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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 computationSun, 15 Dec 2013 07:55:51 -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/2013/Dec/15/t13871121723hk9ddwdnq6nbu1.htm/, Retrieved Fri, 29 Mar 2024 09:08:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232343, Retrieved Fri, 29 Mar 2024 09:08:57 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Wine sales - ACF] [2013-12-15 12:41:55] [e1b6e5c15a370139a1f66dc7648af660]
- R P     [(Partial) Autocorrelation Function] [Wine sales - ACF] [2013-12-15 12:55:51] [e87fe8ad852a0fa5d933f43041f410cc] [Current]
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Dataseries X:
1954
2302
3054
2414
2226
2725
2589
3470
2400
3180
4009
3924
2072
2434
2956
2828
2687
2629
3150
4119
3030
3055
3821
4001
2529
2472
3134
2789
2758
2993
3282
3437
2804
3076
3782
3889
2271
2452
3084
2522
2769
3438
2839
3746
2632
2851
3871
3618
2389
2344
2678
2492
2858
2246
2800
3869
3007
3023
3907
4209




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232343&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]3 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=232343&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232343&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.1201690.83260.20461
20.0100680.06980.47234
30.1717341.18980.119987
40.1337120.92640.179441
50.1406630.97450.167337
6-0.044383-0.30750.379899
7-0.08096-0.56090.288736
80.1487891.03080.153891
90.0282610.19580.422798
10-0.054481-0.37750.353749
110.1679561.16360.125162
12-0.252965-1.75260.043029
13-0.036667-0.2540.400277
140.1088510.75410.227225
15-0.049715-0.34440.366011
16-0.066514-0.46080.323504
17-0.001154-0.0080.496826

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.120169 & 0.8326 & 0.20461 \tabularnewline
2 & 0.010068 & 0.0698 & 0.47234 \tabularnewline
3 & 0.171734 & 1.1898 & 0.119987 \tabularnewline
4 & 0.133712 & 0.9264 & 0.179441 \tabularnewline
5 & 0.140663 & 0.9745 & 0.167337 \tabularnewline
6 & -0.044383 & -0.3075 & 0.379899 \tabularnewline
7 & -0.08096 & -0.5609 & 0.288736 \tabularnewline
8 & 0.148789 & 1.0308 & 0.153891 \tabularnewline
9 & 0.028261 & 0.1958 & 0.422798 \tabularnewline
10 & -0.054481 & -0.3775 & 0.353749 \tabularnewline
11 & 0.167956 & 1.1636 & 0.125162 \tabularnewline
12 & -0.252965 & -1.7526 & 0.043029 \tabularnewline
13 & -0.036667 & -0.254 & 0.400277 \tabularnewline
14 & 0.108851 & 0.7541 & 0.227225 \tabularnewline
15 & -0.049715 & -0.3444 & 0.366011 \tabularnewline
16 & -0.066514 & -0.4608 & 0.323504 \tabularnewline
17 & -0.001154 & -0.008 & 0.496826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232343&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]0.120169[/C][C]0.8326[/C][C]0.20461[/C][/ROW]
[ROW][C]2[/C][C]0.010068[/C][C]0.0698[/C][C]0.47234[/C][/ROW]
[ROW][C]3[/C][C]0.171734[/C][C]1.1898[/C][C]0.119987[/C][/ROW]
[ROW][C]4[/C][C]0.133712[/C][C]0.9264[/C][C]0.179441[/C][/ROW]
[ROW][C]5[/C][C]0.140663[/C][C]0.9745[/C][C]0.167337[/C][/ROW]
[ROW][C]6[/C][C]-0.044383[/C][C]-0.3075[/C][C]0.379899[/C][/ROW]
[ROW][C]7[/C][C]-0.08096[/C][C]-0.5609[/C][C]0.288736[/C][/ROW]
[ROW][C]8[/C][C]0.148789[/C][C]1.0308[/C][C]0.153891[/C][/ROW]
[ROW][C]9[/C][C]0.028261[/C][C]0.1958[/C][C]0.422798[/C][/ROW]
[ROW][C]10[/C][C]-0.054481[/C][C]-0.3775[/C][C]0.353749[/C][/ROW]
[ROW][C]11[/C][C]0.167956[/C][C]1.1636[/C][C]0.125162[/C][/ROW]
[ROW][C]12[/C][C]-0.252965[/C][C]-1.7526[/C][C]0.043029[/C][/ROW]
[ROW][C]13[/C][C]-0.036667[/C][C]-0.254[/C][C]0.400277[/C][/ROW]
[ROW][C]14[/C][C]0.108851[/C][C]0.7541[/C][C]0.227225[/C][/ROW]
[ROW][C]15[/C][C]-0.049715[/C][C]-0.3444[/C][C]0.366011[/C][/ROW]
[ROW][C]16[/C][C]-0.066514[/C][C]-0.4608[/C][C]0.323504[/C][/ROW]
[ROW][C]17[/C][C]-0.001154[/C][C]-0.008[/C][C]0.496826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232343&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232343&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
10.1201690.83260.20461
20.0100680.06980.47234
30.1717341.18980.119987
40.1337120.92640.179441
50.1406630.97450.167337
6-0.044383-0.30750.379899
7-0.08096-0.56090.288736
80.1487891.03080.153891
90.0282610.19580.422798
10-0.054481-0.37750.353749
110.1679561.16360.125162
12-0.252965-1.75260.043029
13-0.036667-0.2540.400277
140.1088510.75410.227225
15-0.049715-0.34440.366011
16-0.066514-0.46080.323504
17-0.001154-0.0080.496826







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.1201690.83260.20461
2-0.004436-0.03070.487803
30.1735611.20250.11754
40.096510.66860.253463
50.1239480.85870.197377
6-0.102637-0.71110.240235
7-0.106564-0.73830.231965
80.1174070.81340.209997
9-0.005459-0.03780.484995
10-0.024184-0.16760.433819
110.1894511.31260.097787
12-0.348421-2.41390.009822
130.0162810.11280.455331
140.0933230.64660.260497
150.0007390.00510.497969
16-0.054086-0.37470.35476
170.1043780.72320.236548

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.120169 & 0.8326 & 0.20461 \tabularnewline
2 & -0.004436 & -0.0307 & 0.487803 \tabularnewline
3 & 0.173561 & 1.2025 & 0.11754 \tabularnewline
4 & 0.09651 & 0.6686 & 0.253463 \tabularnewline
5 & 0.123948 & 0.8587 & 0.197377 \tabularnewline
6 & -0.102637 & -0.7111 & 0.240235 \tabularnewline
7 & -0.106564 & -0.7383 & 0.231965 \tabularnewline
8 & 0.117407 & 0.8134 & 0.209997 \tabularnewline
9 & -0.005459 & -0.0378 & 0.484995 \tabularnewline
10 & -0.024184 & -0.1676 & 0.433819 \tabularnewline
11 & 0.189451 & 1.3126 & 0.097787 \tabularnewline
12 & -0.348421 & -2.4139 & 0.009822 \tabularnewline
13 & 0.016281 & 0.1128 & 0.455331 \tabularnewline
14 & 0.093323 & 0.6466 & 0.260497 \tabularnewline
15 & 0.000739 & 0.0051 & 0.497969 \tabularnewline
16 & -0.054086 & -0.3747 & 0.35476 \tabularnewline
17 & 0.104378 & 0.7232 & 0.236548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232343&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]0.120169[/C][C]0.8326[/C][C]0.20461[/C][/ROW]
[ROW][C]2[/C][C]-0.004436[/C][C]-0.0307[/C][C]0.487803[/C][/ROW]
[ROW][C]3[/C][C]0.173561[/C][C]1.2025[/C][C]0.11754[/C][/ROW]
[ROW][C]4[/C][C]0.09651[/C][C]0.6686[/C][C]0.253463[/C][/ROW]
[ROW][C]5[/C][C]0.123948[/C][C]0.8587[/C][C]0.197377[/C][/ROW]
[ROW][C]6[/C][C]-0.102637[/C][C]-0.7111[/C][C]0.240235[/C][/ROW]
[ROW][C]7[/C][C]-0.106564[/C][C]-0.7383[/C][C]0.231965[/C][/ROW]
[ROW][C]8[/C][C]0.117407[/C][C]0.8134[/C][C]0.209997[/C][/ROW]
[ROW][C]9[/C][C]-0.005459[/C][C]-0.0378[/C][C]0.484995[/C][/ROW]
[ROW][C]10[/C][C]-0.024184[/C][C]-0.1676[/C][C]0.433819[/C][/ROW]
[ROW][C]11[/C][C]0.189451[/C][C]1.3126[/C][C]0.097787[/C][/ROW]
[ROW][C]12[/C][C]-0.348421[/C][C]-2.4139[/C][C]0.009822[/C][/ROW]
[ROW][C]13[/C][C]0.016281[/C][C]0.1128[/C][C]0.455331[/C][/ROW]
[ROW][C]14[/C][C]0.093323[/C][C]0.6466[/C][C]0.260497[/C][/ROW]
[ROW][C]15[/C][C]0.000739[/C][C]0.0051[/C][C]0.497969[/C][/ROW]
[ROW][C]16[/C][C]-0.054086[/C][C]-0.3747[/C][C]0.35476[/C][/ROW]
[ROW][C]17[/C][C]0.104378[/C][C]0.7232[/C][C]0.236548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232343&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232343&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
10.1201690.83260.20461
2-0.004436-0.03070.487803
30.1735611.20250.11754
40.096510.66860.253463
50.1239480.85870.197377
6-0.102637-0.71110.240235
7-0.106564-0.73830.231965
80.1174070.81340.209997
9-0.005459-0.03780.484995
10-0.024184-0.16760.433819
110.1894511.31260.097787
12-0.348421-2.41390.009822
130.0162810.11280.455331
140.0933230.64660.260497
150.0007390.00510.497969
16-0.054086-0.37470.35476
170.1043780.72320.236548



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')