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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 computationThu, 22 Dec 2011 11:18:57 -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/2011/Dec/22/t1324570756jz3nwpc9t20jhau.htm/, Retrieved Fri, 03 May 2024 04:32:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159682, Retrieved Fri, 03 May 2024 04:32:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2011-12-06 13:49:56] [ad2d4c5ace9fa07b356a7b5098237581]
- R  D    [(Partial) Autocorrelation Function] [] [2011-12-22 16:18:57] [daf26cf00f2f7a7ee0a1368c8ac8117e] [Current]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-22 16:25:34] [ad2d4c5ace9fa07b356a7b5098237581]
-   P         [(Partial) Autocorrelation Function] [] [2011-12-22 16:32:30] [ad2d4c5ace9fa07b356a7b5098237581]
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Dataseries X:
315.71
317.45
317.5
317.12
315.86
314.93
313.2
312.6
313.33
314.67
315.62
316.38
316.71
317.72
318.29
318.16
316.55
314.8
313.84
313.26
314.8
315.59
316.43
316.97
317.58
319.02
320.02
319.59
318.18
315.91
314.16
313.83
315
316.19
316.93
317.7
318.54
319.48
320.58
319.77
318.58
316.79
314.8
315.38
316.1
317.01
317.94
318.55
319.68
320.63
321.01
320.55
319.58
317.4
316.26
315.42
316.69
317.7
318.74
319.08
319.86
321.39
322.24
321.47
319.74
317.77
316.21
315.99
317.12
318.31
319.57
320.08
320.75
321.8
322.24
321.89
320.44
318.7
316.7
316.79
317.79
318.71
319.44
320.44
320.89
322.13
322.16
321.87
321.39
318.8
317.81
317.3
318.87
319.42
320.62
321.59
322.39
323.87
324.01
323.75
322.4
320.37
318.64
318.1
319.78
321.08
322.06
322.5
323.04
324.42
325
324.09
322.55
320.92
319.31
319.31
320.72
321.96
322.57
323.15
323.89
325.02
325.57
325.36
324.14
322.03
320.41
320.25
321.31
322.84
324
324.42
325.64
326.66
327.34
326.76
325.88
323.67
322.38
321.78
322.85
324.12
325.03
325.99
326.87
328.14
328.07
327.66
326.35
324.69
323.1
323.16
323.98
325.13
326.17
326.68
327.18
327.78
328.92
328.57
327.34
325.46
323.36
323.56
324.8
326.01
326.77
327.63
327.75
329.72
330.07
329.09
328.05
326.32
324.93
325.06
326.5
327.55
328.55
329.56
330.3
331.5
332.48
332.07
330.87
329.31
327.51
327.18
328.16
328.64
329.35
330.71
331.48
332.65
333.15
332.13
330.99
329.17
327.41
327.21
328.34
329.5
330.68
331.41
331.85
333.29
333.91
333.4
331.74
329.88
328.57
328.35
329.33
330.58
331.66
332.75
333.46
334.78
334.79
334.05
332.95
330.64
328.96
328.77
330.18
331.65
332.69
333.23
334.97
336.03
336.82
336.1
334.79
332.53
331.19
331.21
332.35
333.47
335.09
335.26
336.62
337.77
338
337.98
336.48
334.37
332.33
332.4
333.76
334.83
336.21
336.64
338.13
338.96
339.02
339.2
337.6
335.56
333.93
334.12
335.26
336.77
337.8
338.28
340.04
340.86
341.47
341.26
339.34
337.45
336.1
336.05
337.21
338.29
339.36
340.51
341.57
342.56
343.01
342.52
340.71
338.51
336.96
337.13
338.58
339.91
340.92
341.69
342.87
343.83
344.3
343.42
341.85
339.82
337.98
338.09
339.24
340.67
341.42
342.67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159682&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159682&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'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.98025316.97850
20.94827316.42460
30.91163615.790
40.87980215.23860
50.8574614.85160
60.84530414.64110
70.84131114.57190
80.84566714.64740
90.85786914.85870
100.87326415.12540
110.88432415.31690
120.8823315.28240
130.86311814.94960
140.83111814.39540
150.79532513.77540
160.7641613.23560
170.74227312.85650
180.72984712.64130
190.72566912.5690
200.72927212.63140
210.7405612.82690
220.75499613.07690
230.76510213.25190
240.76250113.20690

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.980253 & 16.9785 & 0 \tabularnewline
2 & 0.948273 & 16.4246 & 0 \tabularnewline
3 & 0.911636 & 15.79 & 0 \tabularnewline
4 & 0.879802 & 15.2386 & 0 \tabularnewline
5 & 0.85746 & 14.8516 & 0 \tabularnewline
6 & 0.845304 & 14.6411 & 0 \tabularnewline
7 & 0.841311 & 14.5719 & 0 \tabularnewline
8 & 0.845667 & 14.6474 & 0 \tabularnewline
9 & 0.857869 & 14.8587 & 0 \tabularnewline
10 & 0.873264 & 15.1254 & 0 \tabularnewline
11 & 0.884324 & 15.3169 & 0 \tabularnewline
12 & 0.88233 & 15.2824 & 0 \tabularnewline
13 & 0.863118 & 14.9496 & 0 \tabularnewline
14 & 0.831118 & 14.3954 & 0 \tabularnewline
15 & 0.795325 & 13.7754 & 0 \tabularnewline
16 & 0.76416 & 13.2356 & 0 \tabularnewline
17 & 0.742273 & 12.8565 & 0 \tabularnewline
18 & 0.729847 & 12.6413 & 0 \tabularnewline
19 & 0.725669 & 12.569 & 0 \tabularnewline
20 & 0.729272 & 12.6314 & 0 \tabularnewline
21 & 0.74056 & 12.8269 & 0 \tabularnewline
22 & 0.754996 & 13.0769 & 0 \tabularnewline
23 & 0.765102 & 13.2519 & 0 \tabularnewline
24 & 0.762501 & 13.2069 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159682&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]0.980253[/C][C]16.9785[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.948273[/C][C]16.4246[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.911636[/C][C]15.79[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.879802[/C][C]15.2386[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.85746[/C][C]14.8516[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.845304[/C][C]14.6411[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.841311[/C][C]14.5719[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.845667[/C][C]14.6474[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.857869[/C][C]14.8587[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.873264[/C][C]15.1254[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.884324[/C][C]15.3169[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.88233[/C][C]15.2824[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.863118[/C][C]14.9496[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.831118[/C][C]14.3954[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.795325[/C][C]13.7754[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.76416[/C][C]13.2356[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.742273[/C][C]12.8565[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.729847[/C][C]12.6413[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.725669[/C][C]12.569[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.729272[/C][C]12.6314[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.74056[/C][C]12.8269[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.754996[/C][C]13.0769[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.765102[/C][C]13.2519[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.762501[/C][C]13.2069[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159682&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
10.98025316.97850
20.94827316.42460
30.91163615.790
40.87980215.23860
50.8574614.85160
60.84530414.64110
70.84131114.57190
80.84566714.64740
90.85786914.85870
100.87326415.12540
110.88432415.31690
120.8823315.28240
130.86311814.94960
140.83111814.39540
150.79532513.77540
160.7641613.23560
170.74227312.85650
180.72984712.64130
190.72566912.5690
200.72927212.63140
210.7405612.82690
220.75499613.07690
230.76510213.25190
240.76250113.20690







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.98025316.97850
2-0.322832-5.59160
3-0.044031-0.76260.223139
40.1654662.86590.002226
50.1665962.88550.002096
60.1216032.10620.018008
70.0894261.54890.06123
80.1771583.06850.001174
90.2084373.61020.000179
100.0984981.7060.044519
11-0.045853-0.79420.213856
12-0.191476-3.31650.000512
13-0.232329-4.02413.6e-05
14-0.12663-2.19330.014527
15-0.014396-0.24940.401629
160.0378030.65480.25656
170.0407020.7050.240687
180.0098120.16990.432583
190.0102660.17780.429497
200.0494850.85710.196034
210.1121381.94230.026519
220.0650671.1270.130322
23-0.006195-0.10730.45731
24-0.091347-1.58220.057331

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.980253 & 16.9785 & 0 \tabularnewline
2 & -0.322832 & -5.5916 & 0 \tabularnewline
3 & -0.044031 & -0.7626 & 0.223139 \tabularnewline
4 & 0.165466 & 2.8659 & 0.002226 \tabularnewline
5 & 0.166596 & 2.8855 & 0.002096 \tabularnewline
6 & 0.121603 & 2.1062 & 0.018008 \tabularnewline
7 & 0.089426 & 1.5489 & 0.06123 \tabularnewline
8 & 0.177158 & 3.0685 & 0.001174 \tabularnewline
9 & 0.208437 & 3.6102 & 0.000179 \tabularnewline
10 & 0.098498 & 1.706 & 0.044519 \tabularnewline
11 & -0.045853 & -0.7942 & 0.213856 \tabularnewline
12 & -0.191476 & -3.3165 & 0.000512 \tabularnewline
13 & -0.232329 & -4.0241 & 3.6e-05 \tabularnewline
14 & -0.12663 & -2.1933 & 0.014527 \tabularnewline
15 & -0.014396 & -0.2494 & 0.401629 \tabularnewline
16 & 0.037803 & 0.6548 & 0.25656 \tabularnewline
17 & 0.040702 & 0.705 & 0.240687 \tabularnewline
18 & 0.009812 & 0.1699 & 0.432583 \tabularnewline
19 & 0.010266 & 0.1778 & 0.429497 \tabularnewline
20 & 0.049485 & 0.8571 & 0.196034 \tabularnewline
21 & 0.112138 & 1.9423 & 0.026519 \tabularnewline
22 & 0.065067 & 1.127 & 0.130322 \tabularnewline
23 & -0.006195 & -0.1073 & 0.45731 \tabularnewline
24 & -0.091347 & -1.5822 & 0.057331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159682&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]0.980253[/C][C]16.9785[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.322832[/C][C]-5.5916[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.044031[/C][C]-0.7626[/C][C]0.223139[/C][/ROW]
[ROW][C]4[/C][C]0.165466[/C][C]2.8659[/C][C]0.002226[/C][/ROW]
[ROW][C]5[/C][C]0.166596[/C][C]2.8855[/C][C]0.002096[/C][/ROW]
[ROW][C]6[/C][C]0.121603[/C][C]2.1062[/C][C]0.018008[/C][/ROW]
[ROW][C]7[/C][C]0.089426[/C][C]1.5489[/C][C]0.06123[/C][/ROW]
[ROW][C]8[/C][C]0.177158[/C][C]3.0685[/C][C]0.001174[/C][/ROW]
[ROW][C]9[/C][C]0.208437[/C][C]3.6102[/C][C]0.000179[/C][/ROW]
[ROW][C]10[/C][C]0.098498[/C][C]1.706[/C][C]0.044519[/C][/ROW]
[ROW][C]11[/C][C]-0.045853[/C][C]-0.7942[/C][C]0.213856[/C][/ROW]
[ROW][C]12[/C][C]-0.191476[/C][C]-3.3165[/C][C]0.000512[/C][/ROW]
[ROW][C]13[/C][C]-0.232329[/C][C]-4.0241[/C][C]3.6e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.12663[/C][C]-2.1933[/C][C]0.014527[/C][/ROW]
[ROW][C]15[/C][C]-0.014396[/C][C]-0.2494[/C][C]0.401629[/C][/ROW]
[ROW][C]16[/C][C]0.037803[/C][C]0.6548[/C][C]0.25656[/C][/ROW]
[ROW][C]17[/C][C]0.040702[/C][C]0.705[/C][C]0.240687[/C][/ROW]
[ROW][C]18[/C][C]0.009812[/C][C]0.1699[/C][C]0.432583[/C][/ROW]
[ROW][C]19[/C][C]0.010266[/C][C]0.1778[/C][C]0.429497[/C][/ROW]
[ROW][C]20[/C][C]0.049485[/C][C]0.8571[/C][C]0.196034[/C][/ROW]
[ROW][C]21[/C][C]0.112138[/C][C]1.9423[/C][C]0.026519[/C][/ROW]
[ROW][C]22[/C][C]0.065067[/C][C]1.127[/C][C]0.130322[/C][/ROW]
[ROW][C]23[/C][C]-0.006195[/C][C]-0.1073[/C][C]0.45731[/C][/ROW]
[ROW][C]24[/C][C]-0.091347[/C][C]-1.5822[/C][C]0.057331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159682&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
10.98025316.97850
2-0.322832-5.59160
3-0.044031-0.76260.223139
40.1654662.86590.002226
50.1665962.88550.002096
60.1216032.10620.018008
70.0894261.54890.06123
80.1771583.06850.001174
90.2084373.61020.000179
100.0984981.7060.044519
11-0.045853-0.79420.213856
12-0.191476-3.31650.000512
13-0.232329-4.02413.6e-05
14-0.12663-2.19330.014527
15-0.014396-0.24940.401629
160.0378030.65480.25656
170.0407020.7050.240687
180.0098120.16990.432583
190.0102660.17780.429497
200.0494850.85710.196034
210.1121381.94230.026519
220.0650671.1270.130322
23-0.006195-0.10730.45731
24-0.091347-1.58220.057331



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; 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')