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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 11:25:34 -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/t1324571151ean18rtyto7ykzd.htm/, Retrieved Fri, 03 May 2024 11:46:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159686, Retrieved Fri, 03 May 2024 11:46:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
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] [ad2d4c5ace9fa07b356a7b5098237581]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-22 16:25:34] [daf26cf00f2f7a7ee0a1368c8ac8117e] [Current]
-   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 time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159686&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159686&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'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.75812512.86580
20.66436711.27470
30.5498639.33150
40.5226218.86920
50.4971348.43660
60.4136727.02030
70.3557376.03710
80.3253145.52080
90.2872754.87521e-06
100.1716242.91260.001933
110.0852521.44680.074525
12-0.064173-1.0890.138522
130.0020630.0350.486049
140.0105120.17840.429268
150.0209240.35510.361388
160.0028020.04750.481055
17-0.005579-0.09470.462319
180.0318680.54080.294528
19-0.002305-0.03910.48441
20-0.020304-0.34460.365334
21-0.023464-0.39820.345387
220.0015030.02550.489836
230.027120.46020.322844
240.0328180.55690.288999

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.758125 & 12.8658 & 0 \tabularnewline
2 & 0.664367 & 11.2747 & 0 \tabularnewline
3 & 0.549863 & 9.3315 & 0 \tabularnewline
4 & 0.522621 & 8.8692 & 0 \tabularnewline
5 & 0.497134 & 8.4366 & 0 \tabularnewline
6 & 0.413672 & 7.0203 & 0 \tabularnewline
7 & 0.355737 & 6.0371 & 0 \tabularnewline
8 & 0.325314 & 5.5208 & 0 \tabularnewline
9 & 0.287275 & 4.8752 & 1e-06 \tabularnewline
10 & 0.171624 & 2.9126 & 0.001933 \tabularnewline
11 & 0.085252 & 1.4468 & 0.074525 \tabularnewline
12 & -0.064173 & -1.089 & 0.138522 \tabularnewline
13 & 0.002063 & 0.035 & 0.486049 \tabularnewline
14 & 0.010512 & 0.1784 & 0.429268 \tabularnewline
15 & 0.020924 & 0.3551 & 0.361388 \tabularnewline
16 & 0.002802 & 0.0475 & 0.481055 \tabularnewline
17 & -0.005579 & -0.0947 & 0.462319 \tabularnewline
18 & 0.031868 & 0.5408 & 0.294528 \tabularnewline
19 & -0.002305 & -0.0391 & 0.48441 \tabularnewline
20 & -0.020304 & -0.3446 & 0.365334 \tabularnewline
21 & -0.023464 & -0.3982 & 0.345387 \tabularnewline
22 & 0.001503 & 0.0255 & 0.489836 \tabularnewline
23 & 0.02712 & 0.4602 & 0.322844 \tabularnewline
24 & 0.032818 & 0.5569 & 0.288999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159686&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]0.758125[/C][C]12.8658[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.664367[/C][C]11.2747[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.549863[/C][C]9.3315[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.522621[/C][C]8.8692[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.497134[/C][C]8.4366[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.413672[/C][C]7.0203[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.355737[/C][C]6.0371[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.325314[/C][C]5.5208[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.287275[/C][C]4.8752[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.171624[/C][C]2.9126[/C][C]0.001933[/C][/ROW]
[ROW][C]11[/C][C]0.085252[/C][C]1.4468[/C][C]0.074525[/C][/ROW]
[ROW][C]12[/C][C]-0.064173[/C][C]-1.089[/C][C]0.138522[/C][/ROW]
[ROW][C]13[/C][C]0.002063[/C][C]0.035[/C][C]0.486049[/C][/ROW]
[ROW][C]14[/C][C]0.010512[/C][C]0.1784[/C][C]0.429268[/C][/ROW]
[ROW][C]15[/C][C]0.020924[/C][C]0.3551[/C][C]0.361388[/C][/ROW]
[ROW][C]16[/C][C]0.002802[/C][C]0.0475[/C][C]0.481055[/C][/ROW]
[ROW][C]17[/C][C]-0.005579[/C][C]-0.0947[/C][C]0.462319[/C][/ROW]
[ROW][C]18[/C][C]0.031868[/C][C]0.5408[/C][C]0.294528[/C][/ROW]
[ROW][C]19[/C][C]-0.002305[/C][C]-0.0391[/C][C]0.48441[/C][/ROW]
[ROW][C]20[/C][C]-0.020304[/C][C]-0.3446[/C][C]0.365334[/C][/ROW]
[ROW][C]21[/C][C]-0.023464[/C][C]-0.3982[/C][C]0.345387[/C][/ROW]
[ROW][C]22[/C][C]0.001503[/C][C]0.0255[/C][C]0.489836[/C][/ROW]
[ROW][C]23[/C][C]0.02712[/C][C]0.4602[/C][C]0.322844[/C][/ROW]
[ROW][C]24[/C][C]0.032818[/C][C]0.5569[/C][C]0.288999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159686&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
10.75812512.86580
20.66436711.27470
30.5498639.33150
40.5226218.86920
50.4971348.43660
60.4136727.02030
70.3557376.03710
80.3253145.52080
90.2872754.87521e-06
100.1716242.91260.001933
110.0852521.44680.074525
12-0.064173-1.0890.138522
130.0020630.0350.486049
140.0105120.17840.429268
150.0209240.35510.361388
160.0028020.04750.481055
17-0.005579-0.09470.462319
180.0318680.54080.294528
19-0.002305-0.03910.48441
20-0.020304-0.34460.365334
21-0.023464-0.39820.345387
220.0015030.02550.489836
230.027120.46020.322844
240.0328180.55690.288999







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.75812512.86580
20.2107343.57630.000204
3-0.018288-0.31040.378258
40.142962.42610.007938
50.0943311.60080.055253
6-0.11684-1.98280.024167
7-0.016611-0.28190.389115
80.068561.16350.122794
9-0.037714-0.640.261329
10-0.235482-3.99634.1e-05
11-0.071605-1.21520.112648
12-0.24569-4.16952e-05
130.2713994.60583e-06
140.1121371.9030.029017
150.0117710.19980.420908
160.0451810.76680.221927
170.0718931.22010.111719
180.0516170.8760.19089
19-0.113329-1.92330.027717
200.0004760.00810.496777
210.0445880.75670.224929
22-0.111306-1.88890.029953
23-0.018943-0.32150.374044
24-0.102262-1.73540.041866

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.758125 & 12.8658 & 0 \tabularnewline
2 & 0.210734 & 3.5763 & 0.000204 \tabularnewline
3 & -0.018288 & -0.3104 & 0.378258 \tabularnewline
4 & 0.14296 & 2.4261 & 0.007938 \tabularnewline
5 & 0.094331 & 1.6008 & 0.055253 \tabularnewline
6 & -0.11684 & -1.9828 & 0.024167 \tabularnewline
7 & -0.016611 & -0.2819 & 0.389115 \tabularnewline
8 & 0.06856 & 1.1635 & 0.122794 \tabularnewline
9 & -0.037714 & -0.64 & 0.261329 \tabularnewline
10 & -0.235482 & -3.9963 & 4.1e-05 \tabularnewline
11 & -0.071605 & -1.2152 & 0.112648 \tabularnewline
12 & -0.24569 & -4.1695 & 2e-05 \tabularnewline
13 & 0.271399 & 4.6058 & 3e-06 \tabularnewline
14 & 0.112137 & 1.903 & 0.029017 \tabularnewline
15 & 0.011771 & 0.1998 & 0.420908 \tabularnewline
16 & 0.045181 & 0.7668 & 0.221927 \tabularnewline
17 & 0.071893 & 1.2201 & 0.111719 \tabularnewline
18 & 0.051617 & 0.876 & 0.19089 \tabularnewline
19 & -0.113329 & -1.9233 & 0.027717 \tabularnewline
20 & 0.000476 & 0.0081 & 0.496777 \tabularnewline
21 & 0.044588 & 0.7567 & 0.224929 \tabularnewline
22 & -0.111306 & -1.8889 & 0.029953 \tabularnewline
23 & -0.018943 & -0.3215 & 0.374044 \tabularnewline
24 & -0.102262 & -1.7354 & 0.041866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159686&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]0.758125[/C][C]12.8658[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.210734[/C][C]3.5763[/C][C]0.000204[/C][/ROW]
[ROW][C]3[/C][C]-0.018288[/C][C]-0.3104[/C][C]0.378258[/C][/ROW]
[ROW][C]4[/C][C]0.14296[/C][C]2.4261[/C][C]0.007938[/C][/ROW]
[ROW][C]5[/C][C]0.094331[/C][C]1.6008[/C][C]0.055253[/C][/ROW]
[ROW][C]6[/C][C]-0.11684[/C][C]-1.9828[/C][C]0.024167[/C][/ROW]
[ROW][C]7[/C][C]-0.016611[/C][C]-0.2819[/C][C]0.389115[/C][/ROW]
[ROW][C]8[/C][C]0.06856[/C][C]1.1635[/C][C]0.122794[/C][/ROW]
[ROW][C]9[/C][C]-0.037714[/C][C]-0.64[/C][C]0.261329[/C][/ROW]
[ROW][C]10[/C][C]-0.235482[/C][C]-3.9963[/C][C]4.1e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.071605[/C][C]-1.2152[/C][C]0.112648[/C][/ROW]
[ROW][C]12[/C][C]-0.24569[/C][C]-4.1695[/C][C]2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.271399[/C][C]4.6058[/C][C]3e-06[/C][/ROW]
[ROW][C]14[/C][C]0.112137[/C][C]1.903[/C][C]0.029017[/C][/ROW]
[ROW][C]15[/C][C]0.011771[/C][C]0.1998[/C][C]0.420908[/C][/ROW]
[ROW][C]16[/C][C]0.045181[/C][C]0.7668[/C][C]0.221927[/C][/ROW]
[ROW][C]17[/C][C]0.071893[/C][C]1.2201[/C][C]0.111719[/C][/ROW]
[ROW][C]18[/C][C]0.051617[/C][C]0.876[/C][C]0.19089[/C][/ROW]
[ROW][C]19[/C][C]-0.113329[/C][C]-1.9233[/C][C]0.027717[/C][/ROW]
[ROW][C]20[/C][C]0.000476[/C][C]0.0081[/C][C]0.496777[/C][/ROW]
[ROW][C]21[/C][C]0.044588[/C][C]0.7567[/C][C]0.224929[/C][/ROW]
[ROW][C]22[/C][C]-0.111306[/C][C]-1.8889[/C][C]0.029953[/C][/ROW]
[ROW][C]23[/C][C]-0.018943[/C][C]-0.3215[/C][C]0.374044[/C][/ROW]
[ROW][C]24[/C][C]-0.102262[/C][C]-1.7354[/C][C]0.041866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159686&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159686&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
10.75812512.86580
20.2107343.57630.000204
3-0.018288-0.31040.378258
40.142962.42610.007938
50.0943311.60080.055253
6-0.11684-1.98280.024167
7-0.016611-0.28190.389115
80.068561.16350.122794
9-0.037714-0.640.261329
10-0.235482-3.99634.1e-05
11-0.071605-1.21520.112648
12-0.24569-4.16952e-05
130.2713994.60583e-06
140.1121371.9030.029017
150.0117710.19980.420908
160.0451810.76680.221927
170.0718931.22010.111719
180.0516170.8760.19089
19-0.113329-1.92330.027717
200.0004760.00810.496777
210.0445880.75670.224929
22-0.111306-1.88890.029953
23-0.018943-0.32150.374044
24-0.102262-1.73540.041866



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