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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_spectrum.wasp
Title produced by softwareSpectral Analysis
Date of computationWed, 21 Dec 2016 00:03:30 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482275025ie3trzjcpyzas13.htm/, Retrieved Mon, 12 May 2025 17:07:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301829, Retrieved Mon, 12 May 2025 17:07:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D  [(Partial) Autocorrelation Function] [] [2016-12-18 13:25:37] [683f400e1b95307fc738e729f07c4fce]
- RMP       [Spectral Analysis] [] [2016-12-20 23:03:30] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2280
3640
3950
3860
3500
4740
3690
4810
6150
4530
4760
4670
3510
2990
3240
2700
2610
3280
3170
3440
4710
4320
3650
3340
3050
2960
2810
2670
2440
2580
2520
2860
3500
3460
3310
3050
2730
2760
2800
2490
2310
2350
2370
2560
2740
2830
3010
2500
2630
2270
2410
2210
2330
2690
3150
2330
2260
2330
2240
2230
2270
2220
2290
2240
2110
2240
2230
2320
2320
2540
2530
2400
2470
2290
2110
2050
2170
2070
2330
2190
2260
2300
2220
2220
2380
2280
2150
2190
2080
2120
2140
2130
2210
2210
2190
2160
2290
2270
2200
2120
2050
2080
2180
2070
2170
2240
2320
2250

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R ServerBig 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301829&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301829&T=0

As an alternative you can also use a QR Code:  
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 Outputview raw output of R engine
Computing time0 seconds
R ServerBig Analytics Cloud Computing Center






Raw Periodogram
ParameterValue
Box-Cox transformation parameter (lambda)1
Degree of non-seasonal differencing (d)0
Degree of seasonal differencing (D)0
Seasonal Period (s)1
Frequency (Period)Spectrum
0.0093 (108)3098155.53242
0.0185 (54)235824.11642
0.0278 (36)284280.845517
0.037 (27)213346.223455
0.0463 (21.6)459884.771478
0.0556 (18)172963.908164
0.0648 (15.4286)1379402.845979
0.0741 (13.5)1319721.747584
0.0833 (12)2552750.81051
0.0926 (10.8)813533.347898
0.1019 (9.8182)92785.078323
0.1111 (9)264029.46622
0.1204 (8.3077)95014.70512
0.1296 (7.7143)70662.378744
0.1389 (7.2)30803.548762
0.1481 (6.75)53866.817535
0.1574 (6.3529)263025.591384
0.1667 (6)117425.145674
0.1759 (5.6842)124531.996307
0.1852 (5.4)47763.907678
0.1944 (5.1429)5203.187471
0.2037 (4.9091)8186.582866
0.213 (4.6957)22252.81729
0.2222 (4.5)19633.921607
0.2315 (4.32)60822.962421
0.2407 (4.1538)107697.468767
0.25 (4)31998.280582
0.2593 (3.8571)42143.473528
0.2685 (3.7241)8686.621505
0.2778 (3.6)27846.617011
0.287 (3.4839)50948.117897
0.2963 (3.375)75406.987437
0.3056 (3.2727)161189.135087
0.3148 (3.1765)110942.651951
0.3241 (3.0857)313437.563721
0.3333 (3)193239.872303
0.3426 (2.9189)197359.857523
0.3519 (2.8421)81880.034451
0.3611 (2.7692)3331.071032
0.3704 (2.7)92028.723071
0.3796 (2.6341)3415.983813
0.3889 (2.5714)31697.382735
0.3981 (2.5116)29106.621763
0.4074 (2.4545)38516.597198
0.4167 (2.4)52091.207737
0.4259 (2.3478)35261.637772
0.4352 (2.2979)1076.24134
0.4444 (2.25)3533.40678
0.4537 (2.2041)28955.883985
0.463 (2.16)11922.564941
0.4722 (2.1176)34973.627435
0.4815 (2.0769)3536.183861
0.4907 (2.0377)7477.621514
0.5 (2)36634.940915

\begin{tabular}{lllllllll}
\hline
Raw Periodogram \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) & 1 \tabularnewline
Degree of non-seasonal differencing (d) & 0 \tabularnewline
Degree of seasonal differencing (D) & 0 \tabularnewline
Seasonal Period (s) & 1 \tabularnewline
Frequency (Period) & Spectrum \tabularnewline
0.0093 (108) & 3098155.53242 \tabularnewline
0.0185 (54) & 235824.11642 \tabularnewline
0.0278 (36) & 284280.845517 \tabularnewline
0.037 (27) & 213346.223455 \tabularnewline
0.0463 (21.6) & 459884.771478 \tabularnewline
0.0556 (18) & 172963.908164 \tabularnewline
0.0648 (15.4286) & 1379402.845979 \tabularnewline
0.0741 (13.5) & 1319721.747584 \tabularnewline
0.0833 (12) & 2552750.81051 \tabularnewline
0.0926 (10.8) & 813533.347898 \tabularnewline
0.1019 (9.8182) & 92785.078323 \tabularnewline
0.1111 (9) & 264029.46622 \tabularnewline
0.1204 (8.3077) & 95014.70512 \tabularnewline
0.1296 (7.7143) & 70662.378744 \tabularnewline
0.1389 (7.2) & 30803.548762 \tabularnewline
0.1481 (6.75) & 53866.817535 \tabularnewline
0.1574 (6.3529) & 263025.591384 \tabularnewline
0.1667 (6) & 117425.145674 \tabularnewline
0.1759 (5.6842) & 124531.996307 \tabularnewline
0.1852 (5.4) & 47763.907678 \tabularnewline
0.1944 (5.1429) & 5203.187471 \tabularnewline
0.2037 (4.9091) & 8186.582866 \tabularnewline
0.213 (4.6957) & 22252.81729 \tabularnewline
0.2222 (4.5) & 19633.921607 \tabularnewline
0.2315 (4.32) & 60822.962421 \tabularnewline
0.2407 (4.1538) & 107697.468767 \tabularnewline
0.25 (4) & 31998.280582 \tabularnewline
0.2593 (3.8571) & 42143.473528 \tabularnewline
0.2685 (3.7241) & 8686.621505 \tabularnewline
0.2778 (3.6) & 27846.617011 \tabularnewline
0.287 (3.4839) & 50948.117897 \tabularnewline
0.2963 (3.375) & 75406.987437 \tabularnewline
0.3056 (3.2727) & 161189.135087 \tabularnewline
0.3148 (3.1765) & 110942.651951 \tabularnewline
0.3241 (3.0857) & 313437.563721 \tabularnewline
0.3333 (3) & 193239.872303 \tabularnewline
0.3426 (2.9189) & 197359.857523 \tabularnewline
0.3519 (2.8421) & 81880.034451 \tabularnewline
0.3611 (2.7692) & 3331.071032 \tabularnewline
0.3704 (2.7) & 92028.723071 \tabularnewline
0.3796 (2.6341) & 3415.983813 \tabularnewline
0.3889 (2.5714) & 31697.382735 \tabularnewline
0.3981 (2.5116) & 29106.621763 \tabularnewline
0.4074 (2.4545) & 38516.597198 \tabularnewline
0.4167 (2.4) & 52091.207737 \tabularnewline
0.4259 (2.3478) & 35261.637772 \tabularnewline
0.4352 (2.2979) & 1076.24134 \tabularnewline
0.4444 (2.25) & 3533.40678 \tabularnewline
0.4537 (2.2041) & 28955.883985 \tabularnewline
0.463 (2.16) & 11922.564941 \tabularnewline
0.4722 (2.1176) & 34973.627435 \tabularnewline
0.4815 (2.0769) & 3536.183861 \tabularnewline
0.4907 (2.0377) & 7477.621514 \tabularnewline
0.5 (2) & 36634.940915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301829&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]1[/C][/ROW]
[ROW][C]Degree of non-seasonal differencing (d)[/C][C]0[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D)[/C][C]0[/C][/ROW]
[ROW][C]Seasonal Period (s)[/C][C]1[/C][/ROW]
[ROW][C]Frequency (Period)[/C][C]Spectrum[/C][/ROW]
[ROW][C]0.0093 (108)[/C][C]3098155.53242[/C][/ROW]
[ROW][C]0.0185 (54)[/C][C]235824.11642[/C][/ROW]
[ROW][C]0.0278 (36)[/C][C]284280.845517[/C][/ROW]
[ROW][C]0.037 (27)[/C][C]213346.223455[/C][/ROW]
[ROW][C]0.0463 (21.6)[/C][C]459884.771478[/C][/ROW]
[ROW][C]0.0556 (18)[/C][C]172963.908164[/C][/ROW]
[ROW][C]0.0648 (15.4286)[/C][C]1379402.845979[/C][/ROW]
[ROW][C]0.0741 (13.5)[/C][C]1319721.747584[/C][/ROW]
[ROW][C]0.0833 (12)[/C][C]2552750.81051[/C][/ROW]
[ROW][C]0.0926 (10.8)[/C][C]813533.347898[/C][/ROW]
[ROW][C]0.1019 (9.8182)[/C][C]92785.078323[/C][/ROW]
[ROW][C]0.1111 (9)[/C][C]264029.46622[/C][/ROW]
[ROW][C]0.1204 (8.3077)[/C][C]95014.70512[/C][/ROW]
[ROW][C]0.1296 (7.7143)[/C][C]70662.378744[/C][/ROW]
[ROW][C]0.1389 (7.2)[/C][C]30803.548762[/C][/ROW]
[ROW][C]0.1481 (6.75)[/C][C]53866.817535[/C][/ROW]
[ROW][C]0.1574 (6.3529)[/C][C]263025.591384[/C][/ROW]
[ROW][C]0.1667 (6)[/C][C]117425.145674[/C][/ROW]
[ROW][C]0.1759 (5.6842)[/C][C]124531.996307[/C][/ROW]
[ROW][C]0.1852 (5.4)[/C][C]47763.907678[/C][/ROW]
[ROW][C]0.1944 (5.1429)[/C][C]5203.187471[/C][/ROW]
[ROW][C]0.2037 (4.9091)[/C][C]8186.582866[/C][/ROW]
[ROW][C]0.213 (4.6957)[/C][C]22252.81729[/C][/ROW]
[ROW][C]0.2222 (4.5)[/C][C]19633.921607[/C][/ROW]
[ROW][C]0.2315 (4.32)[/C][C]60822.962421[/C][/ROW]
[ROW][C]0.2407 (4.1538)[/C][C]107697.468767[/C][/ROW]
[ROW][C]0.25 (4)[/C][C]31998.280582[/C][/ROW]
[ROW][C]0.2593 (3.8571)[/C][C]42143.473528[/C][/ROW]
[ROW][C]0.2685 (3.7241)[/C][C]8686.621505[/C][/ROW]
[ROW][C]0.2778 (3.6)[/C][C]27846.617011[/C][/ROW]
[ROW][C]0.287 (3.4839)[/C][C]50948.117897[/C][/ROW]
[ROW][C]0.2963 (3.375)[/C][C]75406.987437[/C][/ROW]
[ROW][C]0.3056 (3.2727)[/C][C]161189.135087[/C][/ROW]
[ROW][C]0.3148 (3.1765)[/C][C]110942.651951[/C][/ROW]
[ROW][C]0.3241 (3.0857)[/C][C]313437.563721[/C][/ROW]
[ROW][C]0.3333 (3)[/C][C]193239.872303[/C][/ROW]
[ROW][C]0.3426 (2.9189)[/C][C]197359.857523[/C][/ROW]
[ROW][C]0.3519 (2.8421)[/C][C]81880.034451[/C][/ROW]
[ROW][C]0.3611 (2.7692)[/C][C]3331.071032[/C][/ROW]
[ROW][C]0.3704 (2.7)[/C][C]92028.723071[/C][/ROW]
[ROW][C]0.3796 (2.6341)[/C][C]3415.983813[/C][/ROW]
[ROW][C]0.3889 (2.5714)[/C][C]31697.382735[/C][/ROW]
[ROW][C]0.3981 (2.5116)[/C][C]29106.621763[/C][/ROW]
[ROW][C]0.4074 (2.4545)[/C][C]38516.597198[/C][/ROW]
[ROW][C]0.4167 (2.4)[/C][C]52091.207737[/C][/ROW]
[ROW][C]0.4259 (2.3478)[/C][C]35261.637772[/C][/ROW]
[ROW][C]0.4352 (2.2979)[/C][C]1076.24134[/C][/ROW]
[ROW][C]0.4444 (2.25)[/C][C]3533.40678[/C][/ROW]
[ROW][C]0.4537 (2.2041)[/C][C]28955.883985[/C][/ROW]
[ROW][C]0.463 (2.16)[/C][C]11922.564941[/C][/ROW]
[ROW][C]0.4722 (2.1176)[/C][C]34973.627435[/C][/ROW]
[ROW][C]0.4815 (2.0769)[/C][C]3536.183861[/C][/ROW]
[ROW][C]0.4907 (2.0377)[/C][C]7477.621514[/C][/ROW]
[ROW][C]0.5 (2)[/C][C]36634.940915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301829&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Raw Periodogram
ParameterValue
Box-Cox transformation parameter (lambda)1
Degree of non-seasonal differencing (d)0
Degree of seasonal differencing (D)0
Seasonal Period (s)1
Frequency (Period)Spectrum
0.0093 (108)3098155.53242
0.0185 (54)235824.11642
0.0278 (36)284280.845517
0.037 (27)213346.223455
0.0463 (21.6)459884.771478
0.0556 (18)172963.908164
0.0648 (15.4286)1379402.845979
0.0741 (13.5)1319721.747584
0.0833 (12)2552750.81051
0.0926 (10.8)813533.347898
0.1019 (9.8182)92785.078323
0.1111 (9)264029.46622
0.1204 (8.3077)95014.70512
0.1296 (7.7143)70662.378744
0.1389 (7.2)30803.548762
0.1481 (6.75)53866.817535
0.1574 (6.3529)263025.591384
0.1667 (6)117425.145674
0.1759 (5.6842)124531.996307
0.1852 (5.4)47763.907678
0.1944 (5.1429)5203.187471
0.2037 (4.9091)8186.582866
0.213 (4.6957)22252.81729
0.2222 (4.5)19633.921607
0.2315 (4.32)60822.962421
0.2407 (4.1538)107697.468767
0.25 (4)31998.280582
0.2593 (3.8571)42143.473528
0.2685 (3.7241)8686.621505
0.2778 (3.6)27846.617011
0.287 (3.4839)50948.117897
0.2963 (3.375)75406.987437
0.3056 (3.2727)161189.135087
0.3148 (3.1765)110942.651951
0.3241 (3.0857)313437.563721
0.3333 (3)193239.872303
0.3426 (2.9189)197359.857523
0.3519 (2.8421)81880.034451
0.3611 (2.7692)3331.071032
0.3704 (2.7)92028.723071
0.3796 (2.6341)3415.983813
0.3889 (2.5714)31697.382735
0.3981 (2.5116)29106.621763
0.4074 (2.4545)38516.597198
0.4167 (2.4)52091.207737
0.4259 (2.3478)35261.637772
0.4352 (2.2979)1076.24134
0.4444 (2.25)3533.40678
0.4537 (2.2041)28955.883985
0.463 (2.16)11922.564941
0.4722 (2.1176)34973.627435
0.4815 (2.0769)3536.183861
0.4907 (2.0377)7477.621514
0.5 (2)36634.940915


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ;
Parameters (R input):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ;
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')