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Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSat, 12 Mar 2016 21:08:47 +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/2016/Mar/12/t1457816970tffnpbtzjeao3zc.htm/, Retrieved Sun, 05 May 2024 10:51:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293963, Retrieved Sun, 05 May 2024 10:51:20 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [Levendgeborenen v...] [2016-03-12 20:36:41] [81a1e107241d8fde43db5076a3180805]
- RMPD  [(Partial) Autocorrelation Function] [CPI Wijnen - Auto...] [2016-03-12 21:05:03] [81a1e107241d8fde43db5076a3180805]
-   P       [(Partial) Autocorrelation Function] [CPI Wijnen - Auto...] [2016-03-12 21:08:47] [25a5f245cb671e152cfd8b6d35402e87] [Current]
- R           [(Partial) Autocorrelation Function] [CPI Wijnen - Auto...] [2016-03-12 21:15:47] [81a1e107241d8fde43db5076a3180805]
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Dataseries X:
110.27
110.91
110.27
109.41
111.47
110.77
110.83
110.52
110.44
109.99
110.55
109.99
111.2
111.81
110.36
111.24
112.6
111.75
112.49
111.94
113.22
112.85
114.37
113.68
118
118.27
119.2
117.98
117.59
117.41
118.31
118.4
117.92
118.94
118.81
117.44
120.21
119.74
118.79
118.19
119.16
118.88
119.59
119.44
119.84
119.31
118.15
118.23
119.89
118.83
118.95
119.86
119.07
119.52
119.92
119.68
119.81
120.09
119.98
118.96




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=293963&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=293963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293963&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'Sir Maurice George Kendall' @ kendall.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9404787.28490
20.9038037.00080
30.8592026.65540
40.8106066.27890
50.7659575.93310
60.7303125.6570
70.67795.2511e-06
80.6333934.90624e-06
90.5762844.46391.8e-05
100.5163443.99968.8e-05
110.468023.62530.000298
120.4125833.19590.001112
130.3440152.66470.004941
140.301072.33210.011536
150.2323511.79980.038462
160.1750781.35610.090067
170.1260.9760.166493
180.0778760.60320.274317
190.017360.13450.446739
20-0.027555-0.21340.415854
21-0.079742-0.61770.269563
22-0.135944-1.0530.148278
23-0.175955-1.36290.088997
24-0.21615-1.67430.049639

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.940478 & 7.2849 & 0 \tabularnewline
2 & 0.903803 & 7.0008 & 0 \tabularnewline
3 & 0.859202 & 6.6554 & 0 \tabularnewline
4 & 0.810606 & 6.2789 & 0 \tabularnewline
5 & 0.765957 & 5.9331 & 0 \tabularnewline
6 & 0.730312 & 5.657 & 0 \tabularnewline
7 & 0.6779 & 5.251 & 1e-06 \tabularnewline
8 & 0.633393 & 4.9062 & 4e-06 \tabularnewline
9 & 0.576284 & 4.4639 & 1.8e-05 \tabularnewline
10 & 0.516344 & 3.9996 & 8.8e-05 \tabularnewline
11 & 0.46802 & 3.6253 & 0.000298 \tabularnewline
12 & 0.412583 & 3.1959 & 0.001112 \tabularnewline
13 & 0.344015 & 2.6647 & 0.004941 \tabularnewline
14 & 0.30107 & 2.3321 & 0.011536 \tabularnewline
15 & 0.232351 & 1.7998 & 0.038462 \tabularnewline
16 & 0.175078 & 1.3561 & 0.090067 \tabularnewline
17 & 0.126 & 0.976 & 0.166493 \tabularnewline
18 & 0.077876 & 0.6032 & 0.274317 \tabularnewline
19 & 0.01736 & 0.1345 & 0.446739 \tabularnewline
20 & -0.027555 & -0.2134 & 0.415854 \tabularnewline
21 & -0.079742 & -0.6177 & 0.269563 \tabularnewline
22 & -0.135944 & -1.053 & 0.148278 \tabularnewline
23 & -0.175955 & -1.3629 & 0.088997 \tabularnewline
24 & -0.21615 & -1.6743 & 0.049639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293963&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]0.940478[/C][C]7.2849[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.903803[/C][C]7.0008[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.859202[/C][C]6.6554[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.810606[/C][C]6.2789[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.765957[/C][C]5.9331[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.730312[/C][C]5.657[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.6779[/C][C]5.251[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.633393[/C][C]4.9062[/C][C]4e-06[/C][/ROW]
[ROW][C]9[/C][C]0.576284[/C][C]4.4639[/C][C]1.8e-05[/C][/ROW]
[ROW][C]10[/C][C]0.516344[/C][C]3.9996[/C][C]8.8e-05[/C][/ROW]
[ROW][C]11[/C][C]0.46802[/C][C]3.6253[/C][C]0.000298[/C][/ROW]
[ROW][C]12[/C][C]0.412583[/C][C]3.1959[/C][C]0.001112[/C][/ROW]
[ROW][C]13[/C][C]0.344015[/C][C]2.6647[/C][C]0.004941[/C][/ROW]
[ROW][C]14[/C][C]0.30107[/C][C]2.3321[/C][C]0.011536[/C][/ROW]
[ROW][C]15[/C][C]0.232351[/C][C]1.7998[/C][C]0.038462[/C][/ROW]
[ROW][C]16[/C][C]0.175078[/C][C]1.3561[/C][C]0.090067[/C][/ROW]
[ROW][C]17[/C][C]0.126[/C][C]0.976[/C][C]0.166493[/C][/ROW]
[ROW][C]18[/C][C]0.077876[/C][C]0.6032[/C][C]0.274317[/C][/ROW]
[ROW][C]19[/C][C]0.01736[/C][C]0.1345[/C][C]0.446739[/C][/ROW]
[ROW][C]20[/C][C]-0.027555[/C][C]-0.2134[/C][C]0.415854[/C][/ROW]
[ROW][C]21[/C][C]-0.079742[/C][C]-0.6177[/C][C]0.269563[/C][/ROW]
[ROW][C]22[/C][C]-0.135944[/C][C]-1.053[/C][C]0.148278[/C][/ROW]
[ROW][C]23[/C][C]-0.175955[/C][C]-1.3629[/C][C]0.088997[/C][/ROW]
[ROW][C]24[/C][C]-0.21615[/C][C]-1.6743[/C][C]0.049639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293963&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
10.9404787.28490
20.9038037.00080
30.8592026.65540
40.8106066.27890
50.7659575.93310
60.7303125.6570
70.67795.2511e-06
80.6333934.90624e-06
90.5762844.46391.8e-05
100.5163443.99968.8e-05
110.468023.62530.000298
120.4125833.19590.001112
130.3440152.66470.004941
140.301072.33210.011536
150.2323511.79980.038462
160.1750781.35610.090067
170.1260.9760.166493
180.0778760.60320.274317
190.017360.13450.446739
20-0.027555-0.21340.415854
21-0.079742-0.61770.269563
22-0.135944-1.0530.148278
23-0.175955-1.36290.088997
24-0.21615-1.67430.049639







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9404787.28490
20.1671341.29460.100207
3-0.05278-0.40880.342059
4-0.078273-0.60630.2733
5-0.005841-0.04520.482032
60.0706770.54750.293045
7-0.1411-1.0930.139391
8-0.020572-0.15940.436964
9-0.119531-0.92590.179109
10-0.085604-0.66310.254908
110.0584390.45270.326209
12-0.069526-0.53850.296095
13-0.176519-1.36730.088314
140.1200690.930.178036
15-0.169978-1.31660.096483
16-0.004828-0.03740.485147
170.0344130.26660.395362
180.0050350.0390.48451
19-0.148646-1.15140.127067
20-0.001564-0.01210.495186
210.0156590.12130.451932
22-0.156076-1.2090.115711
230.070830.54860.292643
240.0361040.27970.390351

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.940478 & 7.2849 & 0 \tabularnewline
2 & 0.167134 & 1.2946 & 0.100207 \tabularnewline
3 & -0.05278 & -0.4088 & 0.342059 \tabularnewline
4 & -0.078273 & -0.6063 & 0.2733 \tabularnewline
5 & -0.005841 & -0.0452 & 0.482032 \tabularnewline
6 & 0.070677 & 0.5475 & 0.293045 \tabularnewline
7 & -0.1411 & -1.093 & 0.139391 \tabularnewline
8 & -0.020572 & -0.1594 & 0.436964 \tabularnewline
9 & -0.119531 & -0.9259 & 0.179109 \tabularnewline
10 & -0.085604 & -0.6631 & 0.254908 \tabularnewline
11 & 0.058439 & 0.4527 & 0.326209 \tabularnewline
12 & -0.069526 & -0.5385 & 0.296095 \tabularnewline
13 & -0.176519 & -1.3673 & 0.088314 \tabularnewline
14 & 0.120069 & 0.93 & 0.178036 \tabularnewline
15 & -0.169978 & -1.3166 & 0.096483 \tabularnewline
16 & -0.004828 & -0.0374 & 0.485147 \tabularnewline
17 & 0.034413 & 0.2666 & 0.395362 \tabularnewline
18 & 0.005035 & 0.039 & 0.48451 \tabularnewline
19 & -0.148646 & -1.1514 & 0.127067 \tabularnewline
20 & -0.001564 & -0.0121 & 0.495186 \tabularnewline
21 & 0.015659 & 0.1213 & 0.451932 \tabularnewline
22 & -0.156076 & -1.209 & 0.115711 \tabularnewline
23 & 0.07083 & 0.5486 & 0.292643 \tabularnewline
24 & 0.036104 & 0.2797 & 0.390351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293963&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]0.940478[/C][C]7.2849[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.167134[/C][C]1.2946[/C][C]0.100207[/C][/ROW]
[ROW][C]3[/C][C]-0.05278[/C][C]-0.4088[/C][C]0.342059[/C][/ROW]
[ROW][C]4[/C][C]-0.078273[/C][C]-0.6063[/C][C]0.2733[/C][/ROW]
[ROW][C]5[/C][C]-0.005841[/C][C]-0.0452[/C][C]0.482032[/C][/ROW]
[ROW][C]6[/C][C]0.070677[/C][C]0.5475[/C][C]0.293045[/C][/ROW]
[ROW][C]7[/C][C]-0.1411[/C][C]-1.093[/C][C]0.139391[/C][/ROW]
[ROW][C]8[/C][C]-0.020572[/C][C]-0.1594[/C][C]0.436964[/C][/ROW]
[ROW][C]9[/C][C]-0.119531[/C][C]-0.9259[/C][C]0.179109[/C][/ROW]
[ROW][C]10[/C][C]-0.085604[/C][C]-0.6631[/C][C]0.254908[/C][/ROW]
[ROW][C]11[/C][C]0.058439[/C][C]0.4527[/C][C]0.326209[/C][/ROW]
[ROW][C]12[/C][C]-0.069526[/C][C]-0.5385[/C][C]0.296095[/C][/ROW]
[ROW][C]13[/C][C]-0.176519[/C][C]-1.3673[/C][C]0.088314[/C][/ROW]
[ROW][C]14[/C][C]0.120069[/C][C]0.93[/C][C]0.178036[/C][/ROW]
[ROW][C]15[/C][C]-0.169978[/C][C]-1.3166[/C][C]0.096483[/C][/ROW]
[ROW][C]16[/C][C]-0.004828[/C][C]-0.0374[/C][C]0.485147[/C][/ROW]
[ROW][C]17[/C][C]0.034413[/C][C]0.2666[/C][C]0.395362[/C][/ROW]
[ROW][C]18[/C][C]0.005035[/C][C]0.039[/C][C]0.48451[/C][/ROW]
[ROW][C]19[/C][C]-0.148646[/C][C]-1.1514[/C][C]0.127067[/C][/ROW]
[ROW][C]20[/C][C]-0.001564[/C][C]-0.0121[/C][C]0.495186[/C][/ROW]
[ROW][C]21[/C][C]0.015659[/C][C]0.1213[/C][C]0.451932[/C][/ROW]
[ROW][C]22[/C][C]-0.156076[/C][C]-1.209[/C][C]0.115711[/C][/ROW]
[ROW][C]23[/C][C]0.07083[/C][C]0.5486[/C][C]0.292643[/C][/ROW]
[ROW][C]24[/C][C]0.036104[/C][C]0.2797[/C][C]0.390351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293963&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
10.9404787.28490
20.1671341.29460.100207
3-0.05278-0.40880.342059
4-0.078273-0.60630.2733
5-0.005841-0.04520.482032
60.0706770.54750.293045
7-0.1411-1.0930.139391
8-0.020572-0.15940.436964
9-0.119531-0.92590.179109
10-0.085604-0.66310.254908
110.0584390.45270.326209
12-0.069526-0.53850.296095
13-0.176519-1.36730.088314
140.1200690.930.178036
15-0.169978-1.31660.096483
16-0.004828-0.03740.485147
170.0344130.26660.395362
180.0050350.0390.48451
19-0.148646-1.15140.127067
20-0.001564-0.01210.495186
210.0156590.12130.451932
22-0.156076-1.2090.115711
230.070830.54860.292643
240.0361040.27970.390351



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 24 ; 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):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- '48'
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)
x <- na.omit(x)
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')