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Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationWed, 15 Oct 2014 13:51:44 +0100
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/Oct/15/t1413377548qlvj7j7a24p1dde.htm/, Retrieved Tue, 14 May 2024 20:30:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=241316, Retrieved Tue, 14 May 2024 20:30:59 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [] [2014-10-13 14:39:25] [754a3b16619ece0fc2203bb885e0cd98]
- RMPD  [(Partial) Autocorrelation Function] [] [2014-10-15 12:49:53] [754a3b16619ece0fc2203bb885e0cd98]
- R P       [(Partial) Autocorrelation Function] [] [2014-10-15 12:51:44] [fa76cbd0c9542d7a6f5f3c5daec42b95] [Current]
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Dataseries X:
75
84.3
84
79.1
78.8
82.7
85.3
84.5
80.8
70.1
68.2
68.1
72.3
73.1
71.5
74.1
80.3
80.6
81.4
87.4
89.3
93.2
92.8
96.8
100.3
95.6
89
87.4
86.7
92.8
98.6
100.8
105.5
107.8
113.7
120.3
126.5
134.8
134.5
133.1
128.8
127.1
129.1
128.4
126.5
117.1
114.2
109.1
110.3
109.2
103.6
98.9
95.9
91.2
98.7
94.5
95.6
93.8
89.5
87.1
87.1
84.5
84.2
83.7
82.2
77.7
78.5
79.1
78.6
79
76.2
77.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=241316&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=241316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=241316&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'George Udny Yule' @ yule.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9614428.15810
20.9112887.73250
30.8543517.24940
40.7917856.71850
50.726476.16430
60.6525115.53670
70.5698844.83564e-06
80.4888934.14844.5e-05
90.4096143.47570.000434
100.332722.82320.003072
110.2628072.230.014433
120.1970191.67180.049456
130.1323611.12310.132558
140.0679040.57620.283143
150.0029540.02510.490035
16-0.05867-0.49780.310061
17-0.112244-0.95240.172035
18-0.169204-1.43570.077703

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.961442 & 8.1581 & 0 \tabularnewline
2 & 0.911288 & 7.7325 & 0 \tabularnewline
3 & 0.854351 & 7.2494 & 0 \tabularnewline
4 & 0.791785 & 6.7185 & 0 \tabularnewline
5 & 0.72647 & 6.1643 & 0 \tabularnewline
6 & 0.652511 & 5.5367 & 0 \tabularnewline
7 & 0.569884 & 4.8356 & 4e-06 \tabularnewline
8 & 0.488893 & 4.1484 & 4.5e-05 \tabularnewline
9 & 0.409614 & 3.4757 & 0.000434 \tabularnewline
10 & 0.33272 & 2.8232 & 0.003072 \tabularnewline
11 & 0.262807 & 2.23 & 0.014433 \tabularnewline
12 & 0.197019 & 1.6718 & 0.049456 \tabularnewline
13 & 0.132361 & 1.1231 & 0.132558 \tabularnewline
14 & 0.067904 & 0.5762 & 0.283143 \tabularnewline
15 & 0.002954 & 0.0251 & 0.490035 \tabularnewline
16 & -0.05867 & -0.4978 & 0.310061 \tabularnewline
17 & -0.112244 & -0.9524 & 0.172035 \tabularnewline
18 & -0.169204 & -1.4357 & 0.077703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=241316&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]0.961442[/C][C]8.1581[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.911288[/C][C]7.7325[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.854351[/C][C]7.2494[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.791785[/C][C]6.7185[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.72647[/C][C]6.1643[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.652511[/C][C]5.5367[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.569884[/C][C]4.8356[/C][C]4e-06[/C][/ROW]
[ROW][C]8[/C][C]0.488893[/C][C]4.1484[/C][C]4.5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.409614[/C][C]3.4757[/C][C]0.000434[/C][/ROW]
[ROW][C]10[/C][C]0.33272[/C][C]2.8232[/C][C]0.003072[/C][/ROW]
[ROW][C]11[/C][C]0.262807[/C][C]2.23[/C][C]0.014433[/C][/ROW]
[ROW][C]12[/C][C]0.197019[/C][C]1.6718[/C][C]0.049456[/C][/ROW]
[ROW][C]13[/C][C]0.132361[/C][C]1.1231[/C][C]0.132558[/C][/ROW]
[ROW][C]14[/C][C]0.067904[/C][C]0.5762[/C][C]0.283143[/C][/ROW]
[ROW][C]15[/C][C]0.002954[/C][C]0.0251[/C][C]0.490035[/C][/ROW]
[ROW][C]16[/C][C]-0.05867[/C][C]-0.4978[/C][C]0.310061[/C][/ROW]
[ROW][C]17[/C][C]-0.112244[/C][C]-0.9524[/C][C]0.172035[/C][/ROW]
[ROW][C]18[/C][C]-0.169204[/C][C]-1.4357[/C][C]0.077703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=241316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=241316&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
10.9614428.15810
20.9112887.73250
30.8543517.24940
40.7917856.71850
50.726476.16430
60.6525115.53670
70.5698844.83564e-06
80.4888934.14844.5e-05
90.4096143.47570.000434
100.332722.82320.003072
110.2628072.230.014433
120.1970191.67180.049456
130.1323611.12310.132558
140.0679040.57620.283143
150.0029540.02510.490035
16-0.05867-0.49780.310061
17-0.112244-0.95240.172035
18-0.169204-1.43570.077703







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9614428.15810
2-0.172992-1.46790.073246
3-0.096026-0.81480.208934
4-0.085952-0.72930.234085
5-0.0506-0.42940.334474
6-0.14313-1.21450.114262
7-0.135307-1.14810.127361
80.0061110.05190.479394
9-0.019746-0.16750.433704
10-0.024021-0.20380.419532
110.0385320.3270.372327
12-0.003786-0.03210.487229
13-0.061918-0.52540.300463
14-0.084305-0.71530.238353
15-0.082787-0.70250.242326
16-0.037869-0.32130.374445
170.017590.14930.440885
18-0.13954-1.1840.120146

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.961442 & 8.1581 & 0 \tabularnewline
2 & -0.172992 & -1.4679 & 0.073246 \tabularnewline
3 & -0.096026 & -0.8148 & 0.208934 \tabularnewline
4 & -0.085952 & -0.7293 & 0.234085 \tabularnewline
5 & -0.0506 & -0.4294 & 0.334474 \tabularnewline
6 & -0.14313 & -1.2145 & 0.114262 \tabularnewline
7 & -0.135307 & -1.1481 & 0.127361 \tabularnewline
8 & 0.006111 & 0.0519 & 0.479394 \tabularnewline
9 & -0.019746 & -0.1675 & 0.433704 \tabularnewline
10 & -0.024021 & -0.2038 & 0.419532 \tabularnewline
11 & 0.038532 & 0.327 & 0.372327 \tabularnewline
12 & -0.003786 & -0.0321 & 0.487229 \tabularnewline
13 & -0.061918 & -0.5254 & 0.300463 \tabularnewline
14 & -0.084305 & -0.7153 & 0.238353 \tabularnewline
15 & -0.082787 & -0.7025 & 0.242326 \tabularnewline
16 & -0.037869 & -0.3213 & 0.374445 \tabularnewline
17 & 0.01759 & 0.1493 & 0.440885 \tabularnewline
18 & -0.13954 & -1.184 & 0.120146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=241316&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]0.961442[/C][C]8.1581[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.172992[/C][C]-1.4679[/C][C]0.073246[/C][/ROW]
[ROW][C]3[/C][C]-0.096026[/C][C]-0.8148[/C][C]0.208934[/C][/ROW]
[ROW][C]4[/C][C]-0.085952[/C][C]-0.7293[/C][C]0.234085[/C][/ROW]
[ROW][C]5[/C][C]-0.0506[/C][C]-0.4294[/C][C]0.334474[/C][/ROW]
[ROW][C]6[/C][C]-0.14313[/C][C]-1.2145[/C][C]0.114262[/C][/ROW]
[ROW][C]7[/C][C]-0.135307[/C][C]-1.1481[/C][C]0.127361[/C][/ROW]
[ROW][C]8[/C][C]0.006111[/C][C]0.0519[/C][C]0.479394[/C][/ROW]
[ROW][C]9[/C][C]-0.019746[/C][C]-0.1675[/C][C]0.433704[/C][/ROW]
[ROW][C]10[/C][C]-0.024021[/C][C]-0.2038[/C][C]0.419532[/C][/ROW]
[ROW][C]11[/C][C]0.038532[/C][C]0.327[/C][C]0.372327[/C][/ROW]
[ROW][C]12[/C][C]-0.003786[/C][C]-0.0321[/C][C]0.487229[/C][/ROW]
[ROW][C]13[/C][C]-0.061918[/C][C]-0.5254[/C][C]0.300463[/C][/ROW]
[ROW][C]14[/C][C]-0.084305[/C][C]-0.7153[/C][C]0.238353[/C][/ROW]
[ROW][C]15[/C][C]-0.082787[/C][C]-0.7025[/C][C]0.242326[/C][/ROW]
[ROW][C]16[/C][C]-0.037869[/C][C]-0.3213[/C][C]0.374445[/C][/ROW]
[ROW][C]17[/C][C]0.01759[/C][C]0.1493[/C][C]0.440885[/C][/ROW]
[ROW][C]18[/C][C]-0.13954[/C][C]-1.184[/C][C]0.120146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=241316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=241316&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
10.9614428.15810
2-0.172992-1.46790.073246
3-0.096026-0.81480.208934
4-0.085952-0.72930.234085
5-0.0506-0.42940.334474
6-0.14313-1.21450.114262
7-0.135307-1.14810.127361
80.0061110.05190.479394
9-0.019746-0.16750.433704
10-0.024021-0.20380.419532
110.0385320.3270.372327
12-0.003786-0.03210.487229
13-0.061918-0.52540.300463
14-0.084305-0.71530.238353
15-0.082787-0.70250.242326
16-0.037869-0.32130.374445
170.017590.14930.440885
18-0.13954-1.1840.120146



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 48 ; par2 = 1 ; par3 = 1 ; 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 <- 'Default'
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')