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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 20 Nov 2013 13:56:12 -0500

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/2013/Nov/20/t13849737952et7oozqlccl7yf.htm/, Retrieved Wed, 01 May 2024 19:25:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226714, Retrieved Wed, 01 May 2024 19:25:43 +0000

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

-       [(Partial) Autocorrelation Function] [] [2013-11-20 18:56:12] [f6b0814d1ccce07ea30140b42d9cb647] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226714&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226714&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226714&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.295207	-3.5302	0.00028
2	-0.073822	-0.8828	0.189419
3	0.05815	0.6954	0.243974
4	-0.07273	-0.8697	0.192954
5	0.043695	0.5225	0.30106
6	-0.283811	-3.3939	0.000446
7	0.07291	0.8719	0.192368
8	-0.058947	-0.7049	0.241009
9	0.032144	0.3844	0.350631
10	-0.065705	-0.7857	0.216667
11	-0.211999	-2.5351	0.006158
12	0.75181	8.9903	0
13	-0.227632	-2.7221	0.003647
14	0.005781	0.0691	0.472493
15	-0.014628	-0.1749	0.430692
16	-0.083426	-0.9976	0.160072
17	0.112922	1.3504	0.089518
18	-0.291101	-3.4811	0.000331
19	0.035512	0.4247	0.335861
20	-0.014776	-0.1767	0.429998
21	0.047296	0.5656	0.286282

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.295207 & -3.5302 & 0.00028 \tabularnewline
2 & -0.073822 & -0.8828 & 0.189419 \tabularnewline
3 & 0.05815 & 0.6954 & 0.243974 \tabularnewline
4 & -0.07273 & -0.8697 & 0.192954 \tabularnewline
5 & 0.043695 & 0.5225 & 0.30106 \tabularnewline
6 & -0.283811 & -3.3939 & 0.000446 \tabularnewline
7 & 0.07291 & 0.8719 & 0.192368 \tabularnewline
8 & -0.058947 & -0.7049 & 0.241009 \tabularnewline
9 & 0.032144 & 0.3844 & 0.350631 \tabularnewline
10 & -0.065705 & -0.7857 & 0.216667 \tabularnewline
11 & -0.211999 & -2.5351 & 0.006158 \tabularnewline
12 & 0.75181 & 8.9903 & 0 \tabularnewline
13 & -0.227632 & -2.7221 & 0.003647 \tabularnewline
14 & 0.005781 & 0.0691 & 0.472493 \tabularnewline
15 & -0.014628 & -0.1749 & 0.430692 \tabularnewline
16 & -0.083426 & -0.9976 & 0.160072 \tabularnewline
17 & 0.112922 & 1.3504 & 0.089518 \tabularnewline
18 & -0.291101 & -3.4811 & 0.000331 \tabularnewline
19 & 0.035512 & 0.4247 & 0.335861 \tabularnewline
20 & -0.014776 & -0.1767 & 0.429998 \tabularnewline
21 & 0.047296 & 0.5656 & 0.286282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226714&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]-0.295207[/C][C]-3.5302[/C][C]0.00028[/C][/ROW]
[ROW][C]2[/C][C]-0.073822[/C][C]-0.8828[/C][C]0.189419[/C][/ROW]
[ROW][C]3[/C][C]0.05815[/C][C]0.6954[/C][C]0.243974[/C][/ROW]
[ROW][C]4[/C][C]-0.07273[/C][C]-0.8697[/C][C]0.192954[/C][/ROW]
[ROW][C]5[/C][C]0.043695[/C][C]0.5225[/C][C]0.30106[/C][/ROW]
[ROW][C]6[/C][C]-0.283811[/C][C]-3.3939[/C][C]0.000446[/C][/ROW]
[ROW][C]7[/C][C]0.07291[/C][C]0.8719[/C][C]0.192368[/C][/ROW]
[ROW][C]8[/C][C]-0.058947[/C][C]-0.7049[/C][C]0.241009[/C][/ROW]
[ROW][C]9[/C][C]0.032144[/C][C]0.3844[/C][C]0.350631[/C][/ROW]
[ROW][C]10[/C][C]-0.065705[/C][C]-0.7857[/C][C]0.216667[/C][/ROW]
[ROW][C]11[/C][C]-0.211999[/C][C]-2.5351[/C][C]0.006158[/C][/ROW]
[ROW][C]12[/C][C]0.75181[/C][C]8.9903[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.227632[/C][C]-2.7221[/C][C]0.003647[/C][/ROW]
[ROW][C]14[/C][C]0.005781[/C][C]0.0691[/C][C]0.472493[/C][/ROW]
[ROW][C]15[/C][C]-0.014628[/C][C]-0.1749[/C][C]0.430692[/C][/ROW]
[ROW][C]16[/C][C]-0.083426[/C][C]-0.9976[/C][C]0.160072[/C][/ROW]
[ROW][C]17[/C][C]0.112922[/C][C]1.3504[/C][C]0.089518[/C][/ROW]
[ROW][C]18[/C][C]-0.291101[/C][C]-3.4811[/C][C]0.000331[/C][/ROW]
[ROW][C]19[/C][C]0.035512[/C][C]0.4247[/C][C]0.335861[/C][/ROW]
[ROW][C]20[/C][C]-0.014776[/C][C]-0.1767[/C][C]0.429998[/C][/ROW]
[ROW][C]21[/C][C]0.047296[/C][C]0.5656[/C][C]0.286282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226714&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226714&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	-0.295207	-3.5302	0.00028
2	-0.073822	-0.8828	0.189419
3	0.05815	0.6954	0.243974
4	-0.07273	-0.8697	0.192954
5	0.043695	0.5225	0.30106
6	-0.283811	-3.3939	0.000446
7	0.07291	0.8719	0.192368
8	-0.058947	-0.7049	0.241009
9	0.032144	0.3844	0.350631
10	-0.065705	-0.7857	0.216667
11	-0.211999	-2.5351	0.006158
12	0.75181	8.9903	0
13	-0.227632	-2.7221	0.003647
14	0.005781	0.0691	0.472493
15	-0.014628	-0.1749	0.430692
16	-0.083426	-0.9976	0.160072
17	0.112922	1.3504	0.089518
18	-0.291101	-3.4811	0.000331
19	0.035512	0.4247	0.335861
20	-0.014776	-0.1767	0.429998
21	0.047296	0.5656	0.286282

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.295207	-3.5302	0.00028
2	-0.176335	-2.1087	0.018358
3	-0.022093	-0.2642	0.396006
4	-0.081915	-0.9796	0.164478
5	0.001895	0.0227	0.490977
6	-0.324985	-3.8863	7.8e-05
7	-0.150046	-1.7943	0.03744
8	-0.220936	-2.642	0.00458
9	-0.089841	-1.0743	0.14224
10	-0.238136	-2.8477	0.002527
11	-0.513456	-6.14	0
12	0.522577	6.2491	0
13	0.145326	1.7378	0.042196
14	0.227301	2.7181	0.003689
15	-0.088653	-1.0601	0.145436
16	-0.117917	-1.4101	0.080344
17	0.100108	1.1971	0.11662
18	0.054421	0.6508	0.258116
19	-0.069446	-0.8304	0.203835
20	-0.042155	-0.5041	0.307485
21	0.024518	0.2932	0.384898

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.295207 & -3.5302 & 0.00028 \tabularnewline
2 & -0.176335 & -2.1087 & 0.018358 \tabularnewline
3 & -0.022093 & -0.2642 & 0.396006 \tabularnewline
4 & -0.081915 & -0.9796 & 0.164478 \tabularnewline
5 & 0.001895 & 0.0227 & 0.490977 \tabularnewline
6 & -0.324985 & -3.8863 & 7.8e-05 \tabularnewline
7 & -0.150046 & -1.7943 & 0.03744 \tabularnewline
8 & -0.220936 & -2.642 & 0.00458 \tabularnewline
9 & -0.089841 & -1.0743 & 0.14224 \tabularnewline
10 & -0.238136 & -2.8477 & 0.002527 \tabularnewline
11 & -0.513456 & -6.14 & 0 \tabularnewline
12 & 0.522577 & 6.2491 & 0 \tabularnewline
13 & 0.145326 & 1.7378 & 0.042196 \tabularnewline
14 & 0.227301 & 2.7181 & 0.003689 \tabularnewline
15 & -0.088653 & -1.0601 & 0.145436 \tabularnewline
16 & -0.117917 & -1.4101 & 0.080344 \tabularnewline
17 & 0.100108 & 1.1971 & 0.11662 \tabularnewline
18 & 0.054421 & 0.6508 & 0.258116 \tabularnewline
19 & -0.069446 & -0.8304 & 0.203835 \tabularnewline
20 & -0.042155 & -0.5041 & 0.307485 \tabularnewline
21 & 0.024518 & 0.2932 & 0.384898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226714&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]-0.295207[/C][C]-3.5302[/C][C]0.00028[/C][/ROW]
[ROW][C]2[/C][C]-0.176335[/C][C]-2.1087[/C][C]0.018358[/C][/ROW]
[ROW][C]3[/C][C]-0.022093[/C][C]-0.2642[/C][C]0.396006[/C][/ROW]
[ROW][C]4[/C][C]-0.081915[/C][C]-0.9796[/C][C]0.164478[/C][/ROW]
[ROW][C]5[/C][C]0.001895[/C][C]0.0227[/C][C]0.490977[/C][/ROW]
[ROW][C]6[/C][C]-0.324985[/C][C]-3.8863[/C][C]7.8e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.150046[/C][C]-1.7943[/C][C]0.03744[/C][/ROW]
[ROW][C]8[/C][C]-0.220936[/C][C]-2.642[/C][C]0.00458[/C][/ROW]
[ROW][C]9[/C][C]-0.089841[/C][C]-1.0743[/C][C]0.14224[/C][/ROW]
[ROW][C]10[/C][C]-0.238136[/C][C]-2.8477[/C][C]0.002527[/C][/ROW]
[ROW][C]11[/C][C]-0.513456[/C][C]-6.14[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.522577[/C][C]6.2491[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.145326[/C][C]1.7378[/C][C]0.042196[/C][/ROW]
[ROW][C]14[/C][C]0.227301[/C][C]2.7181[/C][C]0.003689[/C][/ROW]
[ROW][C]15[/C][C]-0.088653[/C][C]-1.0601[/C][C]0.145436[/C][/ROW]
[ROW][C]16[/C][C]-0.117917[/C][C]-1.4101[/C][C]0.080344[/C][/ROW]
[ROW][C]17[/C][C]0.100108[/C][C]1.1971[/C][C]0.11662[/C][/ROW]
[ROW][C]18[/C][C]0.054421[/C][C]0.6508[/C][C]0.258116[/C][/ROW]
[ROW][C]19[/C][C]-0.069446[/C][C]-0.8304[/C][C]0.203835[/C][/ROW]
[ROW][C]20[/C][C]-0.042155[/C][C]-0.5041[/C][C]0.307485[/C][/ROW]
[ROW][C]21[/C][C]0.024518[/C][C]0.2932[/C][C]0.384898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226714&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226714&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	-0.295207	-3.5302	0.00028
2	-0.176335	-2.1087	0.018358
3	-0.022093	-0.2642	0.396006
4	-0.081915	-0.9796	0.164478
5	0.001895	0.0227	0.490977
6	-0.324985	-3.8863	7.8e-05
7	-0.150046	-1.7943	0.03744
8	-0.220936	-2.642	0.00458
9	-0.089841	-1.0743	0.14224
10	-0.238136	-2.8477	0.002527
11	-0.513456	-6.14	0
12	0.522577	6.2491	0
13	0.145326	1.7378	0.042196
14	0.227301	2.7181	0.003689
15	-0.088653	-1.0601	0.145436
16	-0.117917	-1.4101	0.080344
17	0.100108	1.1971	0.11662
18	0.054421	0.6508	0.258116
19	-0.069446	-0.8304	0.203835
20	-0.042155	-0.5041	0.307485
21	0.024518	0.2932	0.384898

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; 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):

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code