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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationMon, 30 Nov 2015 14:12:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/30/t14488930400tl7yan3dbf4lkf.htm/, Retrieved Tue, 14 May 2024 13:28:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284597, Retrieved Tue, 14 May 2024 13:28:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsd=0 en D=0
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2015-11-30 14:12:13] [f6bae6d252fa79c7f404cd3700ec66e0] [Current]
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Dataseries X:
501
488
504
578
545
632
728
725
585
542
480
530
518
489
528
599
572
659
739
758
602
587
497
558
555
523
532
623
598
683
774
780
609
604
531
592
578
543
565
648
615
697
785
830
645
643
551
606
585
553
576
665
656
720
826
838
652
661
584
644
623
553
599
657
680
759
878
881
705
684
577
656
645
593
617
686
679
773
906
934
713
710
600
676
645
602
601
709
706
817
930
983
745
735
620
698
665
626
649
740
729
824
937
994
781
759
643
728
691
649
656
735
748
837
995
1040
809
793
692
763
723
655
658
761
768
885
1067
1038
812
790
692
782
758
709
715
788
794
893
1046
1075
812
822
714
802
748
731
748
827
788
937
1076
1125
840
864
717
813
811
732
745
844
833
935
1110
1124
868
860
762
877
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284597&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284597&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284597&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.78140210.12810
20.5591017.24680
30.3414844.42619e-06
40.2322983.01090.001503
50.1102181.42860.077489
60.0996491.29160.099135
70.1019621.32160.094053
80.2074462.68880.003947
90.3014033.90666.8e-05
100.489216.34090
110.6798788.81220
120.86035911.15150
130.6646778.61520
140.4600915.96350
150.257213.33380.000527
160.1567392.03160.021887
170.0395370.51250.3045
180.0247480.32080.37439
190.0253360.32840.371514
200.1228841.59280.056547
210.2091812.71130.003699
220.3813464.94281e-06
230.5582597.23590
240.7249439.39630

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.781402 & 10.1281 & 0 \tabularnewline
2 & 0.559101 & 7.2468 & 0 \tabularnewline
3 & 0.341484 & 4.4261 & 9e-06 \tabularnewline
4 & 0.232298 & 3.0109 & 0.001503 \tabularnewline
5 & 0.110218 & 1.4286 & 0.077489 \tabularnewline
6 & 0.099649 & 1.2916 & 0.099135 \tabularnewline
7 & 0.101962 & 1.3216 & 0.094053 \tabularnewline
8 & 0.207446 & 2.6888 & 0.003947 \tabularnewline
9 & 0.301403 & 3.9066 & 6.8e-05 \tabularnewline
10 & 0.48921 & 6.3409 & 0 \tabularnewline
11 & 0.679878 & 8.8122 & 0 \tabularnewline
12 & 0.860359 & 11.1515 & 0 \tabularnewline
13 & 0.664677 & 8.6152 & 0 \tabularnewline
14 & 0.460091 & 5.9635 & 0 \tabularnewline
15 & 0.25721 & 3.3338 & 0.000527 \tabularnewline
16 & 0.156739 & 2.0316 & 0.021887 \tabularnewline
17 & 0.039537 & 0.5125 & 0.3045 \tabularnewline
18 & 0.024748 & 0.3208 & 0.37439 \tabularnewline
19 & 0.025336 & 0.3284 & 0.371514 \tabularnewline
20 & 0.122884 & 1.5928 & 0.056547 \tabularnewline
21 & 0.209181 & 2.7113 & 0.003699 \tabularnewline
22 & 0.381346 & 4.9428 & 1e-06 \tabularnewline
23 & 0.558259 & 7.2359 & 0 \tabularnewline
24 & 0.724943 & 9.3963 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284597&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.781402[/C][C]10.1281[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.559101[/C][C]7.2468[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.341484[/C][C]4.4261[/C][C]9e-06[/C][/ROW]
[ROW][C]4[/C][C]0.232298[/C][C]3.0109[/C][C]0.001503[/C][/ROW]
[ROW][C]5[/C][C]0.110218[/C][C]1.4286[/C][C]0.077489[/C][/ROW]
[ROW][C]6[/C][C]0.099649[/C][C]1.2916[/C][C]0.099135[/C][/ROW]
[ROW][C]7[/C][C]0.101962[/C][C]1.3216[/C][C]0.094053[/C][/ROW]
[ROW][C]8[/C][C]0.207446[/C][C]2.6888[/C][C]0.003947[/C][/ROW]
[ROW][C]9[/C][C]0.301403[/C][C]3.9066[/C][C]6.8e-05[/C][/ROW]
[ROW][C]10[/C][C]0.48921[/C][C]6.3409[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.679878[/C][C]8.8122[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.860359[/C][C]11.1515[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.664677[/C][C]8.6152[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.460091[/C][C]5.9635[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.25721[/C][C]3.3338[/C][C]0.000527[/C][/ROW]
[ROW][C]16[/C][C]0.156739[/C][C]2.0316[/C][C]0.021887[/C][/ROW]
[ROW][C]17[/C][C]0.039537[/C][C]0.5125[/C][C]0.3045[/C][/ROW]
[ROW][C]18[/C][C]0.024748[/C][C]0.3208[/C][C]0.37439[/C][/ROW]
[ROW][C]19[/C][C]0.025336[/C][C]0.3284[/C][C]0.371514[/C][/ROW]
[ROW][C]20[/C][C]0.122884[/C][C]1.5928[/C][C]0.056547[/C][/ROW]
[ROW][C]21[/C][C]0.209181[/C][C]2.7113[/C][C]0.003699[/C][/ROW]
[ROW][C]22[/C][C]0.381346[/C][C]4.9428[/C][C]1e-06[/C][/ROW]
[ROW][C]23[/C][C]0.558259[/C][C]7.2359[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.724943[/C][C]9.3963[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284597&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284597&T=1

As an alternative you can also use a QR Code:  

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

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.78140210.12810
20.5591017.24680
30.3414844.42619e-06
40.2322983.01090.001503
50.1102181.42860.077489
60.0996491.29160.099135
70.1019621.32160.094053
80.2074462.68880.003947
90.3014033.90666.8e-05
100.489216.34090
110.6798788.81220
120.86035911.15150
130.6646778.61520
140.4600915.96350
150.257213.33380.000527
160.1567392.03160.021887
170.0395370.51250.3045
180.0247480.32080.37439
190.0253360.32840.371514
200.1228841.59280.056547
210.2091812.71130.003699
220.3813464.94281e-06
230.5582597.23590
240.7249439.39630







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.78140210.12810
2-0.132221-1.71380.044207
3-0.130283-1.68870.04657
40.1258881.63170.052309
5-0.147285-1.9090.028981
60.1829982.37190.009414
70.0200340.25970.397717
80.2297472.97790.001666
90.1204121.56070.060236
100.3635054.71163e-06
110.4270645.53540
120.494226.40580
13-0.66063-8.56270
140.0032850.04260.483044
150.0240060.31110.378037
16-0.062217-0.80640.210568
17-0.016325-0.21160.416337
18-0.103031-1.33540.09177
19-0.005195-0.06730.473197
200.0008270.01070.495731
21-0.029491-0.38220.351381
220.0383930.49760.309698
230.0453090.58730.278905
240.0776431.00640.157843

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.781402 & 10.1281 & 0 \tabularnewline
2 & -0.132221 & -1.7138 & 0.044207 \tabularnewline
3 & -0.130283 & -1.6887 & 0.04657 \tabularnewline
4 & 0.125888 & 1.6317 & 0.052309 \tabularnewline
5 & -0.147285 & -1.909 & 0.028981 \tabularnewline
6 & 0.182998 & 2.3719 & 0.009414 \tabularnewline
7 & 0.020034 & 0.2597 & 0.397717 \tabularnewline
8 & 0.229747 & 2.9779 & 0.001666 \tabularnewline
9 & 0.120412 & 1.5607 & 0.060236 \tabularnewline
10 & 0.363505 & 4.7116 & 3e-06 \tabularnewline
11 & 0.427064 & 5.5354 & 0 \tabularnewline
12 & 0.49422 & 6.4058 & 0 \tabularnewline
13 & -0.66063 & -8.5627 & 0 \tabularnewline
14 & 0.003285 & 0.0426 & 0.483044 \tabularnewline
15 & 0.024006 & 0.3111 & 0.378037 \tabularnewline
16 & -0.062217 & -0.8064 & 0.210568 \tabularnewline
17 & -0.016325 & -0.2116 & 0.416337 \tabularnewline
18 & -0.103031 & -1.3354 & 0.09177 \tabularnewline
19 & -0.005195 & -0.0673 & 0.473197 \tabularnewline
20 & 0.000827 & 0.0107 & 0.495731 \tabularnewline
21 & -0.029491 & -0.3822 & 0.351381 \tabularnewline
22 & 0.038393 & 0.4976 & 0.309698 \tabularnewline
23 & 0.045309 & 0.5873 & 0.278905 \tabularnewline
24 & 0.077643 & 1.0064 & 0.157843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284597&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.781402[/C][C]10.1281[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.132221[/C][C]-1.7138[/C][C]0.044207[/C][/ROW]
[ROW][C]3[/C][C]-0.130283[/C][C]-1.6887[/C][C]0.04657[/C][/ROW]
[ROW][C]4[/C][C]0.125888[/C][C]1.6317[/C][C]0.052309[/C][/ROW]
[ROW][C]5[/C][C]-0.147285[/C][C]-1.909[/C][C]0.028981[/C][/ROW]
[ROW][C]6[/C][C]0.182998[/C][C]2.3719[/C][C]0.009414[/C][/ROW]
[ROW][C]7[/C][C]0.020034[/C][C]0.2597[/C][C]0.397717[/C][/ROW]
[ROW][C]8[/C][C]0.229747[/C][C]2.9779[/C][C]0.001666[/C][/ROW]
[ROW][C]9[/C][C]0.120412[/C][C]1.5607[/C][C]0.060236[/C][/ROW]
[ROW][C]10[/C][C]0.363505[/C][C]4.7116[/C][C]3e-06[/C][/ROW]
[ROW][C]11[/C][C]0.427064[/C][C]5.5354[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.49422[/C][C]6.4058[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.66063[/C][C]-8.5627[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.003285[/C][C]0.0426[/C][C]0.483044[/C][/ROW]
[ROW][C]15[/C][C]0.024006[/C][C]0.3111[/C][C]0.378037[/C][/ROW]
[ROW][C]16[/C][C]-0.062217[/C][C]-0.8064[/C][C]0.210568[/C][/ROW]
[ROW][C]17[/C][C]-0.016325[/C][C]-0.2116[/C][C]0.416337[/C][/ROW]
[ROW][C]18[/C][C]-0.103031[/C][C]-1.3354[/C][C]0.09177[/C][/ROW]
[ROW][C]19[/C][C]-0.005195[/C][C]-0.0673[/C][C]0.473197[/C][/ROW]
[ROW][C]20[/C][C]0.000827[/C][C]0.0107[/C][C]0.495731[/C][/ROW]
[ROW][C]21[/C][C]-0.029491[/C][C]-0.3822[/C][C]0.351381[/C][/ROW]
[ROW][C]22[/C][C]0.038393[/C][C]0.4976[/C][C]0.309698[/C][/ROW]
[ROW][C]23[/C][C]0.045309[/C][C]0.5873[/C][C]0.278905[/C][/ROW]
[ROW][C]24[/C][C]0.077643[/C][C]1.0064[/C][C]0.157843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284597&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284597&T=2

As an alternative you can also use a QR Code:  

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

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.78140210.12810
2-0.132221-1.71380.044207
3-0.130283-1.68870.04657
40.1258881.63170.052309
5-0.147285-1.9090.028981
60.1829982.37190.009414
70.0200340.25970.397717
80.2297472.97790.001666
90.1204121.56070.060236
100.3635054.71163e-06
110.4270645.53540
120.494226.40580
13-0.66063-8.56270
140.0032850.04260.483044
150.0240060.31110.378037
16-0.062217-0.80640.210568
17-0.016325-0.21160.416337
18-0.103031-1.33540.09177
19-0.005195-0.06730.473197
200.0008270.01070.495731
21-0.029491-0.38220.351381
220.0383930.49760.309698
230.0453090.58730.278905
240.0776431.00640.157843



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')