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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationThu, 05 Mar 2015 21:33:41 +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/Mar/05/t1425591235isq50xll2lfqiy7.htm/, Retrieved Fri, 17 May 2024 12:24:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278031, Retrieved Fri, 17 May 2024 12:24:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

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] [] [2015-03-05 21:33:41] [d3245c242fac7b2d7caab09de558415e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20
23
27
23
21
18
16
11
14
-3
2
26
11
11
11
3
8
8
7
3
4
-7
0
-5
5
-1
-4
4
7
6
13
20
21
37
52
59
66
73
71
69
63
68
58
50
50
50
47
60
62
63
56
38
45
39
26
25
19
14
6
4
5
-3
-5
0
-6
4
-3
14
16
17
25
25
30
51
31
31
25
35
39
48
41
47
61
55
63
45
62
55
50
52
45
36
40
32
29
24
28
27
33
33
24
26
38
32
30
26
21
21

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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278031&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278031&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278031&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'Sir Maurice George Kendall' @ kendall.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9273459.63720
20.8807719.15320
30.8188218.50940
40.7348597.63690
50.651166.76710
60.5554255.77210
70.4457914.63285e-06
80.3512183.650.000203
90.2583642.6850.004199
100.1702811.76960.039807
110.0820720.85290.197795
12-0.008357-0.08680.465477
13-0.087592-0.91030.18235
14-0.171349-1.78070.038886
15-0.253348-2.63290.004854
16-0.324797-3.37540.000512
17-0.395471-4.10993.9e-05
18-0.458862-4.76863e-06
19-0.496888-5.16381e-06
20-0.539485-5.60650

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927345 & 9.6372 & 0 \tabularnewline
2 & 0.880771 & 9.1532 & 0 \tabularnewline
3 & 0.818821 & 8.5094 & 0 \tabularnewline
4 & 0.734859 & 7.6369 & 0 \tabularnewline
5 & 0.65116 & 6.7671 & 0 \tabularnewline
6 & 0.555425 & 5.7721 & 0 \tabularnewline
7 & 0.445791 & 4.6328 & 5e-06 \tabularnewline
8 & 0.351218 & 3.65 & 0.000203 \tabularnewline
9 & 0.258364 & 2.685 & 0.004199 \tabularnewline
10 & 0.170281 & 1.7696 & 0.039807 \tabularnewline
11 & 0.082072 & 0.8529 & 0.197795 \tabularnewline
12 & -0.008357 & -0.0868 & 0.465477 \tabularnewline
13 & -0.087592 & -0.9103 & 0.18235 \tabularnewline
14 & -0.171349 & -1.7807 & 0.038886 \tabularnewline
15 & -0.253348 & -2.6329 & 0.004854 \tabularnewline
16 & -0.324797 & -3.3754 & 0.000512 \tabularnewline
17 & -0.395471 & -4.1099 & 3.9e-05 \tabularnewline
18 & -0.458862 & -4.7686 & 3e-06 \tabularnewline
19 & -0.496888 & -5.1638 & 1e-06 \tabularnewline
20 & -0.539485 & -5.6065 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278031&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]0.927345[/C][C]9.6372[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.880771[/C][C]9.1532[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.818821[/C][C]8.5094[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.734859[/C][C]7.6369[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.65116[/C][C]6.7671[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.555425[/C][C]5.7721[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.445791[/C][C]4.6328[/C][C]5e-06[/C][/ROW]
[ROW][C]8[/C][C]0.351218[/C][C]3.65[/C][C]0.000203[/C][/ROW]
[ROW][C]9[/C][C]0.258364[/C][C]2.685[/C][C]0.004199[/C][/ROW]
[ROW][C]10[/C][C]0.170281[/C][C]1.7696[/C][C]0.039807[/C][/ROW]
[ROW][C]11[/C][C]0.082072[/C][C]0.8529[/C][C]0.197795[/C][/ROW]
[ROW][C]12[/C][C]-0.008357[/C][C]-0.0868[/C][C]0.465477[/C][/ROW]
[ROW][C]13[/C][C]-0.087592[/C][C]-0.9103[/C][C]0.18235[/C][/ROW]
[ROW][C]14[/C][C]-0.171349[/C][C]-1.7807[/C][C]0.038886[/C][/ROW]
[ROW][C]15[/C][C]-0.253348[/C][C]-2.6329[/C][C]0.004854[/C][/ROW]
[ROW][C]16[/C][C]-0.324797[/C][C]-3.3754[/C][C]0.000512[/C][/ROW]
[ROW][C]17[/C][C]-0.395471[/C][C]-4.1099[/C][C]3.9e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.458862[/C][C]-4.7686[/C][C]3e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.496888[/C][C]-5.1638[/C][C]1e-06[/C][/ROW]
[ROW][C]20[/C][C]-0.539485[/C][C]-5.6065[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278031&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278031&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
10.9273459.63720
20.8807719.15320
30.8188218.50940
40.7348597.63690
50.651166.76710
60.5554255.77210
70.4457914.63285e-06
80.3512183.650.000203
90.2583642.6850.004199
100.1702811.76960.039807
110.0820720.85290.197795
12-0.008357-0.08680.465477
13-0.087592-0.91030.18235
14-0.171349-1.78070.038886
15-0.253348-2.63290.004854
16-0.324797-3.37540.000512
17-0.395471-4.10993.9e-05
18-0.458862-4.76863e-06
19-0.496888-5.16381e-06
20-0.539485-5.60650






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9273459.63720
20.1485621.54390.062768
3-0.105036-1.09160.138727
4-0.228386-2.37350.009695
5-0.104483-1.08580.139989
6-0.121931-1.26710.103915
7-0.17139-1.78110.03885
80.0154310.16040.436445
90.0294980.30660.379886
100.0094570.09830.460947
11-0.082606-0.85850.196268
12-0.121146-1.2590.105375
13-0.041052-0.42660.335251
14-0.127272-1.32260.094373
15-0.121407-1.26170.104888
16-0.03552-0.36910.356375
17-0.039974-0.41540.339329
18-0.052758-0.54830.292317
190.0835920.86870.193465
20-0.051088-0.53090.298283

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927345 & 9.6372 & 0 \tabularnewline
2 & 0.148562 & 1.5439 & 0.062768 \tabularnewline
3 & -0.105036 & -1.0916 & 0.138727 \tabularnewline
4 & -0.228386 & -2.3735 & 0.009695 \tabularnewline
5 & -0.104483 & -1.0858 & 0.139989 \tabularnewline
6 & -0.121931 & -1.2671 & 0.103915 \tabularnewline
7 & -0.17139 & -1.7811 & 0.03885 \tabularnewline
8 & 0.015431 & 0.1604 & 0.436445 \tabularnewline
9 & 0.029498 & 0.3066 & 0.379886 \tabularnewline
10 & 0.009457 & 0.0983 & 0.460947 \tabularnewline
11 & -0.082606 & -0.8585 & 0.196268 \tabularnewline
12 & -0.121146 & -1.259 & 0.105375 \tabularnewline
13 & -0.041052 & -0.4266 & 0.335251 \tabularnewline
14 & -0.127272 & -1.3226 & 0.094373 \tabularnewline
15 & -0.121407 & -1.2617 & 0.104888 \tabularnewline
16 & -0.03552 & -0.3691 & 0.356375 \tabularnewline
17 & -0.039974 & -0.4154 & 0.339329 \tabularnewline
18 & -0.052758 & -0.5483 & 0.292317 \tabularnewline
19 & 0.083592 & 0.8687 & 0.193465 \tabularnewline
20 & -0.051088 & -0.5309 & 0.298283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278031&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]0.927345[/C][C]9.6372[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.148562[/C][C]1.5439[/C][C]0.062768[/C][/ROW]
[ROW][C]3[/C][C]-0.105036[/C][C]-1.0916[/C][C]0.138727[/C][/ROW]
[ROW][C]4[/C][C]-0.228386[/C][C]-2.3735[/C][C]0.009695[/C][/ROW]
[ROW][C]5[/C][C]-0.104483[/C][C]-1.0858[/C][C]0.139989[/C][/ROW]
[ROW][C]6[/C][C]-0.121931[/C][C]-1.2671[/C][C]0.103915[/C][/ROW]
[ROW][C]7[/C][C]-0.17139[/C][C]-1.7811[/C][C]0.03885[/C][/ROW]
[ROW][C]8[/C][C]0.015431[/C][C]0.1604[/C][C]0.436445[/C][/ROW]
[ROW][C]9[/C][C]0.029498[/C][C]0.3066[/C][C]0.379886[/C][/ROW]
[ROW][C]10[/C][C]0.009457[/C][C]0.0983[/C][C]0.460947[/C][/ROW]
[ROW][C]11[/C][C]-0.082606[/C][C]-0.8585[/C][C]0.196268[/C][/ROW]
[ROW][C]12[/C][C]-0.121146[/C][C]-1.259[/C][C]0.105375[/C][/ROW]
[ROW][C]13[/C][C]-0.041052[/C][C]-0.4266[/C][C]0.335251[/C][/ROW]
[ROW][C]14[/C][C]-0.127272[/C][C]-1.3226[/C][C]0.094373[/C][/ROW]
[ROW][C]15[/C][C]-0.121407[/C][C]-1.2617[/C][C]0.104888[/C][/ROW]
[ROW][C]16[/C][C]-0.03552[/C][C]-0.3691[/C][C]0.356375[/C][/ROW]
[ROW][C]17[/C][C]-0.039974[/C][C]-0.4154[/C][C]0.339329[/C][/ROW]
[ROW][C]18[/C][C]-0.052758[/C][C]-0.5483[/C][C]0.292317[/C][/ROW]
[ROW][C]19[/C][C]0.083592[/C][C]0.8687[/C][C]0.193465[/C][/ROW]
[ROW][C]20[/C][C]-0.051088[/C][C]-0.5309[/C][C]0.298283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278031&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278031&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
10.9273459.63720
20.1485621.54390.062768
3-0.105036-1.09160.138727
4-0.228386-2.37350.009695
5-0.104483-1.08580.139989
6-0.121931-1.26710.103915
7-0.17139-1.78110.03885
80.0154310.16040.436445
90.0294980.30660.379886
100.0094570.09830.460947
11-0.082606-0.85850.196268
12-0.121146-1.2590.105375
13-0.041052-0.42660.335251
14-0.127272-1.32260.094373
15-0.121407-1.26170.104888
16-0.03552-0.36910.356375
17-0.039974-0.41540.339329
18-0.052758-0.54830.292317
190.0835920.86870.193465
20-0.051088-0.53090.298283


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')