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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

Sat, 17 Dec 2016 21:12:27 +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/17/t1482005590kvknukfgyvkgdy2.htm/, Retrieved Thu, 02 May 2024 07:10:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300939, Retrieved Thu, 02 May 2024 07:10:42 +0000

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

-       [Spectral Analysis] [spectral analysis ] [2016-12-17 20:12:27] [f20c721eaecf28dbff8d9b9768e8b0c7] [Current]

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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=300939&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=300939&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300939&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)	0
Degree of non-seasonal differencing (d)	1
Degree of seasonal differencing (D)	1
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0093 (108)	0.000241
0.0185 (54)	0.000194
0.0278 (36)	0.000355
0.037 (27)	0.000119
0.0463 (21.6)	0.001005
0.0556 (18)	0.000553
0.0648 (15.4286)	7.1e-05
0.0741 (13.5)	5.9e-05
0.0833 (12)	4.8e-05
0.0926 (10.8)	3.7e-05
0.1019 (9.8182)	0.001091
0.1111 (9)	0.000136
0.1204 (8.3077)	0.001073
0.1296 (7.7143)	1.7e-05
0.1389 (7.2)	0.000973
0.1481 (6.75)	3.2e-05
0.1574 (6.3529)	0.000224
0.1667 (6)	5e-05
0.1759 (5.6842)	1.6e-05
0.1852 (5.4)	0.000152
0.1944 (5.1429)	0.000646
0.2037 (4.9091)	1.3e-05
0.213 (4.6957)	0.000831
0.2222 (4.5)	0.000925
0.2315 (4.32)	0.000674
0.2407 (4.1538)	4e-06
0.25 (4)	1e-05
0.2593 (3.8571)	5.3e-05
0.2685 (3.7241)	5.6e-05
0.2778 (3.6)	0.000328
0.287 (3.4839)	0.000561
0.2963 (3.375)	0.000245
0.3056 (3.2727)	0.000295
0.3148 (3.1765)	0.000195
0.3241 (3.0857)	0.000188
0.3333 (3)	0.000118
0.3426 (2.9189)	0.000152
0.3519 (2.8421)	0.000491
0.3611 (2.7692)	2.6e-05
0.3704 (2.7)	7.7e-05
0.3796 (2.6341)	0.002753
0.3889 (2.5714)	0.000546
0.3981 (2.5116)	0.000886
0.4074 (2.4545)	5.4e-05
0.4167 (2.4)	6e-06
0.4259 (2.3478)	0.000838
0.4352 (2.2979)	0.00019
0.4444 (2.25)	0.000445
0.4537 (2.2041)	0.000548
0.463 (2.16)	0.000518
0.4722 (2.1176)	0.000274
0.4815 (2.0769)	0.000112
0.4907 (2.0377)	9.3e-05
0.5 (2)	2.1e-05

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 0 \tabularnewline
Degree of non-seasonal differencing (d) & 1 \tabularnewline
Degree of seasonal differencing (D) & 1 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0093 (108) & 0.000241 \tabularnewline
0.0185 (54) & 0.000194 \tabularnewline
0.0278 (36) & 0.000355 \tabularnewline
0.037 (27) & 0.000119 \tabularnewline
0.0463 (21.6) & 0.001005 \tabularnewline
0.0556 (18) & 0.000553 \tabularnewline
0.0648 (15.4286) & 7.1e-05 \tabularnewline
0.0741 (13.5) & 5.9e-05 \tabularnewline
0.0833 (12) & 4.8e-05 \tabularnewline
0.0926 (10.8) & 3.7e-05 \tabularnewline
0.1019 (9.8182) & 0.001091 \tabularnewline
0.1111 (9) & 0.000136 \tabularnewline
0.1204 (8.3077) & 0.001073 \tabularnewline
0.1296 (7.7143) & 1.7e-05 \tabularnewline
0.1389 (7.2) & 0.000973 \tabularnewline
0.1481 (6.75) & 3.2e-05 \tabularnewline
0.1574 (6.3529) & 0.000224 \tabularnewline
0.1667 (6) & 5e-05 \tabularnewline
0.1759 (5.6842) & 1.6e-05 \tabularnewline
0.1852 (5.4) & 0.000152 \tabularnewline
0.1944 (5.1429) & 0.000646 \tabularnewline
0.2037 (4.9091) & 1.3e-05 \tabularnewline
0.213 (4.6957) & 0.000831 \tabularnewline
0.2222 (4.5) & 0.000925 \tabularnewline
0.2315 (4.32) & 0.000674 \tabularnewline
0.2407 (4.1538) & 4e-06 \tabularnewline
0.25 (4) & 1e-05 \tabularnewline
0.2593 (3.8571) & 5.3e-05 \tabularnewline
0.2685 (3.7241) & 5.6e-05 \tabularnewline
0.2778 (3.6) & 0.000328 \tabularnewline
0.287 (3.4839) & 0.000561 \tabularnewline
0.2963 (3.375) & 0.000245 \tabularnewline
0.3056 (3.2727) & 0.000295 \tabularnewline
0.3148 (3.1765) & 0.000195 \tabularnewline
0.3241 (3.0857) & 0.000188 \tabularnewline
0.3333 (3) & 0.000118 \tabularnewline
0.3426 (2.9189) & 0.000152 \tabularnewline
0.3519 (2.8421) & 0.000491 \tabularnewline
0.3611 (2.7692) & 2.6e-05 \tabularnewline
0.3704 (2.7) & 7.7e-05 \tabularnewline
0.3796 (2.6341) & 0.002753 \tabularnewline
0.3889 (2.5714) & 0.000546 \tabularnewline
0.3981 (2.5116) & 0.000886 \tabularnewline
0.4074 (2.4545) & 5.4e-05 \tabularnewline
0.4167 (2.4) & 6e-06 \tabularnewline
0.4259 (2.3478) & 0.000838 \tabularnewline
0.4352 (2.2979) & 0.00019 \tabularnewline
0.4444 (2.25) & 0.000445 \tabularnewline
0.4537 (2.2041) & 0.000548 \tabularnewline
0.463 (2.16) & 0.000518 \tabularnewline
0.4722 (2.1176) & 0.000274 \tabularnewline
0.4815 (2.0769) & 0.000112 \tabularnewline
0.4907 (2.0377) & 9.3e-05 \tabularnewline
0.5 (2) & 2.1e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300939&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]0[/C][/ROW]
[ROW][C]Degree of non-seasonal differencing (d)[/C][C]1[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D)[/C][C]1[/C][/ROW]
[ROW][C]Seasonal Period (s)[/C][C]12[/C][/ROW]
[ROW][C]Frequency (Period)[/C][C]Spectrum[/C][/ROW]
[ROW][C]0.0093 (108)[/C][C]0.000241[/C][/ROW]
[ROW][C]0.0185 (54)[/C][C]0.000194[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]0.000355[/C][/ROW]
[ROW][C]0.037 (27)[/C][C]0.000119[/C][/ROW]
[ROW][C]0.0463 (21.6)[/C][C]0.001005[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]0.000553[/C][/ROW]
[ROW][C]0.0648 (15.4286)[/C][C]7.1e-05[/C][/ROW]
[ROW][C]0.0741 (13.5)[/C][C]5.9e-05[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]4.8e-05[/C][/ROW]
[ROW][C]0.0926 (10.8)[/C][C]3.7e-05[/C][/ROW]
[ROW][C]0.1019 (9.8182)[/C][C]0.001091[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]0.000136[/C][/ROW]
[ROW][C]0.1204 (8.3077)[/C][C]0.001073[/C][/ROW]
[ROW][C]0.1296 (7.7143)[/C][C]1.7e-05[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]0.000973[/C][/ROW]
[ROW][C]0.1481 (6.75)[/C][C]3.2e-05[/C][/ROW]
[ROW][C]0.1574 (6.3529)[/C][C]0.000224[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]5e-05[/C][/ROW]
[ROW][C]0.1759 (5.6842)[/C][C]1.6e-05[/C][/ROW]
[ROW][C]0.1852 (5.4)[/C][C]0.000152[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]0.000646[/C][/ROW]
[ROW][C]0.2037 (4.9091)[/C][C]1.3e-05[/C][/ROW]
[ROW][C]0.213 (4.6957)[/C][C]0.000831[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]0.000925[/C][/ROW]
[ROW][C]0.2315 (4.32)[/C][C]0.000674[/C][/ROW]
[ROW][C]0.2407 (4.1538)[/C][C]4e-06[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]1e-05[/C][/ROW]
[ROW][C]0.2593 (3.8571)[/C][C]5.3e-05[/C][/ROW]
[ROW][C]0.2685 (3.7241)[/C][C]5.6e-05[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]0.000328[/C][/ROW]
[ROW][C]0.287 (3.4839)[/C][C]0.000561[/C][/ROW]
[ROW][C]0.2963 (3.375)[/C][C]0.000245[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]0.000295[/C][/ROW]
[ROW][C]0.3148 (3.1765)[/C][C]0.000195[/C][/ROW]
[ROW][C]0.3241 (3.0857)[/C][C]0.000188[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]0.000118[/C][/ROW]
[ROW][C]0.3426 (2.9189)[/C][C]0.000152[/C][/ROW]
[ROW][C]0.3519 (2.8421)[/C][C]0.000491[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]2.6e-05[/C][/ROW]
[ROW][C]0.3704 (2.7)[/C][C]7.7e-05[/C][/ROW]
[ROW][C]0.3796 (2.6341)[/C][C]0.002753[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]0.000546[/C][/ROW]
[ROW][C]0.3981 (2.5116)[/C][C]0.000886[/C][/ROW]
[ROW][C]0.4074 (2.4545)[/C][C]5.4e-05[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]6e-06[/C][/ROW]
[ROW][C]0.4259 (2.3478)[/C][C]0.000838[/C][/ROW]
[ROW][C]0.4352 (2.2979)[/C][C]0.00019[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]0.000445[/C][/ROW]
[ROW][C]0.4537 (2.2041)[/C][C]0.000548[/C][/ROW]
[ROW][C]0.463 (2.16)[/C][C]0.000518[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]0.000274[/C][/ROW]
[ROW][C]0.4815 (2.0769)[/C][C]0.000112[/C][/ROW]
[ROW][C]0.4907 (2.0377)[/C][C]9.3e-05[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]2.1e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300939&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300939&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)	0
Degree of non-seasonal differencing (d)	1
Degree of seasonal differencing (D)	1
Seasonal Period (s)	12
Frequency (Period)	Spectrum
0.0093 (108)	0.000241
0.0185 (54)	0.000194
0.0278 (36)	0.000355
0.037 (27)	0.000119
0.0463 (21.6)	0.001005
0.0556 (18)	0.000553
0.0648 (15.4286)	7.1e-05
0.0741 (13.5)	5.9e-05
0.0833 (12)	4.8e-05
0.0926 (10.8)	3.7e-05
0.1019 (9.8182)	0.001091
0.1111 (9)	0.000136
0.1204 (8.3077)	0.001073
0.1296 (7.7143)	1.7e-05
0.1389 (7.2)	0.000973
0.1481 (6.75)	3.2e-05
0.1574 (6.3529)	0.000224
0.1667 (6)	5e-05
0.1759 (5.6842)	1.6e-05
0.1852 (5.4)	0.000152
0.1944 (5.1429)	0.000646
0.2037 (4.9091)	1.3e-05
0.213 (4.6957)	0.000831
0.2222 (4.5)	0.000925
0.2315 (4.32)	0.000674
0.2407 (4.1538)	4e-06
0.25 (4)	1e-05
0.2593 (3.8571)	5.3e-05
0.2685 (3.7241)	5.6e-05
0.2778 (3.6)	0.000328
0.287 (3.4839)	0.000561
0.2963 (3.375)	0.000245
0.3056 (3.2727)	0.000295
0.3148 (3.1765)	0.000195
0.3241 (3.0857)	0.000188
0.3333 (3)	0.000118
0.3426 (2.9189)	0.000152
0.3519 (2.8421)	0.000491
0.3611 (2.7692)	2.6e-05
0.3704 (2.7)	7.7e-05
0.3796 (2.6341)	0.002753
0.3889 (2.5714)	0.000546
0.3981 (2.5116)	0.000886
0.4074 (2.4545)	5.4e-05
0.4167 (2.4)	6e-06
0.4259 (2.3478)	0.000838
0.4352 (2.2979)	0.00019
0.4444 (2.25)	0.000445
0.4537 (2.2041)	0.000548
0.463 (2.16)	0.000518
0.4722 (2.1176)	0.000274
0.4815 (2.0769)	0.000112
0.4907 (2.0377)	9.3e-05
0.5 (2)	2.1e-05

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0.0 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 0.0 ; par2 = 1 ; par3 = 1 ; 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