Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationMon, 15 Apr 2013 14:28:06 -0400
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/Apr/15/t13660505742xae4qrryqxgvzq.htm/, Retrieved Mon, 29 Apr 2024 12:45:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208069, Retrieved Mon, 29 Apr 2024 12:45:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2013-04-15 18:28:06] [bda1405f45fc71f9cfac8f9f3e5dea22] [Current]
Feedback Forum

Post a new message
Dataseries X:
120.6
119.9
119.48
117.45
118.37
117.07
114.98
112.59
111.7
112.04
110.79
110.79
109.82
109.11
109.84
109.31
108.29
107.42
106.71
105.11
104.43
105.11
104.43
105.55
106.12
105.78
105.33
104.63
104.62
105.57
107.5
107.52
107.76
106.74
106.21
105.77
105.27
104.35
103.52
102.28
100.93
101.04
99.95
99.55
99.56
99.01
98.64
98.98
100.8
100.32
100.72
280.8
280.4
280.4
280.3
281
280.9
279.7
283.1
290.6
291.6
291.7
291.8
291.7
291.5
291.7
293.4
293.1
292.6
292.1
292.2
292
292.1
293.4
292.2
292.1
291.6
290.9
290.9
290.8
290.5
290
290.2
290.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 7 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208069&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208069&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208069&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 time7 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9636868.83230
20.9272268.49820
30.8908828.16510
40.8537967.82520
50.8164427.48280
60.7790717.14030
70.7419776.80030
80.7035976.44860
90.6631376.07780
100.6227165.70730
110.581935.33350
120.5416814.96462e-06
130.5017154.59837e-06
140.4619364.23372.9e-05
150.4224233.87160.000107
160.3824643.50530.000367
170.342553.13950.001168
180.3028022.77520.003399
190.2636922.41680.008912
200.2244012.05670.021411
210.185081.69630.046767
220.145271.33140.093326
230.1048320.96080.169704
240.0648460.59430.276946

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963686 & 8.8323 & 0 \tabularnewline
2 & 0.927226 & 8.4982 & 0 \tabularnewline
3 & 0.890882 & 8.1651 & 0 \tabularnewline
4 & 0.853796 & 7.8252 & 0 \tabularnewline
5 & 0.816442 & 7.4828 & 0 \tabularnewline
6 & 0.779071 & 7.1403 & 0 \tabularnewline
7 & 0.741977 & 6.8003 & 0 \tabularnewline
8 & 0.703597 & 6.4486 & 0 \tabularnewline
9 & 0.663137 & 6.0778 & 0 \tabularnewline
10 & 0.622716 & 5.7073 & 0 \tabularnewline
11 & 0.58193 & 5.3335 & 0 \tabularnewline
12 & 0.541681 & 4.9646 & 2e-06 \tabularnewline
13 & 0.501715 & 4.5983 & 7e-06 \tabularnewline
14 & 0.461936 & 4.2337 & 2.9e-05 \tabularnewline
15 & 0.422423 & 3.8716 & 0.000107 \tabularnewline
16 & 0.382464 & 3.5053 & 0.000367 \tabularnewline
17 & 0.34255 & 3.1395 & 0.001168 \tabularnewline
18 & 0.302802 & 2.7752 & 0.003399 \tabularnewline
19 & 0.263692 & 2.4168 & 0.008912 \tabularnewline
20 & 0.224401 & 2.0567 & 0.021411 \tabularnewline
21 & 0.18508 & 1.6963 & 0.046767 \tabularnewline
22 & 0.14527 & 1.3314 & 0.093326 \tabularnewline
23 & 0.104832 & 0.9608 & 0.169704 \tabularnewline
24 & 0.064846 & 0.5943 & 0.276946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208069&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]0.963686[/C][C]8.8323[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.927226[/C][C]8.4982[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.890882[/C][C]8.1651[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.853796[/C][C]7.8252[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.816442[/C][C]7.4828[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.779071[/C][C]7.1403[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.741977[/C][C]6.8003[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.703597[/C][C]6.4486[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.663137[/C][C]6.0778[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.622716[/C][C]5.7073[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.58193[/C][C]5.3335[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.541681[/C][C]4.9646[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.501715[/C][C]4.5983[/C][C]7e-06[/C][/ROW]
[ROW][C]14[/C][C]0.461936[/C][C]4.2337[/C][C]2.9e-05[/C][/ROW]
[ROW][C]15[/C][C]0.422423[/C][C]3.8716[/C][C]0.000107[/C][/ROW]
[ROW][C]16[/C][C]0.382464[/C][C]3.5053[/C][C]0.000367[/C][/ROW]
[ROW][C]17[/C][C]0.34255[/C][C]3.1395[/C][C]0.001168[/C][/ROW]
[ROW][C]18[/C][C]0.302802[/C][C]2.7752[/C][C]0.003399[/C][/ROW]
[ROW][C]19[/C][C]0.263692[/C][C]2.4168[/C][C]0.008912[/C][/ROW]
[ROW][C]20[/C][C]0.224401[/C][C]2.0567[/C][C]0.021411[/C][/ROW]
[ROW][C]21[/C][C]0.18508[/C][C]1.6963[/C][C]0.046767[/C][/ROW]
[ROW][C]22[/C][C]0.14527[/C][C]1.3314[/C][C]0.093326[/C][/ROW]
[ROW][C]23[/C][C]0.104832[/C][C]0.9608[/C][C]0.169704[/C][/ROW]
[ROW][C]24[/C][C]0.064846[/C][C]0.5943[/C][C]0.276946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208069&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208069&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
10.9636868.83230
20.9272268.49820
30.8908828.16510
40.8537967.82520
50.8164427.48280
60.7790717.14030
70.7419776.80030
80.7035976.44860
90.6631376.07780
100.6227165.70730
110.581935.33350
120.5416814.96462e-06
130.5017154.59837e-06
140.4619364.23372.9e-05
150.4224233.87160.000107
160.3824643.50530.000367
170.342553.13950.001168
180.3028022.77520.003399
190.2636922.41680.008912
200.2244012.05670.021411
210.185081.69630.046767
220.145271.33140.093326
230.1048320.96080.169704
240.0648460.59430.276946







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9636868.83230
2-0.020531-0.18820.425597
3-0.01729-0.15850.437234
4-0.02965-0.27170.393244
5-0.023726-0.21750.414192
6-0.020821-0.19080.424562
7-0.017031-0.15610.438167
8-0.039309-0.36030.359774
9-0.051766-0.47440.318209
10-0.023947-0.21950.413407
11-0.029957-0.27460.392164
12-0.017617-0.16150.436057
13-0.022027-0.20190.420249
14-0.024047-0.22040.413049
15-0.023548-0.21580.414824
16-0.033247-0.30470.380669
17-0.027565-0.25260.400583
18-0.027265-0.24990.401642
19-0.021285-0.19510.4229
20-0.034027-0.31190.37796
21-0.032759-0.30020.382367
22-0.040749-0.37350.35487
23-0.043733-0.40080.344785
24-0.02987-0.27380.39247

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963686 & 8.8323 & 0 \tabularnewline
2 & -0.020531 & -0.1882 & 0.425597 \tabularnewline
3 & -0.01729 & -0.1585 & 0.437234 \tabularnewline
4 & -0.02965 & -0.2717 & 0.393244 \tabularnewline
5 & -0.023726 & -0.2175 & 0.414192 \tabularnewline
6 & -0.020821 & -0.1908 & 0.424562 \tabularnewline
7 & -0.017031 & -0.1561 & 0.438167 \tabularnewline
8 & -0.039309 & -0.3603 & 0.359774 \tabularnewline
9 & -0.051766 & -0.4744 & 0.318209 \tabularnewline
10 & -0.023947 & -0.2195 & 0.413407 \tabularnewline
11 & -0.029957 & -0.2746 & 0.392164 \tabularnewline
12 & -0.017617 & -0.1615 & 0.436057 \tabularnewline
13 & -0.022027 & -0.2019 & 0.420249 \tabularnewline
14 & -0.024047 & -0.2204 & 0.413049 \tabularnewline
15 & -0.023548 & -0.2158 & 0.414824 \tabularnewline
16 & -0.033247 & -0.3047 & 0.380669 \tabularnewline
17 & -0.027565 & -0.2526 & 0.400583 \tabularnewline
18 & -0.027265 & -0.2499 & 0.401642 \tabularnewline
19 & -0.021285 & -0.1951 & 0.4229 \tabularnewline
20 & -0.034027 & -0.3119 & 0.37796 \tabularnewline
21 & -0.032759 & -0.3002 & 0.382367 \tabularnewline
22 & -0.040749 & -0.3735 & 0.35487 \tabularnewline
23 & -0.043733 & -0.4008 & 0.344785 \tabularnewline
24 & -0.02987 & -0.2738 & 0.39247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208069&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]0.963686[/C][C]8.8323[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.020531[/C][C]-0.1882[/C][C]0.425597[/C][/ROW]
[ROW][C]3[/C][C]-0.01729[/C][C]-0.1585[/C][C]0.437234[/C][/ROW]
[ROW][C]4[/C][C]-0.02965[/C][C]-0.2717[/C][C]0.393244[/C][/ROW]
[ROW][C]5[/C][C]-0.023726[/C][C]-0.2175[/C][C]0.414192[/C][/ROW]
[ROW][C]6[/C][C]-0.020821[/C][C]-0.1908[/C][C]0.424562[/C][/ROW]
[ROW][C]7[/C][C]-0.017031[/C][C]-0.1561[/C][C]0.438167[/C][/ROW]
[ROW][C]8[/C][C]-0.039309[/C][C]-0.3603[/C][C]0.359774[/C][/ROW]
[ROW][C]9[/C][C]-0.051766[/C][C]-0.4744[/C][C]0.318209[/C][/ROW]
[ROW][C]10[/C][C]-0.023947[/C][C]-0.2195[/C][C]0.413407[/C][/ROW]
[ROW][C]11[/C][C]-0.029957[/C][C]-0.2746[/C][C]0.392164[/C][/ROW]
[ROW][C]12[/C][C]-0.017617[/C][C]-0.1615[/C][C]0.436057[/C][/ROW]
[ROW][C]13[/C][C]-0.022027[/C][C]-0.2019[/C][C]0.420249[/C][/ROW]
[ROW][C]14[/C][C]-0.024047[/C][C]-0.2204[/C][C]0.413049[/C][/ROW]
[ROW][C]15[/C][C]-0.023548[/C][C]-0.2158[/C][C]0.414824[/C][/ROW]
[ROW][C]16[/C][C]-0.033247[/C][C]-0.3047[/C][C]0.380669[/C][/ROW]
[ROW][C]17[/C][C]-0.027565[/C][C]-0.2526[/C][C]0.400583[/C][/ROW]
[ROW][C]18[/C][C]-0.027265[/C][C]-0.2499[/C][C]0.401642[/C][/ROW]
[ROW][C]19[/C][C]-0.021285[/C][C]-0.1951[/C][C]0.4229[/C][/ROW]
[ROW][C]20[/C][C]-0.034027[/C][C]-0.3119[/C][C]0.37796[/C][/ROW]
[ROW][C]21[/C][C]-0.032759[/C][C]-0.3002[/C][C]0.382367[/C][/ROW]
[ROW][C]22[/C][C]-0.040749[/C][C]-0.3735[/C][C]0.35487[/C][/ROW]
[ROW][C]23[/C][C]-0.043733[/C][C]-0.4008[/C][C]0.344785[/C][/ROW]
[ROW][C]24[/C][C]-0.02987[/C][C]-0.2738[/C][C]0.39247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208069&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208069&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
10.9636868.83230
2-0.020531-0.18820.425597
3-0.01729-0.15850.437234
4-0.02965-0.27170.393244
5-0.023726-0.21750.414192
6-0.020821-0.19080.424562
7-0.017031-0.15610.438167
8-0.039309-0.36030.359774
9-0.051766-0.47440.318209
10-0.023947-0.21950.413407
11-0.029957-0.27460.392164
12-0.017617-0.16150.436057
13-0.022027-0.20190.420249
14-0.024047-0.22040.413049
15-0.023548-0.21580.414824
16-0.033247-0.30470.380669
17-0.027565-0.25260.400583
18-0.027265-0.24990.401642
19-0.021285-0.19510.4229
20-0.034027-0.31190.37796
21-0.032759-0.30020.382367
22-0.040749-0.37350.35487
23-0.043733-0.40080.344785
24-0.02987-0.27380.39247



Parameters (Session):
par1 = 24 ; 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 <- '1'
par2 <- '1'
par1 <- '24'
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')