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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 computationSun, 16 Dec 2012 14:22:24 -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/2012/Dec/16/t1355685808q35lhw0qif56jby.htm/, Retrieved Thu, 28 Mar 2024 13:35:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200557, Retrieved Thu, 28 Mar 2024 13:35:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- R PD        [Univariate Data Series] [Paper : tijdreeks...] [2012-12-16 12:14:11] [5423d5951ef739cb88e60f5b30c308a9]
- RMPD            [(Partial) Autocorrelation Function] [paper: deel 4 aut...] [2012-12-16 19:22:24] [292b44c97cfd231f70174a072f53fc18] [Current]
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Dataseries X:
1.894
1.757
3.582
5.321
5.561
5.907
4.944
4.966
3.258
1.964
1.743
1.262
2.086
1.793
3.548
5.672
6.084
4.914
4.990
5.139
3.218
2.179
2.238
1.442
2.205
2.025
3.531
4.977
7.998
4.880
5.231
5.202
3.303
2.683
2.202
1.376
2.422
1.997
3.163
5.964
5.657
6.415
6.208
4.500
2.939
2.702
2.090
1.504
2.549
1.931
3.013
6.204
5.788
5.611
5.594
4.647
3.490
2.487
1.992
1.507
2.306
2.002
3.075
5.331
5.589
5.813
4.876
4.665
3.601
2.192
2.111
1.580
2.288
1.993
3.228
5.000
5.480
5.770
4.962
4.685
3.607
2.222
2.467
1.594
2.228
1.910
3.157
4.809
6.249
4.607
4.975
4.784
3.028
2.461
2.218
1.351
2.070
1.887
3.024
4.596
6.398
4.459
5.382
4.359
2.687
2.249
2.154
1.169
2.429
1.762
2.846
5.627
5.749
4.502
5.720
4.403
2.867
2.635
2.059
1.511
2.359
1.741
2.917
6.249
5.760
6.250
5.134
4.831
3.695
2.462
2.146
1.579




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200557&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200557&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200557&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.7295548.38190
20.3858734.43331e-05
30.0006330.00730.497103
4-0.433131-4.97631e-06
5-0.728574-8.37070
6-0.813002-9.34070
7-0.72075-8.28080
8-0.388618-4.46499e-06
90.030830.35420.361875
100.3663434.2092.4e-05
110.6874737.89850
120.8566259.84190
130.6651797.64230
140.3596344.13193.2e-05
15-0.012164-0.13970.444536
16-0.389613-4.47638e-06
17-0.642634-7.38330
18-0.738432-8.48390
19-0.653104-7.50360
20-0.345582-3.97045.9e-05
210.0071440.08210.467353

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.729554 & 8.3819 & 0 \tabularnewline
2 & 0.385873 & 4.4333 & 1e-05 \tabularnewline
3 & 0.000633 & 0.0073 & 0.497103 \tabularnewline
4 & -0.433131 & -4.9763 & 1e-06 \tabularnewline
5 & -0.728574 & -8.3707 & 0 \tabularnewline
6 & -0.813002 & -9.3407 & 0 \tabularnewline
7 & -0.72075 & -8.2808 & 0 \tabularnewline
8 & -0.388618 & -4.4649 & 9e-06 \tabularnewline
9 & 0.03083 & 0.3542 & 0.361875 \tabularnewline
10 & 0.366343 & 4.209 & 2.4e-05 \tabularnewline
11 & 0.687473 & 7.8985 & 0 \tabularnewline
12 & 0.856625 & 9.8419 & 0 \tabularnewline
13 & 0.665179 & 7.6423 & 0 \tabularnewline
14 & 0.359634 & 4.1319 & 3.2e-05 \tabularnewline
15 & -0.012164 & -0.1397 & 0.444536 \tabularnewline
16 & -0.389613 & -4.4763 & 8e-06 \tabularnewline
17 & -0.642634 & -7.3833 & 0 \tabularnewline
18 & -0.738432 & -8.4839 & 0 \tabularnewline
19 & -0.653104 & -7.5036 & 0 \tabularnewline
20 & -0.345582 & -3.9704 & 5.9e-05 \tabularnewline
21 & 0.007144 & 0.0821 & 0.467353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200557&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]0.729554[/C][C]8.3819[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.385873[/C][C]4.4333[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.000633[/C][C]0.0073[/C][C]0.497103[/C][/ROW]
[ROW][C]4[/C][C]-0.433131[/C][C]-4.9763[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.728574[/C][C]-8.3707[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.813002[/C][C]-9.3407[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.72075[/C][C]-8.2808[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.388618[/C][C]-4.4649[/C][C]9e-06[/C][/ROW]
[ROW][C]9[/C][C]0.03083[/C][C]0.3542[/C][C]0.361875[/C][/ROW]
[ROW][C]10[/C][C]0.366343[/C][C]4.209[/C][C]2.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.687473[/C][C]7.8985[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.856625[/C][C]9.8419[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.665179[/C][C]7.6423[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.359634[/C][C]4.1319[/C][C]3.2e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.012164[/C][C]-0.1397[/C][C]0.444536[/C][/ROW]
[ROW][C]16[/C][C]-0.389613[/C][C]-4.4763[/C][C]8e-06[/C][/ROW]
[ROW][C]17[/C][C]-0.642634[/C][C]-7.3833[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.738432[/C][C]-8.4839[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.653104[/C][C]-7.5036[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.345582[/C][C]-3.9704[/C][C]5.9e-05[/C][/ROW]
[ROW][C]21[/C][C]0.007144[/C][C]0.0821[/C][C]0.467353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200557&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200557&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
10.7295548.38190
20.3858734.43331e-05
30.0006330.00730.497103
4-0.433131-4.97631e-06
5-0.728574-8.37070
6-0.813002-9.34070
7-0.72075-8.28080
8-0.388618-4.46499e-06
90.030830.35420.361875
100.3663434.2092.4e-05
110.6874737.89850
120.8566259.84190
130.6651797.64230
140.3596344.13193.2e-05
15-0.012164-0.13970.444536
16-0.389613-4.47638e-06
17-0.642634-7.38330
18-0.738432-8.48390
19-0.653104-7.50360
20-0.345582-3.97045.9e-05
210.0071440.08210.467353







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.7295548.38190
2-0.312935-3.59530.000228
3-0.333398-3.83049.8e-05
4-0.514378-5.90980
5-0.357729-4.113.5e-05
6-0.26746-3.07290.001288
7-0.312997-3.59610.000228
8-0.020074-0.23060.40898
9-0.008544-0.09820.460977
10-0.213708-2.45530.007689
110.1413141.62360.053426
120.3517834.04174.5e-05
13-0.172154-1.97790.025012
14-0.066494-0.7640.223126
150.0279360.3210.374374
160.1579881.81510.035886
170.0710280.81610.20797
180.0043410.04990.48015
190.0272550.31310.377337
200.0160920.18490.4268
21-0.095615-1.09850.136986

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.729554 & 8.3819 & 0 \tabularnewline
2 & -0.312935 & -3.5953 & 0.000228 \tabularnewline
3 & -0.333398 & -3.8304 & 9.8e-05 \tabularnewline
4 & -0.514378 & -5.9098 & 0 \tabularnewline
5 & -0.357729 & -4.11 & 3.5e-05 \tabularnewline
6 & -0.26746 & -3.0729 & 0.001288 \tabularnewline
7 & -0.312997 & -3.5961 & 0.000228 \tabularnewline
8 & -0.020074 & -0.2306 & 0.40898 \tabularnewline
9 & -0.008544 & -0.0982 & 0.460977 \tabularnewline
10 & -0.213708 & -2.4553 & 0.007689 \tabularnewline
11 & 0.141314 & 1.6236 & 0.053426 \tabularnewline
12 & 0.351783 & 4.0417 & 4.5e-05 \tabularnewline
13 & -0.172154 & -1.9779 & 0.025012 \tabularnewline
14 & -0.066494 & -0.764 & 0.223126 \tabularnewline
15 & 0.027936 & 0.321 & 0.374374 \tabularnewline
16 & 0.157988 & 1.8151 & 0.035886 \tabularnewline
17 & 0.071028 & 0.8161 & 0.20797 \tabularnewline
18 & 0.004341 & 0.0499 & 0.48015 \tabularnewline
19 & 0.027255 & 0.3131 & 0.377337 \tabularnewline
20 & 0.016092 & 0.1849 & 0.4268 \tabularnewline
21 & -0.095615 & -1.0985 & 0.136986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200557&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]0.729554[/C][C]8.3819[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.312935[/C][C]-3.5953[/C][C]0.000228[/C][/ROW]
[ROW][C]3[/C][C]-0.333398[/C][C]-3.8304[/C][C]9.8e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.514378[/C][C]-5.9098[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.357729[/C][C]-4.11[/C][C]3.5e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.26746[/C][C]-3.0729[/C][C]0.001288[/C][/ROW]
[ROW][C]7[/C][C]-0.312997[/C][C]-3.5961[/C][C]0.000228[/C][/ROW]
[ROW][C]8[/C][C]-0.020074[/C][C]-0.2306[/C][C]0.40898[/C][/ROW]
[ROW][C]9[/C][C]-0.008544[/C][C]-0.0982[/C][C]0.460977[/C][/ROW]
[ROW][C]10[/C][C]-0.213708[/C][C]-2.4553[/C][C]0.007689[/C][/ROW]
[ROW][C]11[/C][C]0.141314[/C][C]1.6236[/C][C]0.053426[/C][/ROW]
[ROW][C]12[/C][C]0.351783[/C][C]4.0417[/C][C]4.5e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.172154[/C][C]-1.9779[/C][C]0.025012[/C][/ROW]
[ROW][C]14[/C][C]-0.066494[/C][C]-0.764[/C][C]0.223126[/C][/ROW]
[ROW][C]15[/C][C]0.027936[/C][C]0.321[/C][C]0.374374[/C][/ROW]
[ROW][C]16[/C][C]0.157988[/C][C]1.8151[/C][C]0.035886[/C][/ROW]
[ROW][C]17[/C][C]0.071028[/C][C]0.8161[/C][C]0.20797[/C][/ROW]
[ROW][C]18[/C][C]0.004341[/C][C]0.0499[/C][C]0.48015[/C][/ROW]
[ROW][C]19[/C][C]0.027255[/C][C]0.3131[/C][C]0.377337[/C][/ROW]
[ROW][C]20[/C][C]0.016092[/C][C]0.1849[/C][C]0.4268[/C][/ROW]
[ROW][C]21[/C][C]-0.095615[/C][C]-1.0985[/C][C]0.136986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200557&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200557&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
10.7295548.38190
2-0.312935-3.59530.000228
3-0.333398-3.83049.8e-05
4-0.514378-5.90980
5-0.357729-4.113.5e-05
6-0.26746-3.07290.001288
7-0.312997-3.59610.000228
8-0.020074-0.23060.40898
9-0.008544-0.09820.460977
10-0.213708-2.45530.007689
110.1413141.62360.053426
120.3517834.04174.5e-05
13-0.172154-1.97790.025012
14-0.066494-0.7640.223126
150.0279360.3210.374374
160.1579881.81510.035886
170.0710280.81610.20797
180.0043410.04990.48015
190.0272550.31310.377337
200.0160920.18490.4268
21-0.095615-1.09850.136986



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; 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)
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')