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Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by software(Partial) Autocorrelation Function
Date of computationMon, 02 Dec 2013 15:20:19 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/02/t1386015631gve7hxth2beaw90.htm/, Retrieved Fri, 29 Mar 2024 08:19:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230123, Retrieved Fri, 29 Mar 2024 08:19:41 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Autocorrelatiefun...] [2010-12-17 18:13:02] [e7fc384c3b263e46f871dfcba42cc90e]
-       [(Partial) Autocorrelation Function] [Workshop 9 Autoco...] [2011-12-02 11:21:43] [3deae35ae8526e36953f595ad65f3a1f]
- R P     [(Partial) Autocorrelation Function] [WS 9 analyse 2 ] [2013-12-02 19:43:26] [16ce55620e4b91ec00a4b56aea2a2582]
-   P       [(Partial) Autocorrelation Function] [WS 9 analyse 3] [2013-12-02 19:45:13] [16ce55620e4b91ec00a4b56aea2a2582]
-  MP           [(Partial) Autocorrelation Function] [WS 9 Autocorrelat...] [2013-12-02 20:20:19] [4c736a442787d42e94a9d9bc48424aaa] [Current]
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Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230123&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230123&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230123&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.692354-5.31811e-06
20.2314561.77780.040291
30.0053560.04110.483661
4-0.084512-0.64910.259381
50.0966080.74210.230498
6-0.016336-0.12550.450285
7-0.086927-0.66770.253465
80.0428890.32940.371495
90.0750110.57620.283347
10-0.226283-1.73810.043704
110.3853712.96010.002212
12-0.434989-3.34120.000726
130.2484541.90840.030604
14-0.041019-0.31510.376909
15-0.011111-0.08530.466139
16-0.013262-0.10190.459603
17-0.017221-0.13230.447609
180.0904650.69490.244931

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.692354 & -5.3181 & 1e-06 \tabularnewline
2 & 0.231456 & 1.7778 & 0.040291 \tabularnewline
3 & 0.005356 & 0.0411 & 0.483661 \tabularnewline
4 & -0.084512 & -0.6491 & 0.259381 \tabularnewline
5 & 0.096608 & 0.7421 & 0.230498 \tabularnewline
6 & -0.016336 & -0.1255 & 0.450285 \tabularnewline
7 & -0.086927 & -0.6677 & 0.253465 \tabularnewline
8 & 0.042889 & 0.3294 & 0.371495 \tabularnewline
9 & 0.075011 & 0.5762 & 0.283347 \tabularnewline
10 & -0.226283 & -1.7381 & 0.043704 \tabularnewline
11 & 0.385371 & 2.9601 & 0.002212 \tabularnewline
12 & -0.434989 & -3.3412 & 0.000726 \tabularnewline
13 & 0.248454 & 1.9084 & 0.030604 \tabularnewline
14 & -0.041019 & -0.3151 & 0.376909 \tabularnewline
15 & -0.011111 & -0.0853 & 0.466139 \tabularnewline
16 & -0.013262 & -0.1019 & 0.459603 \tabularnewline
17 & -0.017221 & -0.1323 & 0.447609 \tabularnewline
18 & 0.090465 & 0.6949 & 0.244931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230123&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]-0.692354[/C][C]-5.3181[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.231456[/C][C]1.7778[/C][C]0.040291[/C][/ROW]
[ROW][C]3[/C][C]0.005356[/C][C]0.0411[/C][C]0.483661[/C][/ROW]
[ROW][C]4[/C][C]-0.084512[/C][C]-0.6491[/C][C]0.259381[/C][/ROW]
[ROW][C]5[/C][C]0.096608[/C][C]0.7421[/C][C]0.230498[/C][/ROW]
[ROW][C]6[/C][C]-0.016336[/C][C]-0.1255[/C][C]0.450285[/C][/ROW]
[ROW][C]7[/C][C]-0.086927[/C][C]-0.6677[/C][C]0.253465[/C][/ROW]
[ROW][C]8[/C][C]0.042889[/C][C]0.3294[/C][C]0.371495[/C][/ROW]
[ROW][C]9[/C][C]0.075011[/C][C]0.5762[/C][C]0.283347[/C][/ROW]
[ROW][C]10[/C][C]-0.226283[/C][C]-1.7381[/C][C]0.043704[/C][/ROW]
[ROW][C]11[/C][C]0.385371[/C][C]2.9601[/C][C]0.002212[/C][/ROW]
[ROW][C]12[/C][C]-0.434989[/C][C]-3.3412[/C][C]0.000726[/C][/ROW]
[ROW][C]13[/C][C]0.248454[/C][C]1.9084[/C][C]0.030604[/C][/ROW]
[ROW][C]14[/C][C]-0.041019[/C][C]-0.3151[/C][C]0.376909[/C][/ROW]
[ROW][C]15[/C][C]-0.011111[/C][C]-0.0853[/C][C]0.466139[/C][/ROW]
[ROW][C]16[/C][C]-0.013262[/C][C]-0.1019[/C][C]0.459603[/C][/ROW]
[ROW][C]17[/C][C]-0.017221[/C][C]-0.1323[/C][C]0.447609[/C][/ROW]
[ROW][C]18[/C][C]0.090465[/C][C]0.6949[/C][C]0.244931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230123&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230123&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
1-0.692354-5.31811e-06
20.2314561.77780.040291
30.0053560.04110.483661
4-0.084512-0.64910.259381
50.0966080.74210.230498
6-0.016336-0.12550.450285
7-0.086927-0.66770.253465
80.0428890.32940.371495
90.0750110.57620.283347
10-0.226283-1.73810.043704
110.3853712.96010.002212
12-0.434989-3.34120.000726
130.2484541.90840.030604
14-0.041019-0.31510.376909
15-0.011111-0.08530.466139
16-0.013262-0.10190.459603
17-0.017221-0.13230.447609
180.0904650.69490.244931







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.692354-5.31811e-06
2-0.476138-3.65730.000272
3-0.217952-1.67410.0497
4-0.176331-1.35440.090383
5-0.062089-0.47690.317592
60.1150670.88380.190184
70.0047510.03650.485506
8-0.191178-1.46850.073645
9-0.043298-0.33260.370317
10-0.334295-2.56780.006394
110.1173320.90120.185562
12-0.062268-0.47830.317106
13-0.205152-1.57580.060209
14-0.244043-1.87450.032905
15-0.097677-0.75030.228036
16-0.157624-1.21070.115413
17-0.296038-2.27390.013312
18-0.045629-0.35050.363612

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.692354 & -5.3181 & 1e-06 \tabularnewline
2 & -0.476138 & -3.6573 & 0.000272 \tabularnewline
3 & -0.217952 & -1.6741 & 0.0497 \tabularnewline
4 & -0.176331 & -1.3544 & 0.090383 \tabularnewline
5 & -0.062089 & -0.4769 & 0.317592 \tabularnewline
6 & 0.115067 & 0.8838 & 0.190184 \tabularnewline
7 & 0.004751 & 0.0365 & 0.485506 \tabularnewline
8 & -0.191178 & -1.4685 & 0.073645 \tabularnewline
9 & -0.043298 & -0.3326 & 0.370317 \tabularnewline
10 & -0.334295 & -2.5678 & 0.006394 \tabularnewline
11 & 0.117332 & 0.9012 & 0.185562 \tabularnewline
12 & -0.062268 & -0.4783 & 0.317106 \tabularnewline
13 & -0.205152 & -1.5758 & 0.060209 \tabularnewline
14 & -0.244043 & -1.8745 & 0.032905 \tabularnewline
15 & -0.097677 & -0.7503 & 0.228036 \tabularnewline
16 & -0.157624 & -1.2107 & 0.115413 \tabularnewline
17 & -0.296038 & -2.2739 & 0.013312 \tabularnewline
18 & -0.045629 & -0.3505 & 0.363612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230123&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]-0.692354[/C][C]-5.3181[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.476138[/C][C]-3.6573[/C][C]0.000272[/C][/ROW]
[ROW][C]3[/C][C]-0.217952[/C][C]-1.6741[/C][C]0.0497[/C][/ROW]
[ROW][C]4[/C][C]-0.176331[/C][C]-1.3544[/C][C]0.090383[/C][/ROW]
[ROW][C]5[/C][C]-0.062089[/C][C]-0.4769[/C][C]0.317592[/C][/ROW]
[ROW][C]6[/C][C]0.115067[/C][C]0.8838[/C][C]0.190184[/C][/ROW]
[ROW][C]7[/C][C]0.004751[/C][C]0.0365[/C][C]0.485506[/C][/ROW]
[ROW][C]8[/C][C]-0.191178[/C][C]-1.4685[/C][C]0.073645[/C][/ROW]
[ROW][C]9[/C][C]-0.043298[/C][C]-0.3326[/C][C]0.370317[/C][/ROW]
[ROW][C]10[/C][C]-0.334295[/C][C]-2.5678[/C][C]0.006394[/C][/ROW]
[ROW][C]11[/C][C]0.117332[/C][C]0.9012[/C][C]0.185562[/C][/ROW]
[ROW][C]12[/C][C]-0.062268[/C][C]-0.4783[/C][C]0.317106[/C][/ROW]
[ROW][C]13[/C][C]-0.205152[/C][C]-1.5758[/C][C]0.060209[/C][/ROW]
[ROW][C]14[/C][C]-0.244043[/C][C]-1.8745[/C][C]0.032905[/C][/ROW]
[ROW][C]15[/C][C]-0.097677[/C][C]-0.7503[/C][C]0.228036[/C][/ROW]
[ROW][C]16[/C][C]-0.157624[/C][C]-1.2107[/C][C]0.115413[/C][/ROW]
[ROW][C]17[/C][C]-0.296038[/C][C]-2.2739[/C][C]0.013312[/C][/ROW]
[ROW][C]18[/C][C]-0.045629[/C][C]-0.3505[/C][C]0.363612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230123&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230123&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
1-0.692354-5.31811e-06
2-0.476138-3.65730.000272
3-0.217952-1.67410.0497
4-0.176331-1.35440.090383
5-0.062089-0.47690.317592
60.1150670.88380.190184
70.0047510.03650.485506
8-0.191178-1.46850.073645
9-0.043298-0.33260.370317
10-0.334295-2.56780.006394
110.1173320.90120.185562
12-0.062268-0.47830.317106
13-0.205152-1.57580.060209
14-0.244043-1.87450.032905
15-0.097677-0.75030.228036
16-0.157624-1.21070.115413
17-0.296038-2.27390.013312
18-0.045629-0.35050.363612



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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)
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')