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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 computationFri, 16 Jan 2015 09:38:58 +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/Jan/16/t1421401195phn60a8nuc1fxco.htm/, Retrieved Wed, 15 May 2024 07:55:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=273774, Retrieved Wed, 15 May 2024 07:55:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Two-Way ANOVA] [] [2015-01-16 09:20:27] [9922f47a08b670aeeb7c38448acbfea1]
- RMPD    [(Partial) Autocorrelation Function] [] [2015-01-16 09:38:58] [e9774d91d06602b4e3bbce6871390c37] [Current]
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Dataseries X:
67
72
74
62
56
66
65
59
61
69
74
69
66
68
58
64
66
57
68
62
59
73
61
61
57
58
57
67
81
79
76
78
74
67
84
85
79
82
87
90
87
93
92
82
80
79
77
72
65
73
76
77
76
76
76
75
78
73
80
77
83
84
85
81
84
83
83
88
92
92
89
82
73
81
91
80
81
82
84
87
85
74
81
82
86
85
82
86
88
86
83
81
81
81
82
86
85
87
89
90
90
92
86
86
82
80
79
77
79
76
78
78
77
72
75
79
81
86
88
97
94
96
94
91
92
93
93
87
84
80
78
75
73
81
76
77
71
71
78
67
76
68
82
64
71
81
69
63
70
77
75
76
68




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=273774&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=273774&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273774&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
10.7477468.8790
20.6265677.44010
30.5462166.4860
40.413214.90661e-06
50.3128673.71510.000146
60.1953082.31920.010912
70.1003621.19170.117683
8-0.005348-0.06350.474727
9-0.104387-1.23950.108606
10-0.203823-2.42030.008391
11-0.327497-3.88887.7e-05
12-0.496324-5.89350
13-0.428164-5.08421e-06
14-0.420464-4.99271e-06
15-0.391026-4.64324e-06
16-0.316806-3.76190.000123
17-0.310493-3.68690.000162
18-0.221103-2.62540.004804
19-0.146167-1.73560.042407
20-0.120374-1.42940.077557
21-0.050063-0.59450.276578

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.747746 & 8.879 & 0 \tabularnewline
2 & 0.626567 & 7.4401 & 0 \tabularnewline
3 & 0.546216 & 6.486 & 0 \tabularnewline
4 & 0.41321 & 4.9066 & 1e-06 \tabularnewline
5 & 0.312867 & 3.7151 & 0.000146 \tabularnewline
6 & 0.195308 & 2.3192 & 0.010912 \tabularnewline
7 & 0.100362 & 1.1917 & 0.117683 \tabularnewline
8 & -0.005348 & -0.0635 & 0.474727 \tabularnewline
9 & -0.104387 & -1.2395 & 0.108606 \tabularnewline
10 & -0.203823 & -2.4203 & 0.008391 \tabularnewline
11 & -0.327497 & -3.8888 & 7.7e-05 \tabularnewline
12 & -0.496324 & -5.8935 & 0 \tabularnewline
13 & -0.428164 & -5.0842 & 1e-06 \tabularnewline
14 & -0.420464 & -4.9927 & 1e-06 \tabularnewline
15 & -0.391026 & -4.6432 & 4e-06 \tabularnewline
16 & -0.316806 & -3.7619 & 0.000123 \tabularnewline
17 & -0.310493 & -3.6869 & 0.000162 \tabularnewline
18 & -0.221103 & -2.6254 & 0.004804 \tabularnewline
19 & -0.146167 & -1.7356 & 0.042407 \tabularnewline
20 & -0.120374 & -1.4294 & 0.077557 \tabularnewline
21 & -0.050063 & -0.5945 & 0.276578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273774&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]0.747746[/C][C]8.879[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.626567[/C][C]7.4401[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.546216[/C][C]6.486[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.41321[/C][C]4.9066[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.312867[/C][C]3.7151[/C][C]0.000146[/C][/ROW]
[ROW][C]6[/C][C]0.195308[/C][C]2.3192[/C][C]0.010912[/C][/ROW]
[ROW][C]7[/C][C]0.100362[/C][C]1.1917[/C][C]0.117683[/C][/ROW]
[ROW][C]8[/C][C]-0.005348[/C][C]-0.0635[/C][C]0.474727[/C][/ROW]
[ROW][C]9[/C][C]-0.104387[/C][C]-1.2395[/C][C]0.108606[/C][/ROW]
[ROW][C]10[/C][C]-0.203823[/C][C]-2.4203[/C][C]0.008391[/C][/ROW]
[ROW][C]11[/C][C]-0.327497[/C][C]-3.8888[/C][C]7.7e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.496324[/C][C]-5.8935[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.428164[/C][C]-5.0842[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.420464[/C][C]-4.9927[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]-0.391026[/C][C]-4.6432[/C][C]4e-06[/C][/ROW]
[ROW][C]16[/C][C]-0.316806[/C][C]-3.7619[/C][C]0.000123[/C][/ROW]
[ROW][C]17[/C][C]-0.310493[/C][C]-3.6869[/C][C]0.000162[/C][/ROW]
[ROW][C]18[/C][C]-0.221103[/C][C]-2.6254[/C][C]0.004804[/C][/ROW]
[ROW][C]19[/C][C]-0.146167[/C][C]-1.7356[/C][C]0.042407[/C][/ROW]
[ROW][C]20[/C][C]-0.120374[/C][C]-1.4294[/C][C]0.077557[/C][/ROW]
[ROW][C]21[/C][C]-0.050063[/C][C]-0.5945[/C][C]0.276578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273774&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273774&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
10.7477468.8790
20.6265677.44010
30.5462166.4860
40.413214.90661e-06
50.3128673.71510.000146
60.1953082.31920.010912
70.1003621.19170.117683
8-0.005348-0.06350.474727
9-0.104387-1.23950.108606
10-0.203823-2.42030.008391
11-0.327497-3.88887.7e-05
12-0.496324-5.89350
13-0.428164-5.08421e-06
14-0.420464-4.99271e-06
15-0.391026-4.64324e-06
16-0.316806-3.76190.000123
17-0.310493-3.68690.000162
18-0.221103-2.62540.004804
19-0.146167-1.73560.042407
20-0.120374-1.42940.077557
21-0.050063-0.59450.276578







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.7477468.8790
20.1529761.81650.03571
30.0812580.96490.168126
4-0.117636-1.39680.082327
5-0.043491-0.51640.303182
6-0.113856-1.3520.089276
7-0.045493-0.54020.294955
8-0.108787-1.29180.099275
9-0.086631-1.02870.152693
10-0.124259-1.47550.071155
11-0.186247-2.21160.014303
12-0.334175-3.96815.7e-05
130.2920183.46750.000348
140.0250980.2980.383063
150.1227851.4580.073533
160.0261270.31020.37842
17-0.103168-1.2250.1113
180.0667370.79250.214712
190.0687140.81590.207956
20-0.116615-1.38470.084161
210.048980.58160.280879

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.747746 & 8.879 & 0 \tabularnewline
2 & 0.152976 & 1.8165 & 0.03571 \tabularnewline
3 & 0.081258 & 0.9649 & 0.168126 \tabularnewline
4 & -0.117636 & -1.3968 & 0.082327 \tabularnewline
5 & -0.043491 & -0.5164 & 0.303182 \tabularnewline
6 & -0.113856 & -1.352 & 0.089276 \tabularnewline
7 & -0.045493 & -0.5402 & 0.294955 \tabularnewline
8 & -0.108787 & -1.2918 & 0.099275 \tabularnewline
9 & -0.086631 & -1.0287 & 0.152693 \tabularnewline
10 & -0.124259 & -1.4755 & 0.071155 \tabularnewline
11 & -0.186247 & -2.2116 & 0.014303 \tabularnewline
12 & -0.334175 & -3.9681 & 5.7e-05 \tabularnewline
13 & 0.292018 & 3.4675 & 0.000348 \tabularnewline
14 & 0.025098 & 0.298 & 0.383063 \tabularnewline
15 & 0.122785 & 1.458 & 0.073533 \tabularnewline
16 & 0.026127 & 0.3102 & 0.37842 \tabularnewline
17 & -0.103168 & -1.225 & 0.1113 \tabularnewline
18 & 0.066737 & 0.7925 & 0.214712 \tabularnewline
19 & 0.068714 & 0.8159 & 0.207956 \tabularnewline
20 & -0.116615 & -1.3847 & 0.084161 \tabularnewline
21 & 0.04898 & 0.5816 & 0.280879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273774&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]0.747746[/C][C]8.879[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.152976[/C][C]1.8165[/C][C]0.03571[/C][/ROW]
[ROW][C]3[/C][C]0.081258[/C][C]0.9649[/C][C]0.168126[/C][/ROW]
[ROW][C]4[/C][C]-0.117636[/C][C]-1.3968[/C][C]0.082327[/C][/ROW]
[ROW][C]5[/C][C]-0.043491[/C][C]-0.5164[/C][C]0.303182[/C][/ROW]
[ROW][C]6[/C][C]-0.113856[/C][C]-1.352[/C][C]0.089276[/C][/ROW]
[ROW][C]7[/C][C]-0.045493[/C][C]-0.5402[/C][C]0.294955[/C][/ROW]
[ROW][C]8[/C][C]-0.108787[/C][C]-1.2918[/C][C]0.099275[/C][/ROW]
[ROW][C]9[/C][C]-0.086631[/C][C]-1.0287[/C][C]0.152693[/C][/ROW]
[ROW][C]10[/C][C]-0.124259[/C][C]-1.4755[/C][C]0.071155[/C][/ROW]
[ROW][C]11[/C][C]-0.186247[/C][C]-2.2116[/C][C]0.014303[/C][/ROW]
[ROW][C]12[/C][C]-0.334175[/C][C]-3.9681[/C][C]5.7e-05[/C][/ROW]
[ROW][C]13[/C][C]0.292018[/C][C]3.4675[/C][C]0.000348[/C][/ROW]
[ROW][C]14[/C][C]0.025098[/C][C]0.298[/C][C]0.383063[/C][/ROW]
[ROW][C]15[/C][C]0.122785[/C][C]1.458[/C][C]0.073533[/C][/ROW]
[ROW][C]16[/C][C]0.026127[/C][C]0.3102[/C][C]0.37842[/C][/ROW]
[ROW][C]17[/C][C]-0.103168[/C][C]-1.225[/C][C]0.1113[/C][/ROW]
[ROW][C]18[/C][C]0.066737[/C][C]0.7925[/C][C]0.214712[/C][/ROW]
[ROW][C]19[/C][C]0.068714[/C][C]0.8159[/C][C]0.207956[/C][/ROW]
[ROW][C]20[/C][C]-0.116615[/C][C]-1.3847[/C][C]0.084161[/C][/ROW]
[ROW][C]21[/C][C]0.04898[/C][C]0.5816[/C][C]0.280879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273774&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273774&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
10.7477468.8790
20.1529761.81650.03571
30.0812580.96490.168126
4-0.117636-1.39680.082327
5-0.043491-0.51640.303182
6-0.113856-1.3520.089276
7-0.045493-0.54020.294955
8-0.108787-1.29180.099275
9-0.086631-1.02870.152693
10-0.124259-1.47550.071155
11-0.186247-2.21160.014303
12-0.334175-3.96815.7e-05
130.2920183.46750.000348
140.0250980.2980.383063
150.1227851.4580.073533
160.0261270.31020.37842
17-0.103168-1.2250.1113
180.0667370.79250.214712
190.0687140.81590.207956
20-0.116615-1.38470.084161
210.048980.58160.280879



Parameters (Session):
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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')