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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 23 Oct 2014 12:44:16 +0100

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/2014/Oct/23/t1414064706rwb7e8a34hpgbc2.htm/, Retrieved Fri, 10 May 2024 15:14:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=245655, Retrieved Fri, 10 May 2024 15:14:07 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2014-10-23 11:44:16] [fced41568b3cc41e6659ad201d611503] [Current]
- R       [(Partial) Autocorrelation Function] [] [2014-10-23 11:46:10] [46d78fa4bef23992fc20db72a2a0da97] 

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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=245655&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=245655&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=245655&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	0.964005	13.3577	0
2	0.921663	12.7709	0
3	0.877491	12.1589	0
4	0.835223	11.5732	0
5	0.793176	10.9906	0
6	0.750698	10.402	0
7	0.708671	9.8196	0
8	0.666279	9.2322	0
9	0.623877	8.6447	0
10	0.580975	8.0502	0
11	0.534109	7.4008	0
12	0.48036	6.6561	0
13	0.424588	5.8833	0
14	0.36803	5.0996	0
15	0.314176	4.3534	1.1e-05
16	0.264131	3.6599	0.000163
17	0.21699	3.0067	0.001497
18	0.173016	2.3974	0.008736
19	0.131096	1.8165	0.035425
20	0.090933	1.26	0.104597
21	0.053692	0.744	0.2289
22	0.018089	0.2507	0.401176

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964005 & 13.3577 & 0 \tabularnewline
2 & 0.921663 & 12.7709 & 0 \tabularnewline
3 & 0.877491 & 12.1589 & 0 \tabularnewline
4 & 0.835223 & 11.5732 & 0 \tabularnewline
5 & 0.793176 & 10.9906 & 0 \tabularnewline
6 & 0.750698 & 10.402 & 0 \tabularnewline
7 & 0.708671 & 9.8196 & 0 \tabularnewline
8 & 0.666279 & 9.2322 & 0 \tabularnewline
9 & 0.623877 & 8.6447 & 0 \tabularnewline
10 & 0.580975 & 8.0502 & 0 \tabularnewline
11 & 0.534109 & 7.4008 & 0 \tabularnewline
12 & 0.48036 & 6.6561 & 0 \tabularnewline
13 & 0.424588 & 5.8833 & 0 \tabularnewline
14 & 0.36803 & 5.0996 & 0 \tabularnewline
15 & 0.314176 & 4.3534 & 1.1e-05 \tabularnewline
16 & 0.264131 & 3.6599 & 0.000163 \tabularnewline
17 & 0.21699 & 3.0067 & 0.001497 \tabularnewline
18 & 0.173016 & 2.3974 & 0.008736 \tabularnewline
19 & 0.131096 & 1.8165 & 0.035425 \tabularnewline
20 & 0.090933 & 1.26 & 0.104597 \tabularnewline
21 & 0.053692 & 0.744 & 0.2289 \tabularnewline
22 & 0.018089 & 0.2507 & 0.401176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=245655&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]0.964005[/C][C]13.3577[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.921663[/C][C]12.7709[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.877491[/C][C]12.1589[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.835223[/C][C]11.5732[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.793176[/C][C]10.9906[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.750698[/C][C]10.402[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.708671[/C][C]9.8196[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.666279[/C][C]9.2322[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.623877[/C][C]8.6447[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.580975[/C][C]8.0502[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.534109[/C][C]7.4008[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.48036[/C][C]6.6561[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.424588[/C][C]5.8833[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.36803[/C][C]5.0996[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.314176[/C][C]4.3534[/C][C]1.1e-05[/C][/ROW]
[ROW][C]16[/C][C]0.264131[/C][C]3.6599[/C][C]0.000163[/C][/ROW]
[ROW][C]17[/C][C]0.21699[/C][C]3.0067[/C][C]0.001497[/C][/ROW]
[ROW][C]18[/C][C]0.173016[/C][C]2.3974[/C][C]0.008736[/C][/ROW]
[ROW][C]19[/C][C]0.131096[/C][C]1.8165[/C][C]0.035425[/C][/ROW]
[ROW][C]20[/C][C]0.090933[/C][C]1.26[/C][C]0.104597[/C][/ROW]
[ROW][C]21[/C][C]0.053692[/C][C]0.744[/C][C]0.2289[/C][/ROW]
[ROW][C]22[/C][C]0.018089[/C][C]0.2507[/C][C]0.401176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=245655&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=245655&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	0.964005	13.3577	0
2	0.921663	12.7709	0
3	0.877491	12.1589	0
4	0.835223	11.5732	0
5	0.793176	10.9906	0
6	0.750698	10.402	0
7	0.708671	9.8196	0
8	0.666279	9.2322	0
9	0.623877	8.6447	0
10	0.580975	8.0502	0
11	0.534109	7.4008	0
12	0.48036	6.6561	0
13	0.424588	5.8833	0
14	0.36803	5.0996	0
15	0.314176	4.3534	1.1e-05
16	0.264131	3.6599	0.000163
17	0.21699	3.0067	0.001497
18	0.173016	2.3974	0.008736
19	0.131096	1.8165	0.035425
20	0.090933	1.26	0.104597
21	0.053692	0.744	0.2289
22	0.018089	0.2507	0.401176

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964005	13.3577	0
2	-0.108127	-1.4982	0.067856
3	-0.040523	-0.5615	0.287557
4	0.00746	0.1034	0.458889
5	-0.024278	-0.3364	0.368464
6	-0.031113	-0.4311	0.333436
7	-0.015866	-0.2198	0.413115
8	-0.030709	-0.4255	0.335467
9	-0.025392	-0.3518	0.36267
10	-0.032628	-0.4521	0.32585
11	-0.083345	-1.1549	0.124792
12	-0.120968	-1.6762	0.047665
13	-0.049623	-0.6876	0.246268
14	-0.048183	-0.6676	0.25258
15	-0.006732	-0.0933	0.46289
16	0.007538	0.1044	0.458463
17	-0.007259	-0.1006	0.459991
18	0.001076	0.0149	0.494058
19	-0.01158	-0.1605	0.436344
20	-0.015383	-0.2132	0.415717
21	0.006966	0.0965	0.461605
22	-0.007612	-0.1055	0.458056

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964005 & 13.3577 & 0 \tabularnewline
2 & -0.108127 & -1.4982 & 0.067856 \tabularnewline
3 & -0.040523 & -0.5615 & 0.287557 \tabularnewline
4 & 0.00746 & 0.1034 & 0.458889 \tabularnewline
5 & -0.024278 & -0.3364 & 0.368464 \tabularnewline
6 & -0.031113 & -0.4311 & 0.333436 \tabularnewline
7 & -0.015866 & -0.2198 & 0.413115 \tabularnewline
8 & -0.030709 & -0.4255 & 0.335467 \tabularnewline
9 & -0.025392 & -0.3518 & 0.36267 \tabularnewline
10 & -0.032628 & -0.4521 & 0.32585 \tabularnewline
11 & -0.083345 & -1.1549 & 0.124792 \tabularnewline
12 & -0.120968 & -1.6762 & 0.047665 \tabularnewline
13 & -0.049623 & -0.6876 & 0.246268 \tabularnewline
14 & -0.048183 & -0.6676 & 0.25258 \tabularnewline
15 & -0.006732 & -0.0933 & 0.46289 \tabularnewline
16 & 0.007538 & 0.1044 & 0.458463 \tabularnewline
17 & -0.007259 & -0.1006 & 0.459991 \tabularnewline
18 & 0.001076 & 0.0149 & 0.494058 \tabularnewline
19 & -0.01158 & -0.1605 & 0.436344 \tabularnewline
20 & -0.015383 & -0.2132 & 0.415717 \tabularnewline
21 & 0.006966 & 0.0965 & 0.461605 \tabularnewline
22 & -0.007612 & -0.1055 & 0.458056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=245655&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]0.964005[/C][C]13.3577[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.108127[/C][C]-1.4982[/C][C]0.067856[/C][/ROW]
[ROW][C]3[/C][C]-0.040523[/C][C]-0.5615[/C][C]0.287557[/C][/ROW]
[ROW][C]4[/C][C]0.00746[/C][C]0.1034[/C][C]0.458889[/C][/ROW]
[ROW][C]5[/C][C]-0.024278[/C][C]-0.3364[/C][C]0.368464[/C][/ROW]
[ROW][C]6[/C][C]-0.031113[/C][C]-0.4311[/C][C]0.333436[/C][/ROW]
[ROW][C]7[/C][C]-0.015866[/C][C]-0.2198[/C][C]0.413115[/C][/ROW]
[ROW][C]8[/C][C]-0.030709[/C][C]-0.4255[/C][C]0.335467[/C][/ROW]
[ROW][C]9[/C][C]-0.025392[/C][C]-0.3518[/C][C]0.36267[/C][/ROW]
[ROW][C]10[/C][C]-0.032628[/C][C]-0.4521[/C][C]0.32585[/C][/ROW]
[ROW][C]11[/C][C]-0.083345[/C][C]-1.1549[/C][C]0.124792[/C][/ROW]
[ROW][C]12[/C][C]-0.120968[/C][C]-1.6762[/C][C]0.047665[/C][/ROW]
[ROW][C]13[/C][C]-0.049623[/C][C]-0.6876[/C][C]0.246268[/C][/ROW]
[ROW][C]14[/C][C]-0.048183[/C][C]-0.6676[/C][C]0.25258[/C][/ROW]
[ROW][C]15[/C][C]-0.006732[/C][C]-0.0933[/C][C]0.46289[/C][/ROW]
[ROW][C]16[/C][C]0.007538[/C][C]0.1044[/C][C]0.458463[/C][/ROW]
[ROW][C]17[/C][C]-0.007259[/C][C]-0.1006[/C][C]0.459991[/C][/ROW]
[ROW][C]18[/C][C]0.001076[/C][C]0.0149[/C][C]0.494058[/C][/ROW]
[ROW][C]19[/C][C]-0.01158[/C][C]-0.1605[/C][C]0.436344[/C][/ROW]
[ROW][C]20[/C][C]-0.015383[/C][C]-0.2132[/C][C]0.415717[/C][/ROW]
[ROW][C]21[/C][C]0.006966[/C][C]0.0965[/C][C]0.461605[/C][/ROW]
[ROW][C]22[/C][C]-0.007612[/C][C]-0.1055[/C][C]0.458056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=245655&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=245655&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	0.964005	13.3577	0
2	-0.108127	-1.4982	0.067856
3	-0.040523	-0.5615	0.287557
4	0.00746	0.1034	0.458889
5	-0.024278	-0.3364	0.368464
6	-0.031113	-0.4311	0.333436
7	-0.015866	-0.2198	0.413115
8	-0.030709	-0.4255	0.335467
9	-0.025392	-0.3518	0.36267
10	-0.032628	-0.4521	0.32585
11	-0.083345	-1.1549	0.124792
12	-0.120968	-1.6762	0.047665
13	-0.049623	-0.6876	0.246268
14	-0.048183	-0.6676	0.25258
15	-0.006732	-0.0933	0.46289
16	0.007538	0.1044	0.458463
17	-0.007259	-0.1006	0.459991
18	0.001076	0.0149	0.494058
19	-0.01158	-0.1605	0.436344
20	-0.015383	-0.2132	0.415717
21	0.006966	0.0965	0.461605
22	-0.007612	-0.1055	0.458056

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 = 12 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code