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Description of Statistical Computation

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, 11 Dec 2014 15:24:16 +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/11/t14183114819v77oqf0dajv9tv.htm/, Retrieved Thu, 16 May 2024 21:36:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266114, Retrieved Thu, 16 May 2024 21:36:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [uief] [2014-12-11 15:24:16] [7de4f24d5c21ad7c83693f758b02221d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.9
12.2
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
10.6
12.0
6.3
11.3
11.9
9.3
9.6
10.0
6.4
13.8
10.8
13.8
11.7
10.9
16.1
13.4
9.9
11.5
8.3
11.7
9.0
9.7
10.8
10.3
10.4
12.7
9.3
11.8
5.9
11.4
13.0
10.8
12.3
11.3
11.8
7.9
12.7
12.3
11.6
6.7
10.9
12.1
13.3
10.1
5.7
14.3
8.0
13.3
9.3
12.5
7.6
15.9
9.2
9.1
11.1
13.0
14.5
12.2
12.3
11.4
8.8
14.6
12.6
13.0
12.6
13.2
9.9
7.7
10.5
13.4
10.9
4.3
10.3
11.8
11.2
11.4
8.6
13.2
12.6
5.6
9.9
8.8
7.7
9.0
7.3
11.4
13.6
7.9
10.7
10.3
8.3
9.6
14.2
8.5
13.5
4.9
6.4
9.6
11.6
11.1
4.35
12.7
18.1
17.85
16.6
12.6
17.1
19.1
16.1
13.35
18.4
14.7
10.6
12.6
16.2
13.6
18.9
14.1
14.5
16.15
14.75
14.8
12.45
12.65
17.35
8.6
18.4
16.1
11.6
17.75
15.25
17.65
16.35
17.65
13.6
14.35
14.75
18.25
9.9
16
18.25
16.85
14.6
13.85
18.95
15.6
14.85
11.75
18.45
15.9
17.1
16.1
19.9
10.95
18.45
15.1
15
11.35
15.95
18.1
14.6
15.4
15.4
17.6
13.35
19.1
15.35
7.6
13.4
13.9
19.1
15.25
12.9
16.1
17.35
13.15
12.15
12.6
10.35
15.4
9.6
18.2
13.6
14.85
14.75
14.1
14.9
16.25
19.25
13.6
13.6
15.65
12.75
14.6
9.85
12.65
19.2
16.6
11.2
15.25
11.9
13.2
16.35
12.4
15.85
18.15
11.15
15.65
17.75
7.65
12.35
15.6
19.3
15.2
17.1
15.6
18.4
19.05
18.55
19.1
13.1
12.85
9.5
4.5
11.85
13.6
11.7
12.4
13.35
11.4
14.9
19.9
11.2
14.6
17.6
14.05
16.1
13.35
11.85
11.95
14.75
15.15
13.2
16.85
7.85
7.7
12.6
7.85
10.95
12.35
9.95
14.9
16.65
13.4
13.95
15.7
16.85
10.95
15.35
12.2
15.1
17.75
15.2
14.6
16.65
8.1

Tables (Output of Computation)





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=266114&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=266114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266114&T=0

As an alternative you can also use a QR Code:  
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
10.358515.97760
20.3367195.61420
30.3675686.12860
40.3248085.41560
50.3236675.39660
60.2774524.62613e-06
70.2094573.49230.000278
80.2697734.4985e-06
90.2707894.51495e-06
100.2286043.81168.5e-05
110.2776114.62873e-06
120.2389193.98364.3e-05
130.2608984.351e-05
140.2280363.80218.8e-05
150.2711034.52025e-06
160.2669214.45056e-06
170.2493434.15742.1e-05
180.2495164.16032.1e-05
190.2133483.55720.00022
200.2244333.7420.000111
210.2510024.1851.9e-05
220.2681874.47166e-06
230.2324913.87646.6e-05
240.2209543.6840.000138

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.35851 & 5.9776 & 0 \tabularnewline
2 & 0.336719 & 5.6142 & 0 \tabularnewline
3 & 0.367568 & 6.1286 & 0 \tabularnewline
4 & 0.324808 & 5.4156 & 0 \tabularnewline
5 & 0.323667 & 5.3966 & 0 \tabularnewline
6 & 0.277452 & 4.6261 & 3e-06 \tabularnewline
7 & 0.209457 & 3.4923 & 0.000278 \tabularnewline
8 & 0.269773 & 4.498 & 5e-06 \tabularnewline
9 & 0.270789 & 4.5149 & 5e-06 \tabularnewline
10 & 0.228604 & 3.8116 & 8.5e-05 \tabularnewline
11 & 0.277611 & 4.6287 & 3e-06 \tabularnewline
12 & 0.238919 & 3.9836 & 4.3e-05 \tabularnewline
13 & 0.260898 & 4.35 & 1e-05 \tabularnewline
14 & 0.228036 & 3.8021 & 8.8e-05 \tabularnewline
15 & 0.271103 & 4.5202 & 5e-06 \tabularnewline
16 & 0.266921 & 4.4505 & 6e-06 \tabularnewline
17 & 0.249343 & 4.1574 & 2.1e-05 \tabularnewline
18 & 0.249516 & 4.1603 & 2.1e-05 \tabularnewline
19 & 0.213348 & 3.5572 & 0.00022 \tabularnewline
20 & 0.224433 & 3.742 & 0.000111 \tabularnewline
21 & 0.251002 & 4.185 & 1.9e-05 \tabularnewline
22 & 0.268187 & 4.4716 & 6e-06 \tabularnewline
23 & 0.232491 & 3.8764 & 6.6e-05 \tabularnewline
24 & 0.220954 & 3.684 & 0.000138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266114&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]0.35851[/C][C]5.9776[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.336719[/C][C]5.6142[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.367568[/C][C]6.1286[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.324808[/C][C]5.4156[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.323667[/C][C]5.3966[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.277452[/C][C]4.6261[/C][C]3e-06[/C][/ROW]
[ROW][C]7[/C][C]0.209457[/C][C]3.4923[/C][C]0.000278[/C][/ROW]
[ROW][C]8[/C][C]0.269773[/C][C]4.498[/C][C]5e-06[/C][/ROW]
[ROW][C]9[/C][C]0.270789[/C][C]4.5149[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.228604[/C][C]3.8116[/C][C]8.5e-05[/C][/ROW]
[ROW][C]11[/C][C]0.277611[/C][C]4.6287[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.238919[/C][C]3.9836[/C][C]4.3e-05[/C][/ROW]
[ROW][C]13[/C][C]0.260898[/C][C]4.35[/C][C]1e-05[/C][/ROW]
[ROW][C]14[/C][C]0.228036[/C][C]3.8021[/C][C]8.8e-05[/C][/ROW]
[ROW][C]15[/C][C]0.271103[/C][C]4.5202[/C][C]5e-06[/C][/ROW]
[ROW][C]16[/C][C]0.266921[/C][C]4.4505[/C][C]6e-06[/C][/ROW]
[ROW][C]17[/C][C]0.249343[/C][C]4.1574[/C][C]2.1e-05[/C][/ROW]
[ROW][C]18[/C][C]0.249516[/C][C]4.1603[/C][C]2.1e-05[/C][/ROW]
[ROW][C]19[/C][C]0.213348[/C][C]3.5572[/C][C]0.00022[/C][/ROW]
[ROW][C]20[/C][C]0.224433[/C][C]3.742[/C][C]0.000111[/C][/ROW]
[ROW][C]21[/C][C]0.251002[/C][C]4.185[/C][C]1.9e-05[/C][/ROW]
[ROW][C]22[/C][C]0.268187[/C][C]4.4716[/C][C]6e-06[/C][/ROW]
[ROW][C]23[/C][C]0.232491[/C][C]3.8764[/C][C]6.6e-05[/C][/ROW]
[ROW][C]24[/C][C]0.220954[/C][C]3.684[/C][C]0.000138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266114&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.358515.97760
20.3367195.61420
30.3675686.12860
40.3248085.41560
50.3236675.39660
60.2774524.62613e-06
70.2094573.49230.000278
80.2697734.4985e-06
90.2707894.51495e-06
100.2286043.81168.5e-05
110.2776114.62873e-06
120.2389193.98364.3e-05
130.2608984.351e-05
140.2280363.80218.8e-05
150.2711034.52025e-06
160.2669214.45056e-06
170.2493434.15742.1e-05
180.2495164.16032.1e-05
190.2133483.55720.00022
200.2244333.7420.000111
210.2510024.1851.9e-05
220.2681874.47166e-06
230.2324913.87646.6e-05
240.2209543.6840.000138






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.358515.97760
20.2388953.98324.3e-05
30.231273.8567.2e-05
40.1320622.20190.014246
50.1194441.99150.023701
60.0435370.72590.234252
7-0.033893-0.56510.286227
80.0775691.29330.098483
90.0791161.31910.094105
100.0280380.46750.320257
110.0960261.60110.055247
120.0284310.4740.317921
130.05930.98870.161829
14-0.006132-0.10220.459317
150.0832361.38780.08315
160.0566740.94490.172754
170.0287230.47890.316187
180.0341470.56930.284793
19-0.023583-0.39320.347235
200.0075170.12530.450173
210.0483440.80610.210448
220.0831361.38610.083406
230.0228530.3810.351732
24-0.007517-0.12530.450177

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.35851 & 5.9776 & 0 \tabularnewline
2 & 0.238895 & 3.9832 & 4.3e-05 \tabularnewline
3 & 0.23127 & 3.856 & 7.2e-05 \tabularnewline
4 & 0.132062 & 2.2019 & 0.014246 \tabularnewline
5 & 0.119444 & 1.9915 & 0.023701 \tabularnewline
6 & 0.043537 & 0.7259 & 0.234252 \tabularnewline
7 & -0.033893 & -0.5651 & 0.286227 \tabularnewline
8 & 0.077569 & 1.2933 & 0.098483 \tabularnewline
9 & 0.079116 & 1.3191 & 0.094105 \tabularnewline
10 & 0.028038 & 0.4675 & 0.320257 \tabularnewline
11 & 0.096026 & 1.6011 & 0.055247 \tabularnewline
12 & 0.028431 & 0.474 & 0.317921 \tabularnewline
13 & 0.0593 & 0.9887 & 0.161829 \tabularnewline
14 & -0.006132 & -0.1022 & 0.459317 \tabularnewline
15 & 0.083236 & 1.3878 & 0.08315 \tabularnewline
16 & 0.056674 & 0.9449 & 0.172754 \tabularnewline
17 & 0.028723 & 0.4789 & 0.316187 \tabularnewline
18 & 0.034147 & 0.5693 & 0.284793 \tabularnewline
19 & -0.023583 & -0.3932 & 0.347235 \tabularnewline
20 & 0.007517 & 0.1253 & 0.450173 \tabularnewline
21 & 0.048344 & 0.8061 & 0.210448 \tabularnewline
22 & 0.083136 & 1.3861 & 0.083406 \tabularnewline
23 & 0.022853 & 0.381 & 0.351732 \tabularnewline
24 & -0.007517 & -0.1253 & 0.450177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266114&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]0.35851[/C][C]5.9776[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.238895[/C][C]3.9832[/C][C]4.3e-05[/C][/ROW]
[ROW][C]3[/C][C]0.23127[/C][C]3.856[/C][C]7.2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.132062[/C][C]2.2019[/C][C]0.014246[/C][/ROW]
[ROW][C]5[/C][C]0.119444[/C][C]1.9915[/C][C]0.023701[/C][/ROW]
[ROW][C]6[/C][C]0.043537[/C][C]0.7259[/C][C]0.234252[/C][/ROW]
[ROW][C]7[/C][C]-0.033893[/C][C]-0.5651[/C][C]0.286227[/C][/ROW]
[ROW][C]8[/C][C]0.077569[/C][C]1.2933[/C][C]0.098483[/C][/ROW]
[ROW][C]9[/C][C]0.079116[/C][C]1.3191[/C][C]0.094105[/C][/ROW]
[ROW][C]10[/C][C]0.028038[/C][C]0.4675[/C][C]0.320257[/C][/ROW]
[ROW][C]11[/C][C]0.096026[/C][C]1.6011[/C][C]0.055247[/C][/ROW]
[ROW][C]12[/C][C]0.028431[/C][C]0.474[/C][C]0.317921[/C][/ROW]
[ROW][C]13[/C][C]0.0593[/C][C]0.9887[/C][C]0.161829[/C][/ROW]
[ROW][C]14[/C][C]-0.006132[/C][C]-0.1022[/C][C]0.459317[/C][/ROW]
[ROW][C]15[/C][C]0.083236[/C][C]1.3878[/C][C]0.08315[/C][/ROW]
[ROW][C]16[/C][C]0.056674[/C][C]0.9449[/C][C]0.172754[/C][/ROW]
[ROW][C]17[/C][C]0.028723[/C][C]0.4789[/C][C]0.316187[/C][/ROW]
[ROW][C]18[/C][C]0.034147[/C][C]0.5693[/C][C]0.284793[/C][/ROW]
[ROW][C]19[/C][C]-0.023583[/C][C]-0.3932[/C][C]0.347235[/C][/ROW]
[ROW][C]20[/C][C]0.007517[/C][C]0.1253[/C][C]0.450173[/C][/ROW]
[ROW][C]21[/C][C]0.048344[/C][C]0.8061[/C][C]0.210448[/C][/ROW]
[ROW][C]22[/C][C]0.083136[/C][C]1.3861[/C][C]0.083406[/C][/ROW]
[ROW][C]23[/C][C]0.022853[/C][C]0.381[/C][C]0.351732[/C][/ROW]
[ROW][C]24[/C][C]-0.007517[/C][C]-0.1253[/C][C]0.450177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266114&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266114&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.358515.97760
20.2388953.98324.3e-05
30.231273.8567.2e-05
40.1320622.20190.014246
50.1194441.99150.023701
60.0435370.72590.234252
7-0.033893-0.56510.286227
80.0775691.29330.098483
90.0791161.31910.094105
100.0280380.46750.320257
110.0960261.60110.055247
120.0284310.4740.317921
130.05930.98870.161829
14-0.006132-0.10220.459317
150.0832361.38780.08315
160.0566740.94490.172754
170.0287230.47890.316187
180.0341470.56930.284793
19-0.023583-0.39320.347235
200.0075170.12530.450173
210.0483440.80610.210448
220.0831361.38610.083406
230.0228530.3810.351732
24-0.007517-0.12530.450177


Figures (Output of Computation)

Input Parameters & R Code

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')