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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 17:19:49 +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/2016/Dec/16/t1481905210j7bj340i1czhm20.htm/, Retrieved Thu, 02 May 2024 21:29:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300419, Retrieved Thu, 02 May 2024 21:29:40 +0000

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User-defined keywords

Estimated Impact

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

-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- R  D    [ARIMA Backward Selection] [] [2016-12-16 14:51:40] [683f400e1b95307fc738e729f07c4fce]
- RM D        [(Partial) Autocorrelation Function] [] [2016-12-16 16:19:49] [404ac5ee4f7301873f6a96ef36861981] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300419&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300419&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300419&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.526003	-5.441	0
2	0.114968	1.1892	0.11849
3	-0.104197	-1.0778	0.141767
4	0.100189	1.0364	0.151184
5	-0.106139	-1.0979	0.137353
6	0.035351	0.3657	0.357666
7	-0.069977	-0.7238	0.23537
8	0.165094	1.7077	0.045292
9	-0.218686	-2.2621	0.012856
10	0.143478	1.4842	0.070354
11	-0.049924	-0.5164	0.303315
12	0.094313	0.9756	0.165735
13	-0.161821	-1.6739	0.048536
14	0.180581	1.8679	0.032253
15	-0.09513	-0.984	0.163659
16	0.000253	0.0026	0.498959
17	0.041736	0.4317	0.333408
18	0.054514	0.5639	0.287003
19	-0.159765	-1.6526	0.05067
20	0.071326	0.7378	0.231125

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.526003 & -5.441 & 0 \tabularnewline
2 & 0.114968 & 1.1892 & 0.11849 \tabularnewline
3 & -0.104197 & -1.0778 & 0.141767 \tabularnewline
4 & 0.100189 & 1.0364 & 0.151184 \tabularnewline
5 & -0.106139 & -1.0979 & 0.137353 \tabularnewline
6 & 0.035351 & 0.3657 & 0.357666 \tabularnewline
7 & -0.069977 & -0.7238 & 0.23537 \tabularnewline
8 & 0.165094 & 1.7077 & 0.045292 \tabularnewline
9 & -0.218686 & -2.2621 & 0.012856 \tabularnewline
10 & 0.143478 & 1.4842 & 0.070354 \tabularnewline
11 & -0.049924 & -0.5164 & 0.303315 \tabularnewline
12 & 0.094313 & 0.9756 & 0.165735 \tabularnewline
13 & -0.161821 & -1.6739 & 0.048536 \tabularnewline
14 & 0.180581 & 1.8679 & 0.032253 \tabularnewline
15 & -0.09513 & -0.984 & 0.163659 \tabularnewline
16 & 0.000253 & 0.0026 & 0.498959 \tabularnewline
17 & 0.041736 & 0.4317 & 0.333408 \tabularnewline
18 & 0.054514 & 0.5639 & 0.287003 \tabularnewline
19 & -0.159765 & -1.6526 & 0.05067 \tabularnewline
20 & 0.071326 & 0.7378 & 0.231125 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300419&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]-0.526003[/C][C]-5.441[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.114968[/C][C]1.1892[/C][C]0.11849[/C][/ROW]
[ROW][C]3[/C][C]-0.104197[/C][C]-1.0778[/C][C]0.141767[/C][/ROW]
[ROW][C]4[/C][C]0.100189[/C][C]1.0364[/C][C]0.151184[/C][/ROW]
[ROW][C]5[/C][C]-0.106139[/C][C]-1.0979[/C][C]0.137353[/C][/ROW]
[ROW][C]6[/C][C]0.035351[/C][C]0.3657[/C][C]0.357666[/C][/ROW]
[ROW][C]7[/C][C]-0.069977[/C][C]-0.7238[/C][C]0.23537[/C][/ROW]
[ROW][C]8[/C][C]0.165094[/C][C]1.7077[/C][C]0.045292[/C][/ROW]
[ROW][C]9[/C][C]-0.218686[/C][C]-2.2621[/C][C]0.012856[/C][/ROW]
[ROW][C]10[/C][C]0.143478[/C][C]1.4842[/C][C]0.070354[/C][/ROW]
[ROW][C]11[/C][C]-0.049924[/C][C]-0.5164[/C][C]0.303315[/C][/ROW]
[ROW][C]12[/C][C]0.094313[/C][C]0.9756[/C][C]0.165735[/C][/ROW]
[ROW][C]13[/C][C]-0.161821[/C][C]-1.6739[/C][C]0.048536[/C][/ROW]
[ROW][C]14[/C][C]0.180581[/C][C]1.8679[/C][C]0.032253[/C][/ROW]
[ROW][C]15[/C][C]-0.09513[/C][C]-0.984[/C][C]0.163659[/C][/ROW]
[ROW][C]16[/C][C]0.000253[/C][C]0.0026[/C][C]0.498959[/C][/ROW]
[ROW][C]17[/C][C]0.041736[/C][C]0.4317[/C][C]0.333408[/C][/ROW]
[ROW][C]18[/C][C]0.054514[/C][C]0.5639[/C][C]0.287003[/C][/ROW]
[ROW][C]19[/C][C]-0.159765[/C][C]-1.6526[/C][C]0.05067[/C][/ROW]
[ROW][C]20[/C][C]0.071326[/C][C]0.7378[/C][C]0.231125[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300419&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300419&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	-0.526003	-5.441	0
2	0.114968	1.1892	0.11849
3	-0.104197	-1.0778	0.141767
4	0.100189	1.0364	0.151184
5	-0.106139	-1.0979	0.137353
6	0.035351	0.3657	0.357666
7	-0.069977	-0.7238	0.23537
8	0.165094	1.7077	0.045292
9	-0.218686	-2.2621	0.012856
10	0.143478	1.4842	0.070354
11	-0.049924	-0.5164	0.303315
12	0.094313	0.9756	0.165735
13	-0.161821	-1.6739	0.048536
14	0.180581	1.8679	0.032253
15	-0.09513	-0.984	0.163659
16	0.000253	0.0026	0.498959
17	0.041736	0.4317	0.333408
18	0.054514	0.5639	0.287003
19	-0.159765	-1.6526	0.05067
20	0.071326	0.7378	0.231125

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.526003	-5.441	0
2	-0.223568	-2.3126	0.011329
3	-0.215089	-2.2249	0.014094
4	-0.066225	-0.685	0.247402
5	-0.123325	-1.2757	0.102415
6	-0.121294	-1.2547	0.106166
7	-0.184519	-1.9087	0.029491
8	0.028653	0.2964	0.383754
9	-0.173513	-1.7948	0.037752
10	-0.107538	-1.1124	0.134234
11	-0.069152	-0.7153	0.237987
12	0.025933	0.2683	0.394511
13	-0.117985	-1.2204	0.112489
14	0.037037	0.3831	0.351199
15	0.032339	0.3345	0.36932
16	-0.066586	-0.6888	0.24623
17	0.090755	0.9388	0.17498
18	0.154443	1.5976	0.056543
19	-0.042145	-0.436	0.331874
20	-0.049657	-0.5137	0.304276

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.526003 & -5.441 & 0 \tabularnewline
2 & -0.223568 & -2.3126 & 0.011329 \tabularnewline
3 & -0.215089 & -2.2249 & 0.014094 \tabularnewline
4 & -0.066225 & -0.685 & 0.247402 \tabularnewline
5 & -0.123325 & -1.2757 & 0.102415 \tabularnewline
6 & -0.121294 & -1.2547 & 0.106166 \tabularnewline
7 & -0.184519 & -1.9087 & 0.029491 \tabularnewline
8 & 0.028653 & 0.2964 & 0.383754 \tabularnewline
9 & -0.173513 & -1.7948 & 0.037752 \tabularnewline
10 & -0.107538 & -1.1124 & 0.134234 \tabularnewline
11 & -0.069152 & -0.7153 & 0.237987 \tabularnewline
12 & 0.025933 & 0.2683 & 0.394511 \tabularnewline
13 & -0.117985 & -1.2204 & 0.112489 \tabularnewline
14 & 0.037037 & 0.3831 & 0.351199 \tabularnewline
15 & 0.032339 & 0.3345 & 0.36932 \tabularnewline
16 & -0.066586 & -0.6888 & 0.24623 \tabularnewline
17 & 0.090755 & 0.9388 & 0.17498 \tabularnewline
18 & 0.154443 & 1.5976 & 0.056543 \tabularnewline
19 & -0.042145 & -0.436 & 0.331874 \tabularnewline
20 & -0.049657 & -0.5137 & 0.304276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300419&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]-0.526003[/C][C]-5.441[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.223568[/C][C]-2.3126[/C][C]0.011329[/C][/ROW]
[ROW][C]3[/C][C]-0.215089[/C][C]-2.2249[/C][C]0.014094[/C][/ROW]
[ROW][C]4[/C][C]-0.066225[/C][C]-0.685[/C][C]0.247402[/C][/ROW]
[ROW][C]5[/C][C]-0.123325[/C][C]-1.2757[/C][C]0.102415[/C][/ROW]
[ROW][C]6[/C][C]-0.121294[/C][C]-1.2547[/C][C]0.106166[/C][/ROW]
[ROW][C]7[/C][C]-0.184519[/C][C]-1.9087[/C][C]0.029491[/C][/ROW]
[ROW][C]8[/C][C]0.028653[/C][C]0.2964[/C][C]0.383754[/C][/ROW]
[ROW][C]9[/C][C]-0.173513[/C][C]-1.7948[/C][C]0.037752[/C][/ROW]
[ROW][C]10[/C][C]-0.107538[/C][C]-1.1124[/C][C]0.134234[/C][/ROW]
[ROW][C]11[/C][C]-0.069152[/C][C]-0.7153[/C][C]0.237987[/C][/ROW]
[ROW][C]12[/C][C]0.025933[/C][C]0.2683[/C][C]0.394511[/C][/ROW]
[ROW][C]13[/C][C]-0.117985[/C][C]-1.2204[/C][C]0.112489[/C][/ROW]
[ROW][C]14[/C][C]0.037037[/C][C]0.3831[/C][C]0.351199[/C][/ROW]
[ROW][C]15[/C][C]0.032339[/C][C]0.3345[/C][C]0.36932[/C][/ROW]
[ROW][C]16[/C][C]-0.066586[/C][C]-0.6888[/C][C]0.24623[/C][/ROW]
[ROW][C]17[/C][C]0.090755[/C][C]0.9388[/C][C]0.17498[/C][/ROW]
[ROW][C]18[/C][C]0.154443[/C][C]1.5976[/C][C]0.056543[/C][/ROW]
[ROW][C]19[/C][C]-0.042145[/C][C]-0.436[/C][C]0.331874[/C][/ROW]
[ROW][C]20[/C][C]-0.049657[/C][C]-0.5137[/C][C]0.304276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300419&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300419&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	-0.526003	-5.441	0
2	-0.223568	-2.3126	0.011329
3	-0.215089	-2.2249	0.014094
4	-0.066225	-0.685	0.247402
5	-0.123325	-1.2757	0.102415
6	-0.121294	-1.2547	0.106166
7	-0.184519	-1.9087	0.029491
8	0.028653	0.2964	0.383754
9	-0.173513	-1.7948	0.037752
10	-0.107538	-1.1124	0.134234
11	-0.069152	-0.7153	0.237987
12	0.025933	0.2683	0.394511
13	-0.117985	-1.2204	0.112489
14	0.037037	0.3831	0.351199
15	0.032339	0.3345	0.36932
16	-0.066586	-0.6888	0.24623
17	0.090755	0.9388	0.17498
18	0.154443	1.5976	0.056543
19	-0.042145	-0.436	0.331874
20	-0.049657	-0.5137	0.304276

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

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Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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