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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 computationWed, 04 Dec 2013 16:30:50 -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/04/t1386192662dri5do7x9357jy2.htm/, Retrieved Thu, 28 Mar 2024 19:04:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230832, Retrieved Thu, 28 Mar 2024 19:04:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD    [(Partial) Autocorrelation Function] [] [2013-12-04 21:30:50] [be82f1b59bd963d0cf04f5c957f6be33] [Current]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230832&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]5 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=230832&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230832&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.228913-2.47610.007357
2-0.162442-1.75710.04076
3-0.004371-0.04730.481184
4-0.078157-0.84540.199809
50.1017671.10080.136626
6-0.039542-0.42770.334823
7-0.133881-1.44810.075126
80.1624221.75690.040778
9-0.111506-1.20610.115103
10-0.119655-1.29430.099061
110.0825540.8930.186857
120.1444851.56280.060395
13-0.029119-0.3150.376673
140.0535320.5790.281839
15-0.135889-1.46990.072141
160.0227310.24590.403107
170.0075280.08140.467622
18-0.063699-0.6890.246091
190.0511420.55320.290597
200.0248470.26880.394294

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.228913 & -2.4761 & 0.007357 \tabularnewline
2 & -0.162442 & -1.7571 & 0.04076 \tabularnewline
3 & -0.004371 & -0.0473 & 0.481184 \tabularnewline
4 & -0.078157 & -0.8454 & 0.199809 \tabularnewline
5 & 0.101767 & 1.1008 & 0.136626 \tabularnewline
6 & -0.039542 & -0.4277 & 0.334823 \tabularnewline
7 & -0.133881 & -1.4481 & 0.075126 \tabularnewline
8 & 0.162422 & 1.7569 & 0.040778 \tabularnewline
9 & -0.111506 & -1.2061 & 0.115103 \tabularnewline
10 & -0.119655 & -1.2943 & 0.099061 \tabularnewline
11 & 0.082554 & 0.893 & 0.186857 \tabularnewline
12 & 0.144485 & 1.5628 & 0.060395 \tabularnewline
13 & -0.029119 & -0.315 & 0.376673 \tabularnewline
14 & 0.053532 & 0.579 & 0.281839 \tabularnewline
15 & -0.135889 & -1.4699 & 0.072141 \tabularnewline
16 & 0.022731 & 0.2459 & 0.403107 \tabularnewline
17 & 0.007528 & 0.0814 & 0.467622 \tabularnewline
18 & -0.063699 & -0.689 & 0.246091 \tabularnewline
19 & 0.051142 & 0.5532 & 0.290597 \tabularnewline
20 & 0.024847 & 0.2688 & 0.394294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230832&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]-0.228913[/C][C]-2.4761[/C][C]0.007357[/C][/ROW]
[ROW][C]2[/C][C]-0.162442[/C][C]-1.7571[/C][C]0.04076[/C][/ROW]
[ROW][C]3[/C][C]-0.004371[/C][C]-0.0473[/C][C]0.481184[/C][/ROW]
[ROW][C]4[/C][C]-0.078157[/C][C]-0.8454[/C][C]0.199809[/C][/ROW]
[ROW][C]5[/C][C]0.101767[/C][C]1.1008[/C][C]0.136626[/C][/ROW]
[ROW][C]6[/C][C]-0.039542[/C][C]-0.4277[/C][C]0.334823[/C][/ROW]
[ROW][C]7[/C][C]-0.133881[/C][C]-1.4481[/C][C]0.075126[/C][/ROW]
[ROW][C]8[/C][C]0.162422[/C][C]1.7569[/C][C]0.040778[/C][/ROW]
[ROW][C]9[/C][C]-0.111506[/C][C]-1.2061[/C][C]0.115103[/C][/ROW]
[ROW][C]10[/C][C]-0.119655[/C][C]-1.2943[/C][C]0.099061[/C][/ROW]
[ROW][C]11[/C][C]0.082554[/C][C]0.893[/C][C]0.186857[/C][/ROW]
[ROW][C]12[/C][C]0.144485[/C][C]1.5628[/C][C]0.060395[/C][/ROW]
[ROW][C]13[/C][C]-0.029119[/C][C]-0.315[/C][C]0.376673[/C][/ROW]
[ROW][C]14[/C][C]0.053532[/C][C]0.579[/C][C]0.281839[/C][/ROW]
[ROW][C]15[/C][C]-0.135889[/C][C]-1.4699[/C][C]0.072141[/C][/ROW]
[ROW][C]16[/C][C]0.022731[/C][C]0.2459[/C][C]0.403107[/C][/ROW]
[ROW][C]17[/C][C]0.007528[/C][C]0.0814[/C][C]0.467622[/C][/ROW]
[ROW][C]18[/C][C]-0.063699[/C][C]-0.689[/C][C]0.246091[/C][/ROW]
[ROW][C]19[/C][C]0.051142[/C][C]0.5532[/C][C]0.290597[/C][/ROW]
[ROW][C]20[/C][C]0.024847[/C][C]0.2688[/C][C]0.394294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230832&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230832&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
1-0.228913-2.47610.007357
2-0.162442-1.75710.04076
3-0.004371-0.04730.481184
4-0.078157-0.84540.199809
50.1017671.10080.136626
6-0.039542-0.42770.334823
7-0.133881-1.44810.075126
80.1624221.75690.040778
9-0.111506-1.20610.115103
10-0.119655-1.29430.099061
110.0825540.8930.186857
120.1444851.56280.060395
13-0.029119-0.3150.376673
140.0535320.5790.281839
15-0.135889-1.46990.072141
160.0227310.24590.403107
170.0075280.08140.467622
18-0.063699-0.6890.246091
190.0511420.55320.290597
200.0248470.26880.394294







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.228913-2.47610.007357
2-0.226724-2.45240.007834
3-0.113348-1.2260.111322
4-0.166163-1.79730.037431
50.0119360.12910.448749
6-0.063031-0.68180.248362
7-0.168807-1.82590.035206
80.0617990.66850.252579
9-0.122249-1.32230.09432
10-0.202588-2.19130.015205
11-0.0831-0.89890.185286
120.1136691.22950.110672
13-0.022986-0.24860.402043
140.10031.08490.140095
15-0.043789-0.47370.318315
16-0.037031-0.40060.344739
17-0.070407-0.76160.223924
18-0.060585-0.65530.256773
19-0.027498-0.29740.383332
20-0.021363-0.23110.408828

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.228913 & -2.4761 & 0.007357 \tabularnewline
2 & -0.226724 & -2.4524 & 0.007834 \tabularnewline
3 & -0.113348 & -1.226 & 0.111322 \tabularnewline
4 & -0.166163 & -1.7973 & 0.037431 \tabularnewline
5 & 0.011936 & 0.1291 & 0.448749 \tabularnewline
6 & -0.063031 & -0.6818 & 0.248362 \tabularnewline
7 & -0.168807 & -1.8259 & 0.035206 \tabularnewline
8 & 0.061799 & 0.6685 & 0.252579 \tabularnewline
9 & -0.122249 & -1.3223 & 0.09432 \tabularnewline
10 & -0.202588 & -2.1913 & 0.015205 \tabularnewline
11 & -0.0831 & -0.8989 & 0.185286 \tabularnewline
12 & 0.113669 & 1.2295 & 0.110672 \tabularnewline
13 & -0.022986 & -0.2486 & 0.402043 \tabularnewline
14 & 0.1003 & 1.0849 & 0.140095 \tabularnewline
15 & -0.043789 & -0.4737 & 0.318315 \tabularnewline
16 & -0.037031 & -0.4006 & 0.344739 \tabularnewline
17 & -0.070407 & -0.7616 & 0.223924 \tabularnewline
18 & -0.060585 & -0.6553 & 0.256773 \tabularnewline
19 & -0.027498 & -0.2974 & 0.383332 \tabularnewline
20 & -0.021363 & -0.2311 & 0.408828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230832&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]-0.228913[/C][C]-2.4761[/C][C]0.007357[/C][/ROW]
[ROW][C]2[/C][C]-0.226724[/C][C]-2.4524[/C][C]0.007834[/C][/ROW]
[ROW][C]3[/C][C]-0.113348[/C][C]-1.226[/C][C]0.111322[/C][/ROW]
[ROW][C]4[/C][C]-0.166163[/C][C]-1.7973[/C][C]0.037431[/C][/ROW]
[ROW][C]5[/C][C]0.011936[/C][C]0.1291[/C][C]0.448749[/C][/ROW]
[ROW][C]6[/C][C]-0.063031[/C][C]-0.6818[/C][C]0.248362[/C][/ROW]
[ROW][C]7[/C][C]-0.168807[/C][C]-1.8259[/C][C]0.035206[/C][/ROW]
[ROW][C]8[/C][C]0.061799[/C][C]0.6685[/C][C]0.252579[/C][/ROW]
[ROW][C]9[/C][C]-0.122249[/C][C]-1.3223[/C][C]0.09432[/C][/ROW]
[ROW][C]10[/C][C]-0.202588[/C][C]-2.1913[/C][C]0.015205[/C][/ROW]
[ROW][C]11[/C][C]-0.0831[/C][C]-0.8989[/C][C]0.185286[/C][/ROW]
[ROW][C]12[/C][C]0.113669[/C][C]1.2295[/C][C]0.110672[/C][/ROW]
[ROW][C]13[/C][C]-0.022986[/C][C]-0.2486[/C][C]0.402043[/C][/ROW]
[ROW][C]14[/C][C]0.1003[/C][C]1.0849[/C][C]0.140095[/C][/ROW]
[ROW][C]15[/C][C]-0.043789[/C][C]-0.4737[/C][C]0.318315[/C][/ROW]
[ROW][C]16[/C][C]-0.037031[/C][C]-0.4006[/C][C]0.344739[/C][/ROW]
[ROW][C]17[/C][C]-0.070407[/C][C]-0.7616[/C][C]0.223924[/C][/ROW]
[ROW][C]18[/C][C]-0.060585[/C][C]-0.6553[/C][C]0.256773[/C][/ROW]
[ROW][C]19[/C][C]-0.027498[/C][C]-0.2974[/C][C]0.383332[/C][/ROW]
[ROW][C]20[/C][C]-0.021363[/C][C]-0.2311[/C][C]0.408828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230832&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230832&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
1-0.228913-2.47610.007357
2-0.226724-2.45240.007834
3-0.113348-1.2260.111322
4-0.166163-1.79730.037431
50.0119360.12910.448749
6-0.063031-0.68180.248362
7-0.168807-1.82590.035206
80.0617990.66850.252579
9-0.122249-1.32230.09432
10-0.202588-2.19130.015205
11-0.0831-0.89890.185286
120.1136691.22950.110672
13-0.022986-0.24860.402043
140.10031.08490.140095
15-0.043789-0.47370.318315
16-0.037031-0.40060.344739
17-0.070407-0.76160.223924
18-0.060585-0.65530.256773
19-0.027498-0.29740.383332
20-0.021363-0.23110.408828



Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 0.0 ; par3 = 1 ; 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)
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')