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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 16:29:18 -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/t1386192575plys2fzujqtlzf5.htm/, Retrieved Fri, 29 Mar 2024 14:18:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230830, Retrieved Fri, 29 Mar 2024 14:18:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
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 21:29:18] [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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230830&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230830&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230830&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'George Udny Yule' @ yule.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.227768-2.46370.007603
2-0.162023-1.75250.04115
30.0093120.10070.45997
4-0.084489-0.91390.181328
50.097951.05950.145779
6-0.052215-0.56480.28665
7-0.139214-1.50580.067403
80.1726831.86790.032142
9-0.115815-1.25270.106401
10-0.135459-1.46520.072773
110.0823510.89080.187442
120.1536171.66160.049633
13-0.00816-0.08830.464909
140.0514120.55610.289601
15-0.136737-1.4790.070909
160.0142660.15430.438814
170.0179660.19430.423128
18-0.07598-0.82190.206417
190.048680.52660.299751
200.03580.38720.349644

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.227768 & -2.4637 & 0.007603 \tabularnewline
2 & -0.162023 & -1.7525 & 0.04115 \tabularnewline
3 & 0.009312 & 0.1007 & 0.45997 \tabularnewline
4 & -0.084489 & -0.9139 & 0.181328 \tabularnewline
5 & 0.09795 & 1.0595 & 0.145779 \tabularnewline
6 & -0.052215 & -0.5648 & 0.28665 \tabularnewline
7 & -0.139214 & -1.5058 & 0.067403 \tabularnewline
8 & 0.172683 & 1.8679 & 0.032142 \tabularnewline
9 & -0.115815 & -1.2527 & 0.106401 \tabularnewline
10 & -0.135459 & -1.4652 & 0.072773 \tabularnewline
11 & 0.082351 & 0.8908 & 0.187442 \tabularnewline
12 & 0.153617 & 1.6616 & 0.049633 \tabularnewline
13 & -0.00816 & -0.0883 & 0.464909 \tabularnewline
14 & 0.051412 & 0.5561 & 0.289601 \tabularnewline
15 & -0.136737 & -1.479 & 0.070909 \tabularnewline
16 & 0.014266 & 0.1543 & 0.438814 \tabularnewline
17 & 0.017966 & 0.1943 & 0.423128 \tabularnewline
18 & -0.07598 & -0.8219 & 0.206417 \tabularnewline
19 & 0.04868 & 0.5266 & 0.299751 \tabularnewline
20 & 0.0358 & 0.3872 & 0.349644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230830&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]-0.227768[/C][C]-2.4637[/C][C]0.007603[/C][/ROW]
[ROW][C]2[/C][C]-0.162023[/C][C]-1.7525[/C][C]0.04115[/C][/ROW]
[ROW][C]3[/C][C]0.009312[/C][C]0.1007[/C][C]0.45997[/C][/ROW]
[ROW][C]4[/C][C]-0.084489[/C][C]-0.9139[/C][C]0.181328[/C][/ROW]
[ROW][C]5[/C][C]0.09795[/C][C]1.0595[/C][C]0.145779[/C][/ROW]
[ROW][C]6[/C][C]-0.052215[/C][C]-0.5648[/C][C]0.28665[/C][/ROW]
[ROW][C]7[/C][C]-0.139214[/C][C]-1.5058[/C][C]0.067403[/C][/ROW]
[ROW][C]8[/C][C]0.172683[/C][C]1.8679[/C][C]0.032142[/C][/ROW]
[ROW][C]9[/C][C]-0.115815[/C][C]-1.2527[/C][C]0.106401[/C][/ROW]
[ROW][C]10[/C][C]-0.135459[/C][C]-1.4652[/C][C]0.072773[/C][/ROW]
[ROW][C]11[/C][C]0.082351[/C][C]0.8908[/C][C]0.187442[/C][/ROW]
[ROW][C]12[/C][C]0.153617[/C][C]1.6616[/C][C]0.049633[/C][/ROW]
[ROW][C]13[/C][C]-0.00816[/C][C]-0.0883[/C][C]0.464909[/C][/ROW]
[ROW][C]14[/C][C]0.051412[/C][C]0.5561[/C][C]0.289601[/C][/ROW]
[ROW][C]15[/C][C]-0.136737[/C][C]-1.479[/C][C]0.070909[/C][/ROW]
[ROW][C]16[/C][C]0.014266[/C][C]0.1543[/C][C]0.438814[/C][/ROW]
[ROW][C]17[/C][C]0.017966[/C][C]0.1943[/C][C]0.423128[/C][/ROW]
[ROW][C]18[/C][C]-0.07598[/C][C]-0.8219[/C][C]0.206417[/C][/ROW]
[ROW][C]19[/C][C]0.04868[/C][C]0.5266[/C][C]0.299751[/C][/ROW]
[ROW][C]20[/C][C]0.0358[/C][C]0.3872[/C][C]0.349644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230830&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230830&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
1-0.227768-2.46370.007603
2-0.162023-1.75250.04115
30.0093120.10070.45997
4-0.084489-0.91390.181328
50.097951.05950.145779
6-0.052215-0.56480.28665
7-0.139214-1.50580.067403
80.1726831.86790.032142
9-0.115815-1.25270.106401
10-0.135459-1.46520.072773
110.0823510.89080.187442
120.1536171.66160.049633
13-0.00816-0.08830.464909
140.0514120.55610.289601
15-0.136737-1.4790.070909
160.0142660.15430.438814
170.0179660.19430.423128
18-0.07598-0.82190.206417
190.048680.52660.299751
200.03580.38720.349644







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.227768-2.46370.007603
2-0.225605-2.44030.008087
3-0.097018-1.04940.148077
4-0.162357-1.75620.040839
50.0153270.16580.434307
6-0.076947-0.83230.203466
7-0.180832-1.9560.026425
80.0593960.64250.260915
9-0.131012-1.41710.079554
10-0.224211-2.42520.008414
11-0.104712-1.13260.129843
120.1092071.18130.119948
13-0.009017-0.09750.461233
140.1041551.12660.131107
15-0.040606-0.43920.330657
16-0.051155-0.55330.290547
17-0.066191-0.7160.23772
18-0.067389-0.72890.233753
19-0.030939-0.33470.369242
20-0.01527-0.16520.434548

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.227768 & -2.4637 & 0.007603 \tabularnewline
2 & -0.225605 & -2.4403 & 0.008087 \tabularnewline
3 & -0.097018 & -1.0494 & 0.148077 \tabularnewline
4 & -0.162357 & -1.7562 & 0.040839 \tabularnewline
5 & 0.015327 & 0.1658 & 0.434307 \tabularnewline
6 & -0.076947 & -0.8323 & 0.203466 \tabularnewline
7 & -0.180832 & -1.956 & 0.026425 \tabularnewline
8 & 0.059396 & 0.6425 & 0.260915 \tabularnewline
9 & -0.131012 & -1.4171 & 0.079554 \tabularnewline
10 & -0.224211 & -2.4252 & 0.008414 \tabularnewline
11 & -0.104712 & -1.1326 & 0.129843 \tabularnewline
12 & 0.109207 & 1.1813 & 0.119948 \tabularnewline
13 & -0.009017 & -0.0975 & 0.461233 \tabularnewline
14 & 0.104155 & 1.1266 & 0.131107 \tabularnewline
15 & -0.040606 & -0.4392 & 0.330657 \tabularnewline
16 & -0.051155 & -0.5533 & 0.290547 \tabularnewline
17 & -0.066191 & -0.716 & 0.23772 \tabularnewline
18 & -0.067389 & -0.7289 & 0.233753 \tabularnewline
19 & -0.030939 & -0.3347 & 0.369242 \tabularnewline
20 & -0.01527 & -0.1652 & 0.434548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230830&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]-0.227768[/C][C]-2.4637[/C][C]0.007603[/C][/ROW]
[ROW][C]2[/C][C]-0.225605[/C][C]-2.4403[/C][C]0.008087[/C][/ROW]
[ROW][C]3[/C][C]-0.097018[/C][C]-1.0494[/C][C]0.148077[/C][/ROW]
[ROW][C]4[/C][C]-0.162357[/C][C]-1.7562[/C][C]0.040839[/C][/ROW]
[ROW][C]5[/C][C]0.015327[/C][C]0.1658[/C][C]0.434307[/C][/ROW]
[ROW][C]6[/C][C]-0.076947[/C][C]-0.8323[/C][C]0.203466[/C][/ROW]
[ROW][C]7[/C][C]-0.180832[/C][C]-1.956[/C][C]0.026425[/C][/ROW]
[ROW][C]8[/C][C]0.059396[/C][C]0.6425[/C][C]0.260915[/C][/ROW]
[ROW][C]9[/C][C]-0.131012[/C][C]-1.4171[/C][C]0.079554[/C][/ROW]
[ROW][C]10[/C][C]-0.224211[/C][C]-2.4252[/C][C]0.008414[/C][/ROW]
[ROW][C]11[/C][C]-0.104712[/C][C]-1.1326[/C][C]0.129843[/C][/ROW]
[ROW][C]12[/C][C]0.109207[/C][C]1.1813[/C][C]0.119948[/C][/ROW]
[ROW][C]13[/C][C]-0.009017[/C][C]-0.0975[/C][C]0.461233[/C][/ROW]
[ROW][C]14[/C][C]0.104155[/C][C]1.1266[/C][C]0.131107[/C][/ROW]
[ROW][C]15[/C][C]-0.040606[/C][C]-0.4392[/C][C]0.330657[/C][/ROW]
[ROW][C]16[/C][C]-0.051155[/C][C]-0.5533[/C][C]0.290547[/C][/ROW]
[ROW][C]17[/C][C]-0.066191[/C][C]-0.716[/C][C]0.23772[/C][/ROW]
[ROW][C]18[/C][C]-0.067389[/C][C]-0.7289[/C][C]0.233753[/C][/ROW]
[ROW][C]19[/C][C]-0.030939[/C][C]-0.3347[/C][C]0.369242[/C][/ROW]
[ROW][C]20[/C][C]-0.01527[/C][C]-0.1652[/C][C]0.434548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230830&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230830&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
1-0.227768-2.46370.007603
2-0.225605-2.44030.008087
3-0.097018-1.04940.148077
4-0.162357-1.75620.040839
50.0153270.16580.434307
6-0.076947-0.83230.203466
7-0.180832-1.9560.026425
80.0593960.64250.260915
9-0.131012-1.41710.079554
10-0.224211-2.42520.008414
11-0.104712-1.13260.129843
120.1092071.18130.119948
13-0.009017-0.09750.461233
140.1041551.12660.131107
15-0.040606-0.43920.330657
16-0.051155-0.55330.290547
17-0.066191-0.7160.23772
18-0.067389-0.72890.233753
19-0.030939-0.33470.369242
20-0.01527-0.16520.434548



Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 0.1 ; 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')