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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 29 Dec 2010 15:58:07 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t12936382092gtqluga4ihxozy.htm/, Retrieved Fri, 03 May 2024 05:49:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116927, Retrieved Fri, 03 May 2024 05:49:30 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

112

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Paper PAC coins] [2010-12-29 15:58:07] [be9f1751361e0e66b042227828c71db5] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116927&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116927&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.983153	14.4159	0
2	0.964671	14.1449	0
3	0.948777	13.9118	0
4	0.934967	13.7093	0
5	0.918797	13.4722	0
6	0.902039	13.2265	0
7	0.888261	13.0245	0
8	0.875661	12.8397	0
9	0.862042	12.64	0
10	0.849103	12.4503	0
11	0.839145	12.3043	0
12	0.830649	12.1797	0
13	0.815195	11.9531	0
14	0.79835	11.7061	0
15	0.784038	11.4963	0
16	0.77187	11.3178	0
17	0.756365	11.0905	0
18	0.740334	10.8554	0
19	0.727501	10.6673	0
20	0.71517	10.4864	0
21	0.700857	10.2766	0
22	0.687102	10.0749	0
23	0.676242	9.9157	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.983153 & 14.4159 & 0 \tabularnewline
2 & 0.964671 & 14.1449 & 0 \tabularnewline
3 & 0.948777 & 13.9118 & 0 \tabularnewline
4 & 0.934967 & 13.7093 & 0 \tabularnewline
5 & 0.918797 & 13.4722 & 0 \tabularnewline
6 & 0.902039 & 13.2265 & 0 \tabularnewline
7 & 0.888261 & 13.0245 & 0 \tabularnewline
8 & 0.875661 & 12.8397 & 0 \tabularnewline
9 & 0.862042 & 12.64 & 0 \tabularnewline
10 & 0.849103 & 12.4503 & 0 \tabularnewline
11 & 0.839145 & 12.3043 & 0 \tabularnewline
12 & 0.830649 & 12.1797 & 0 \tabularnewline
13 & 0.815195 & 11.9531 & 0 \tabularnewline
14 & 0.79835 & 11.7061 & 0 \tabularnewline
15 & 0.784038 & 11.4963 & 0 \tabularnewline
16 & 0.77187 & 11.3178 & 0 \tabularnewline
17 & 0.756365 & 11.0905 & 0 \tabularnewline
18 & 0.740334 & 10.8554 & 0 \tabularnewline
19 & 0.727501 & 10.6673 & 0 \tabularnewline
20 & 0.71517 & 10.4864 & 0 \tabularnewline
21 & 0.700857 & 10.2766 & 0 \tabularnewline
22 & 0.687102 & 10.0749 & 0 \tabularnewline
23 & 0.676242 & 9.9157 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116927&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]0.983153[/C][C]14.4159[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.964671[/C][C]14.1449[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.948777[/C][C]13.9118[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.934967[/C][C]13.7093[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.918797[/C][C]13.4722[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.902039[/C][C]13.2265[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.888261[/C][C]13.0245[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.875661[/C][C]12.8397[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.862042[/C][C]12.64[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.849103[/C][C]12.4503[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.839145[/C][C]12.3043[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.830649[/C][C]12.1797[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.815195[/C][C]11.9531[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.79835[/C][C]11.7061[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.784038[/C][C]11.4963[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.77187[/C][C]11.3178[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.756365[/C][C]11.0905[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.740334[/C][C]10.8554[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.727501[/C][C]10.6673[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.71517[/C][C]10.4864[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.700857[/C][C]10.2766[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.687102[/C][C]10.0749[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.676242[/C][C]9.9157[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116927&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 k	ACF(k)	T-STAT	P-value
1	0.983153	14.4159	0
2	0.964671	14.1449	0
3	0.948777	13.9118	0
4	0.934967	13.7093	0
5	0.918797	13.4722	0
6	0.902039	13.2265	0
7	0.888261	13.0245	0
8	0.875661	12.8397	0
9	0.862042	12.64	0
10	0.849103	12.4503	0
11	0.839145	12.3043	0
12	0.830649	12.1797	0
13	0.815195	11.9531	0
14	0.79835	11.7061	0
15	0.784038	11.4963	0
16	0.77187	11.3178	0
17	0.756365	11.0905	0
18	0.740334	10.8554	0
19	0.727501	10.6673	0
20	0.71517	10.4864	0
21	0.700857	10.2766	0
22	0.687102	10.0749	0
23	0.676242	9.9157	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.983153	14.4159	0
2	-0.057447	-0.8423	0.200268
3	0.070653	1.036	0.150688
4	0.04677	0.6858	0.246794
5	-0.078441	-1.1502	0.125676
6	-0.010135	-0.1486	0.441
7	0.076066	1.1153	0.132973
8	0.009526	0.1397	0.444525
9	-0.025331	-0.3714	0.355344
10	0.031952	0.4685	0.319948
11	0.069802	1.0235	0.153613
12	0.025632	0.3758	0.353704
13	-0.198975	-2.9176	0.001951
14	-0.013716	-0.2011	0.420397
15	0.041904	0.6144	0.269789
16	0.020887	0.3063	0.379849
17	-0.078142	-1.1458	0.12658
18	0.015387	0.2256	0.410856
19	0.055586	0.8151	0.207972
20	-0.031145	-0.4567	0.324184
21	-0.036683	-0.5379	0.295609
22	0.035409	0.5192	0.302077
23	0.032298	0.4736	0.318139

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.983153 & 14.4159 & 0 \tabularnewline
2 & -0.057447 & -0.8423 & 0.200268 \tabularnewline
3 & 0.070653 & 1.036 & 0.150688 \tabularnewline
4 & 0.04677 & 0.6858 & 0.246794 \tabularnewline
5 & -0.078441 & -1.1502 & 0.125676 \tabularnewline
6 & -0.010135 & -0.1486 & 0.441 \tabularnewline
7 & 0.076066 & 1.1153 & 0.132973 \tabularnewline
8 & 0.009526 & 0.1397 & 0.444525 \tabularnewline
9 & -0.025331 & -0.3714 & 0.355344 \tabularnewline
10 & 0.031952 & 0.4685 & 0.319948 \tabularnewline
11 & 0.069802 & 1.0235 & 0.153613 \tabularnewline
12 & 0.025632 & 0.3758 & 0.353704 \tabularnewline
13 & -0.198975 & -2.9176 & 0.001951 \tabularnewline
14 & -0.013716 & -0.2011 & 0.420397 \tabularnewline
15 & 0.041904 & 0.6144 & 0.269789 \tabularnewline
16 & 0.020887 & 0.3063 & 0.379849 \tabularnewline
17 & -0.078142 & -1.1458 & 0.12658 \tabularnewline
18 & 0.015387 & 0.2256 & 0.410856 \tabularnewline
19 & 0.055586 & 0.8151 & 0.207972 \tabularnewline
20 & -0.031145 & -0.4567 & 0.324184 \tabularnewline
21 & -0.036683 & -0.5379 & 0.295609 \tabularnewline
22 & 0.035409 & 0.5192 & 0.302077 \tabularnewline
23 & 0.032298 & 0.4736 & 0.318139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116927&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]0.983153[/C][C]14.4159[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.057447[/C][C]-0.8423[/C][C]0.200268[/C][/ROW]
[ROW][C]3[/C][C]0.070653[/C][C]1.036[/C][C]0.150688[/C][/ROW]
[ROW][C]4[/C][C]0.04677[/C][C]0.6858[/C][C]0.246794[/C][/ROW]
[ROW][C]5[/C][C]-0.078441[/C][C]-1.1502[/C][C]0.125676[/C][/ROW]
[ROW][C]6[/C][C]-0.010135[/C][C]-0.1486[/C][C]0.441[/C][/ROW]
[ROW][C]7[/C][C]0.076066[/C][C]1.1153[/C][C]0.132973[/C][/ROW]
[ROW][C]8[/C][C]0.009526[/C][C]0.1397[/C][C]0.444525[/C][/ROW]
[ROW][C]9[/C][C]-0.025331[/C][C]-0.3714[/C][C]0.355344[/C][/ROW]
[ROW][C]10[/C][C]0.031952[/C][C]0.4685[/C][C]0.319948[/C][/ROW]
[ROW][C]11[/C][C]0.069802[/C][C]1.0235[/C][C]0.153613[/C][/ROW]
[ROW][C]12[/C][C]0.025632[/C][C]0.3758[/C][C]0.353704[/C][/ROW]
[ROW][C]13[/C][C]-0.198975[/C][C]-2.9176[/C][C]0.001951[/C][/ROW]
[ROW][C]14[/C][C]-0.013716[/C][C]-0.2011[/C][C]0.420397[/C][/ROW]
[ROW][C]15[/C][C]0.041904[/C][C]0.6144[/C][C]0.269789[/C][/ROW]
[ROW][C]16[/C][C]0.020887[/C][C]0.3063[/C][C]0.379849[/C][/ROW]
[ROW][C]17[/C][C]-0.078142[/C][C]-1.1458[/C][C]0.12658[/C][/ROW]
[ROW][C]18[/C][C]0.015387[/C][C]0.2256[/C][C]0.410856[/C][/ROW]
[ROW][C]19[/C][C]0.055586[/C][C]0.8151[/C][C]0.207972[/C][/ROW]
[ROW][C]20[/C][C]-0.031145[/C][C]-0.4567[/C][C]0.324184[/C][/ROW]
[ROW][C]21[/C][C]-0.036683[/C][C]-0.5379[/C][C]0.295609[/C][/ROW]
[ROW][C]22[/C][C]0.035409[/C][C]0.5192[/C][C]0.302077[/C][/ROW]
[ROW][C]23[/C][C]0.032298[/C][C]0.4736[/C][C]0.318139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116927&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 k	PACF(k)	T-STAT	P-value
1	0.983153	14.4159	0
2	-0.057447	-0.8423	0.200268
3	0.070653	1.036	0.150688
4	0.04677	0.6858	0.246794
5	-0.078441	-1.1502	0.125676
6	-0.010135	-0.1486	0.441
7	0.076066	1.1153	0.132973
8	0.009526	0.1397	0.444525
9	-0.025331	-0.3714	0.355344
10	0.031952	0.4685	0.319948
11	0.069802	1.0235	0.153613
12	0.025632	0.3758	0.353704
13	-0.198975	-2.9176	0.001951
14	-0.013716	-0.2011	0.420397
15	0.041904	0.6144	0.269789
16	0.020887	0.3063	0.379849
17	-0.078142	-1.1458	0.12658
18	0.015387	0.2256	0.410856
19	0.055586	0.8151	0.207972
20	-0.031145	-0.4567	0.324184
21	-0.036683	-0.5379	0.295609
22	0.035409	0.5192	0.302077
23	0.032298	0.4736	0.318139

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code