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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 computationSat, 13 Dec 2014 12:53:38 +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/2014/Dec/13/t141847612144rkfvyyvwsks2t.htm/, Retrieved Thu, 16 May 2024 08:47:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267061, Retrieved Thu, 16 May 2024 08:47:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
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]
- RMP   [Spectral Analysis] [] [2014-11-26 13:41:56] [ea990983fba95a758c0bb6d29c9aee24]
- RMPD      [(Partial) Autocorrelation Function] [] [2014-12-13 12:53:38] [baa7d013c3374cabca6c222951a47a9f] [Current]
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Dataseries X:
7.5
2.5
6.0
6.5
1.0
1.0
5.5
8.5
6.5
4.5
2.0
5.0
0.5
5.0
5.0
2.5
5.0
5.5
3.5
3.0
4.0
0.5
6.5
4.5
7.5
5.5
4.0
7.5
7.0
4.0
5.5
2.5
5.5
0.5
3.5
2.5
4.5
4.5
4.5
6.0
2.5
5.0
0.0
5.0
6.5
5.0
6.0
4.5
5.5
1.0
7.5
6.0
5.0
1.0
5.0
6.5
7.0
4.5
0.0
8.5
3.5
7.5
3.5
6.0
1.5
9.0
3.5
3.5
4.0
6.5
7.5
6.0
5.0
5.5
3.5
7.5
1.0
6.5
6.5
6.5
7.0
3.5
1.5
4.0
7.5
4.5
0.0
3.5
5.5
5.0
4.5
2.5
7.5
7.0
0.0
4.5
3.0
1.5
3.5
2.5
5.5
8.0
1.0
5.0
4.5
3.0
3.0
8.0
2.5
7.0
0.0
1.0
3.5
5.5
5.5
0.5
7.5
9
9.5
8.5
7
8
10
7
8.5
9
9.5
4
6
8
5.5
9.5
7.5
7
7.5
8
7
7
6
10
2.5
9
8
6
8.5
6
9
8
8
9
5.5
5
7
5.5
9
2
8.5
9
8.5
9
7.5
10
9
7.5
6
10.5
8.5
8
10
10.5
6.5
9.5
8.5
7.5
5
8
10
7
7.5
7.5
9.5
6
10
7
3
6
7
10
7
3.5
8
10
5.5
6
6.5
6.5
8.5
4
9.5
8
8.5
5.5
7
9
8
10
8
6
8
5
9
4.5
8.5
7
9.5
8.5
7.5
7.5
5
7
8
5.5
8.5
7.5
9.5
7
8
8.5
3.5
6.5
6.5
10.5
8.5
8
10
10
9.5
9
10
7.5
4.5
4.5
0.5
6.5
4.5
5.5
5
6
4
8
10.5
8.5
6.5
8
8.5
5.5
7
5
3.5
5
9
8.5
5
9.5
3
1.5
6
0.5
6.5
7.5
4.5
8
9
7.5
8.5
7
9.5
6.5
9.5
6
8
9.5
8
8
9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267061&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267061&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.2987195.0430
20.3454485.83180
30.2981985.03420
40.3153035.32290
50.3119525.26640
60.2065143.48640.000283
70.2193733.70340.000128
80.2510314.23791.5e-05
90.265454.48135e-06
100.2418964.08372.9e-05
110.2350453.9684.6e-05
120.2416534.07962.9e-05
130.2187393.69270.000133
140.1962493.31310.000521
150.250284.22521.6e-05
160.2063253.48320.000287
170.2061363.480.00029
180.2167713.65950.000151
190.2216543.7420.00011
200.1991313.36170.00044
210.1876923.16860.000849
220.2194733.70510.000127
230.2297593.87886.5e-05
240.2215033.73940.000111

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.298719 & 5.043 & 0 \tabularnewline
2 & 0.345448 & 5.8318 & 0 \tabularnewline
3 & 0.298198 & 5.0342 & 0 \tabularnewline
4 & 0.315303 & 5.3229 & 0 \tabularnewline
5 & 0.311952 & 5.2664 & 0 \tabularnewline
6 & 0.206514 & 3.4864 & 0.000283 \tabularnewline
7 & 0.219373 & 3.7034 & 0.000128 \tabularnewline
8 & 0.251031 & 4.2379 & 1.5e-05 \tabularnewline
9 & 0.26545 & 4.4813 & 5e-06 \tabularnewline
10 & 0.241896 & 4.0837 & 2.9e-05 \tabularnewline
11 & 0.235045 & 3.968 & 4.6e-05 \tabularnewline
12 & 0.241653 & 4.0796 & 2.9e-05 \tabularnewline
13 & 0.218739 & 3.6927 & 0.000133 \tabularnewline
14 & 0.196249 & 3.3131 & 0.000521 \tabularnewline
15 & 0.25028 & 4.2252 & 1.6e-05 \tabularnewline
16 & 0.206325 & 3.4832 & 0.000287 \tabularnewline
17 & 0.206136 & 3.48 & 0.00029 \tabularnewline
18 & 0.216771 & 3.6595 & 0.000151 \tabularnewline
19 & 0.221654 & 3.742 & 0.00011 \tabularnewline
20 & 0.199131 & 3.3617 & 0.00044 \tabularnewline
21 & 0.187692 & 3.1686 & 0.000849 \tabularnewline
22 & 0.219473 & 3.7051 & 0.000127 \tabularnewline
23 & 0.229759 & 3.8788 & 6.5e-05 \tabularnewline
24 & 0.221503 & 3.7394 & 0.000111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267061&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]0.298719[/C][C]5.043[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.345448[/C][C]5.8318[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.298198[/C][C]5.0342[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.315303[/C][C]5.3229[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.311952[/C][C]5.2664[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.206514[/C][C]3.4864[/C][C]0.000283[/C][/ROW]
[ROW][C]7[/C][C]0.219373[/C][C]3.7034[/C][C]0.000128[/C][/ROW]
[ROW][C]8[/C][C]0.251031[/C][C]4.2379[/C][C]1.5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.26545[/C][C]4.4813[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.241896[/C][C]4.0837[/C][C]2.9e-05[/C][/ROW]
[ROW][C]11[/C][C]0.235045[/C][C]3.968[/C][C]4.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.241653[/C][C]4.0796[/C][C]2.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.218739[/C][C]3.6927[/C][C]0.000133[/C][/ROW]
[ROW][C]14[/C][C]0.196249[/C][C]3.3131[/C][C]0.000521[/C][/ROW]
[ROW][C]15[/C][C]0.25028[/C][C]4.2252[/C][C]1.6e-05[/C][/ROW]
[ROW][C]16[/C][C]0.206325[/C][C]3.4832[/C][C]0.000287[/C][/ROW]
[ROW][C]17[/C][C]0.206136[/C][C]3.48[/C][C]0.00029[/C][/ROW]
[ROW][C]18[/C][C]0.216771[/C][C]3.6595[/C][C]0.000151[/C][/ROW]
[ROW][C]19[/C][C]0.221654[/C][C]3.742[/C][C]0.00011[/C][/ROW]
[ROW][C]20[/C][C]0.199131[/C][C]3.3617[/C][C]0.00044[/C][/ROW]
[ROW][C]21[/C][C]0.187692[/C][C]3.1686[/C][C]0.000849[/C][/ROW]
[ROW][C]22[/C][C]0.219473[/C][C]3.7051[/C][C]0.000127[/C][/ROW]
[ROW][C]23[/C][C]0.229759[/C][C]3.8788[/C][C]6.5e-05[/C][/ROW]
[ROW][C]24[/C][C]0.221503[/C][C]3.7394[/C][C]0.000111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267061&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
10.2987195.0430
20.3454485.83180
30.2981985.03420
40.3153035.32290
50.3119525.26640
60.2065143.48640.000283
70.2193733.70340.000128
80.2510314.23791.5e-05
90.265454.48135e-06
100.2418964.08372.9e-05
110.2350453.9684.6e-05
120.2416534.07962.9e-05
130.2187393.69270.000133
140.1962493.31310.000521
150.250284.22521.6e-05
160.2063253.48320.000287
170.2061363.480.00029
180.2167713.65950.000151
190.2216543.7420.00011
200.1991313.36170.00044
210.1876923.16860.000849
220.2194733.70510.000127
230.2297593.87886.5e-05
240.2215033.73940.000111







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.2987195.0430
20.2813174.74922e-06
30.1669282.81810.002585
40.160212.70470.003624
50.1382022.33310.010169
6-0.016198-0.27350.392352
70.016950.28620.387485
80.0859521.4510.073935
90.0973631.64370.050673
100.0591950.99930.159241
110.0523770.88420.188659
120.0471220.79550.213488
130.0053690.09060.463921
14-0.011538-0.19480.422851
150.0863511.45780.073001
160.0230110.38850.348976
170.0113790.19210.423898
180.0424070.71590.237316
190.0395560.66780.252406
20-0.008447-0.14260.443352
210.0002730.00460.498166
220.0558030.94210.173481
230.056510.9540.170445
240.0333720.56340.286806

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.298719 & 5.043 & 0 \tabularnewline
2 & 0.281317 & 4.7492 & 2e-06 \tabularnewline
3 & 0.166928 & 2.8181 & 0.002585 \tabularnewline
4 & 0.16021 & 2.7047 & 0.003624 \tabularnewline
5 & 0.138202 & 2.3331 & 0.010169 \tabularnewline
6 & -0.016198 & -0.2735 & 0.392352 \tabularnewline
7 & 0.01695 & 0.2862 & 0.387485 \tabularnewline
8 & 0.085952 & 1.451 & 0.073935 \tabularnewline
9 & 0.097363 & 1.6437 & 0.050673 \tabularnewline
10 & 0.059195 & 0.9993 & 0.159241 \tabularnewline
11 & 0.052377 & 0.8842 & 0.188659 \tabularnewline
12 & 0.047122 & 0.7955 & 0.213488 \tabularnewline
13 & 0.005369 & 0.0906 & 0.463921 \tabularnewline
14 & -0.011538 & -0.1948 & 0.422851 \tabularnewline
15 & 0.086351 & 1.4578 & 0.073001 \tabularnewline
16 & 0.023011 & 0.3885 & 0.348976 \tabularnewline
17 & 0.011379 & 0.1921 & 0.423898 \tabularnewline
18 & 0.042407 & 0.7159 & 0.237316 \tabularnewline
19 & 0.039556 & 0.6678 & 0.252406 \tabularnewline
20 & -0.008447 & -0.1426 & 0.443352 \tabularnewline
21 & 0.000273 & 0.0046 & 0.498166 \tabularnewline
22 & 0.055803 & 0.9421 & 0.173481 \tabularnewline
23 & 0.05651 & 0.954 & 0.170445 \tabularnewline
24 & 0.033372 & 0.5634 & 0.286806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267061&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]0.298719[/C][C]5.043[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.281317[/C][C]4.7492[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.166928[/C][C]2.8181[/C][C]0.002585[/C][/ROW]
[ROW][C]4[/C][C]0.16021[/C][C]2.7047[/C][C]0.003624[/C][/ROW]
[ROW][C]5[/C][C]0.138202[/C][C]2.3331[/C][C]0.010169[/C][/ROW]
[ROW][C]6[/C][C]-0.016198[/C][C]-0.2735[/C][C]0.392352[/C][/ROW]
[ROW][C]7[/C][C]0.01695[/C][C]0.2862[/C][C]0.387485[/C][/ROW]
[ROW][C]8[/C][C]0.085952[/C][C]1.451[/C][C]0.073935[/C][/ROW]
[ROW][C]9[/C][C]0.097363[/C][C]1.6437[/C][C]0.050673[/C][/ROW]
[ROW][C]10[/C][C]0.059195[/C][C]0.9993[/C][C]0.159241[/C][/ROW]
[ROW][C]11[/C][C]0.052377[/C][C]0.8842[/C][C]0.188659[/C][/ROW]
[ROW][C]12[/C][C]0.047122[/C][C]0.7955[/C][C]0.213488[/C][/ROW]
[ROW][C]13[/C][C]0.005369[/C][C]0.0906[/C][C]0.463921[/C][/ROW]
[ROW][C]14[/C][C]-0.011538[/C][C]-0.1948[/C][C]0.422851[/C][/ROW]
[ROW][C]15[/C][C]0.086351[/C][C]1.4578[/C][C]0.073001[/C][/ROW]
[ROW][C]16[/C][C]0.023011[/C][C]0.3885[/C][C]0.348976[/C][/ROW]
[ROW][C]17[/C][C]0.011379[/C][C]0.1921[/C][C]0.423898[/C][/ROW]
[ROW][C]18[/C][C]0.042407[/C][C]0.7159[/C][C]0.237316[/C][/ROW]
[ROW][C]19[/C][C]0.039556[/C][C]0.6678[/C][C]0.252406[/C][/ROW]
[ROW][C]20[/C][C]-0.008447[/C][C]-0.1426[/C][C]0.443352[/C][/ROW]
[ROW][C]21[/C][C]0.000273[/C][C]0.0046[/C][C]0.498166[/C][/ROW]
[ROW][C]22[/C][C]0.055803[/C][C]0.9421[/C][C]0.173481[/C][/ROW]
[ROW][C]23[/C][C]0.05651[/C][C]0.954[/C][C]0.170445[/C][/ROW]
[ROW][C]24[/C][C]0.033372[/C][C]0.5634[/C][C]0.286806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267061&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
10.2987195.0430
20.2813174.74922e-06
30.1669282.81810.002585
40.160212.70470.003624
50.1382022.33310.010169
6-0.016198-0.27350.392352
70.016950.28620.387485
80.0859521.4510.073935
90.0973631.64370.050673
100.0591950.99930.159241
110.0523770.88420.188659
120.0471220.79550.213488
130.0053690.09060.463921
14-0.011538-0.19480.422851
150.0863511.45780.073001
160.0230110.38850.348976
170.0113790.19210.423898
180.0424070.71590.237316
190.0395560.66780.252406
20-0.008447-0.14260.443352
210.0002730.00460.498166
220.0558030.94210.173481
230.056510.9540.170445
240.0333720.56340.286806



Parameters (Session):
par1 = 12 ;
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')