+86
0.2333 (4.2857)	2.08926069503838e+87
0.2417 (4.1379)	2.64108980140375e+87
0.25 (4)	4.39857399520591e+87
0.2583 (3.871)	7.46339997936155e+87
0.2667 (3.75)	7.47172279209331e+87
0.275 (3.6364)	4.52436123714543e+87
0.2833 (3.5294)	1.14828102881739e+86
0.2917 (3.4286)	1.82147694109642e+86
0.3 (3.3333)	5.06835351213419e+87
0.3083 (3.2432)	1.35329928766425e+88
0.3167 (3.1579)	1.98333213026721e+88
0.325 (3.0769)	4.44925812950219e+88
0.3333 (3)	2.34987357161607e+88
0.3417 (2.9268)	2.39175401797051e+88
0.35 (2.8571)	2.68305268190224e+88
0.3583 (2.7907)	9.50441776702161e+87
0.3667 (2.7273)	1.82652891021259e+88
0.375 (2.6667)	6.13001305290465e+87
0.3833 (2.6087)	1.16881260566606e+88
0.3917 (2.5532)	9.21084252020378e+87
0.4 (2.5)	2.74784940305526e+87
0.4083 (2.449)	2.97682990367597e+87
0.4167 (2.4)	1.55363353805455e+88
0.425 (2.3529)	7.03345502618645e+87
0.4333 (2.3077)	1.78640270075151e+88
0.4417 (2.2642)	2.88388511444933e+87
0.45 (2.2222)	5.63475431016872e+86
0.4583 (2.1818)	4.94739518017185e+87
0.4667 (2.1429)	3.13052112591529e+87
0.475 (2.1053)	6.93360287175015e+87
0.4833 (2.069)	6.87062670803971e+87
0.4917 (2.0339)	2.95974261891254e+88
0.5 (2)	5.69679428236446e+87

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 2 ; par3 = 0 ; par4 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
if (par1 == 0) {
x <- log(x)
} else {
x <- (x ^ par1 - 1) / par1
}
if (par2 > 0) x <- diff(x,lag=1,difference=par2)
if (par3 > 0) x <- diff(x,lag=par4,difference=par3)
bitmap(file='test1.png')
r <- spectrum(x,main='Raw Periodogram')
dev.off()
bitmap(file='test2.png')
cpgram(x,main='Cumulative Periodogram')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Raw Periodogram',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Box-Cox transformation parameter (lambda)',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of non-seasonal differencing (d)',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of seasonal differencing (D)',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal Period (s)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Frequency (Period)',header=TRUE)
a<-table.element(a,'Spectrum',header=TRUE)
a<-table.row.end(a)
for (i in 1:length(r$freq)) {
a<-table.row.start(a)
mylab <- round(r$freq[i],4)
mylab <- paste(mylab,' (',sep='')
mylab <- paste(mylab,round(1/r$freq[i],4),sep='')
mylab <- paste(mylab,')',sep='')
a<-table.element(a,mylab,header=TRUE)
a<-table.element(a,round(r$spec[i],6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code