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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

Tue, 03 Mar 2015 14:12:24 +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/2015/Mar/03/t1425391997k6ebkwl7hc0o5pw.htm/, Retrieved Fri, 17 May 2024 10:41:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277856, Retrieved Fri, 17 May 2024 10:41:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

166

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie me...] [2015-03-03 14:12:24] [fe7f0d9da4a60fe1aade911e6a24ddc7] [Current]

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Dataseries X:

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Histogram

Boxplots

2.08
2.09
2.36
2.99
2.75
1.58
1.69
1.3
1.97
1.84
1.96
1.86
2.75
2.62
2.41
3.61
2.03
1.45
1.4
1.3
1.58
2.1
2.27
2.54
2.55
2.05
2.32
2.6
2.1
1.61
1.55
1.12
1.39
2.18
1.94
2.27
2.41
2.2
2.58
2.9
2.12
1.34
1.07
0.86
1
1.54
1.29
1.44
2.6
2.77
3.31
3.2
2.07
1.42
1.43
1.28
1.59
1.68
2.01
2.52
2.74
3.06
2.69
2.32
1.67
1.04
0.98
0.86
0.97
1.3
1.82
1.99
2.7
2.86
2.91
2.56
2.05
1.62
1.26
1.44
1.27
1.64
1.84
2.1
2.79
2.84
2.76
2.67
2.1
1.55
1.42
1.12
1.12
1.41
1.56
1.8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277856&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277856&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277856&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.157504	1.5352	0.064034
2	0.028642	0.2792	0.390361
3	0.036673	0.3574	0.360776
4	-0.350988	-3.421	0.000461
5	-0.290177	-2.8283	0.002854
6	-0.137899	-1.3441	0.091063
7	-0.328633	-3.2031	0.000925
8	-0.316529	-3.0851	0.001332
9	0.126507	1.233	0.110301
10	0.002737	0.0267	0.489385
11	0.369265	3.5992	0.000255
12	0.558659	5.4451	0
13	0.173697	1.693	0.046867
14	-0.029123	-0.2839	0.388569
15	0.060861	0.5932	0.277227
16	-0.226901	-2.2116	0.014698
17	-0.304402	-2.9669	0.001903
18	-0.074816	-0.7292	0.233832
19	-0.343263	-3.3457	0.000588

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.157504 & 1.5352 & 0.064034 \tabularnewline
2 & 0.028642 & 0.2792 & 0.390361 \tabularnewline
3 & 0.036673 & 0.3574 & 0.360776 \tabularnewline
4 & -0.350988 & -3.421 & 0.000461 \tabularnewline
5 & -0.290177 & -2.8283 & 0.002854 \tabularnewline
6 & -0.137899 & -1.3441 & 0.091063 \tabularnewline
7 & -0.328633 & -3.2031 & 0.000925 \tabularnewline
8 & -0.316529 & -3.0851 & 0.001332 \tabularnewline
9 & 0.126507 & 1.233 & 0.110301 \tabularnewline
10 & 0.002737 & 0.0267 & 0.489385 \tabularnewline
11 & 0.369265 & 3.5992 & 0.000255 \tabularnewline
12 & 0.558659 & 5.4451 & 0 \tabularnewline
13 & 0.173697 & 1.693 & 0.046867 \tabularnewline
14 & -0.029123 & -0.2839 & 0.388569 \tabularnewline
15 & 0.060861 & 0.5932 & 0.277227 \tabularnewline
16 & -0.226901 & -2.2116 & 0.014698 \tabularnewline
17 & -0.304402 & -2.9669 & 0.001903 \tabularnewline
18 & -0.074816 & -0.7292 & 0.233832 \tabularnewline
19 & -0.343263 & -3.3457 & 0.000588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277856&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]0.157504[/C][C]1.5352[/C][C]0.064034[/C][/ROW]
[ROW][C]2[/C][C]0.028642[/C][C]0.2792[/C][C]0.390361[/C][/ROW]
[ROW][C]3[/C][C]0.036673[/C][C]0.3574[/C][C]0.360776[/C][/ROW]
[ROW][C]4[/C][C]-0.350988[/C][C]-3.421[/C][C]0.000461[/C][/ROW]
[ROW][C]5[/C][C]-0.290177[/C][C]-2.8283[/C][C]0.002854[/C][/ROW]
[ROW][C]6[/C][C]-0.137899[/C][C]-1.3441[/C][C]0.091063[/C][/ROW]
[ROW][C]7[/C][C]-0.328633[/C][C]-3.2031[/C][C]0.000925[/C][/ROW]
[ROW][C]8[/C][C]-0.316529[/C][C]-3.0851[/C][C]0.001332[/C][/ROW]
[ROW][C]9[/C][C]0.126507[/C][C]1.233[/C][C]0.110301[/C][/ROW]
[ROW][C]10[/C][C]0.002737[/C][C]0.0267[/C][C]0.489385[/C][/ROW]
[ROW][C]11[/C][C]0.369265[/C][C]3.5992[/C][C]0.000255[/C][/ROW]
[ROW][C]12[/C][C]0.558659[/C][C]5.4451[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.173697[/C][C]1.693[/C][C]0.046867[/C][/ROW]
[ROW][C]14[/C][C]-0.029123[/C][C]-0.2839[/C][C]0.388569[/C][/ROW]
[ROW][C]15[/C][C]0.060861[/C][C]0.5932[/C][C]0.277227[/C][/ROW]
[ROW][C]16[/C][C]-0.226901[/C][C]-2.2116[/C][C]0.014698[/C][/ROW]
[ROW][C]17[/C][C]-0.304402[/C][C]-2.9669[/C][C]0.001903[/C][/ROW]
[ROW][C]18[/C][C]-0.074816[/C][C]-0.7292[/C][C]0.233832[/C][/ROW]
[ROW][C]19[/C][C]-0.343263[/C][C]-3.3457[/C][C]0.000588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277856&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277856&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	0.157504	1.5352	0.064034
2	0.028642	0.2792	0.390361
3	0.036673	0.3574	0.360776
4	-0.350988	-3.421	0.000461
5	-0.290177	-2.8283	0.002854
6	-0.137899	-1.3441	0.091063
7	-0.328633	-3.2031	0.000925
8	-0.316529	-3.0851	0.001332
9	0.126507	1.233	0.110301
10	0.002737	0.0267	0.489385
11	0.369265	3.5992	0.000255
12	0.558659	5.4451	0
13	0.173697	1.693	0.046867
14	-0.029123	-0.2839	0.388569
15	0.060861	0.5932	0.277227
16	-0.226901	-2.2116	0.014698
17	-0.304402	-2.9669	0.001903
18	-0.074816	-0.7292	0.233832
19	-0.343263	-3.3457	0.000588

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.157504	1.5352	0.064034
2	0.003932	0.0383	0.484754
3	0.032364	0.3154	0.376559
4	-0.3714	-3.62	0.000237
5	-0.208362	-2.0309	0.022532
6	-0.082367	-0.8028	0.212042
7	-0.321003	-3.1287	0.001166
8	-0.504109	-4.9134	2e-06
9	-0.138311	-1.3481	0.090418
10	-0.379235	-3.6963	0.000183
11	-0.032071	-0.3126	0.377638
12	0.123538	1.2041	0.115771
13	0.040991	0.3995	0.345199
14	-0.285084	-2.7787	0.003289
15	0.037161	0.3622	0.359002
16	-0.003625	-0.0353	0.485945
17	-0.128629	-1.2537	0.10651
18	-0.037157	-0.3622	0.359018
19	0.014944	0.1457	0.442251

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.157504 & 1.5352 & 0.064034 \tabularnewline
2 & 0.003932 & 0.0383 & 0.484754 \tabularnewline
3 & 0.032364 & 0.3154 & 0.376559 \tabularnewline
4 & -0.3714 & -3.62 & 0.000237 \tabularnewline
5 & -0.208362 & -2.0309 & 0.022532 \tabularnewline
6 & -0.082367 & -0.8028 & 0.212042 \tabularnewline
7 & -0.321003 & -3.1287 & 0.001166 \tabularnewline
8 & -0.504109 & -4.9134 & 2e-06 \tabularnewline
9 & -0.138311 & -1.3481 & 0.090418 \tabularnewline
10 & -0.379235 & -3.6963 & 0.000183 \tabularnewline
11 & -0.032071 & -0.3126 & 0.377638 \tabularnewline
12 & 0.123538 & 1.2041 & 0.115771 \tabularnewline
13 & 0.040991 & 0.3995 & 0.345199 \tabularnewline
14 & -0.285084 & -2.7787 & 0.003289 \tabularnewline
15 & 0.037161 & 0.3622 & 0.359002 \tabularnewline
16 & -0.003625 & -0.0353 & 0.485945 \tabularnewline
17 & -0.128629 & -1.2537 & 0.10651 \tabularnewline
18 & -0.037157 & -0.3622 & 0.359018 \tabularnewline
19 & 0.014944 & 0.1457 & 0.442251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277856&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]0.157504[/C][C]1.5352[/C][C]0.064034[/C][/ROW]
[ROW][C]2[/C][C]0.003932[/C][C]0.0383[/C][C]0.484754[/C][/ROW]
[ROW][C]3[/C][C]0.032364[/C][C]0.3154[/C][C]0.376559[/C][/ROW]
[ROW][C]4[/C][C]-0.3714[/C][C]-3.62[/C][C]0.000237[/C][/ROW]
[ROW][C]5[/C][C]-0.208362[/C][C]-2.0309[/C][C]0.022532[/C][/ROW]
[ROW][C]6[/C][C]-0.082367[/C][C]-0.8028[/C][C]0.212042[/C][/ROW]
[ROW][C]7[/C][C]-0.321003[/C][C]-3.1287[/C][C]0.001166[/C][/ROW]
[ROW][C]8[/C][C]-0.504109[/C][C]-4.9134[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]-0.138311[/C][C]-1.3481[/C][C]0.090418[/C][/ROW]
[ROW][C]10[/C][C]-0.379235[/C][C]-3.6963[/C][C]0.000183[/C][/ROW]
[ROW][C]11[/C][C]-0.032071[/C][C]-0.3126[/C][C]0.377638[/C][/ROW]
[ROW][C]12[/C][C]0.123538[/C][C]1.2041[/C][C]0.115771[/C][/ROW]
[ROW][C]13[/C][C]0.040991[/C][C]0.3995[/C][C]0.345199[/C][/ROW]
[ROW][C]14[/C][C]-0.285084[/C][C]-2.7787[/C][C]0.003289[/C][/ROW]
[ROW][C]15[/C][C]0.037161[/C][C]0.3622[/C][C]0.359002[/C][/ROW]
[ROW][C]16[/C][C]-0.003625[/C][C]-0.0353[/C][C]0.485945[/C][/ROW]
[ROW][C]17[/C][C]-0.128629[/C][C]-1.2537[/C][C]0.10651[/C][/ROW]
[ROW][C]18[/C][C]-0.037157[/C][C]-0.3622[/C][C]0.359018[/C][/ROW]
[ROW][C]19[/C][C]0.014944[/C][C]0.1457[/C][C]0.442251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277856&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277856&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	0.157504	1.5352	0.064034
2	0.003932	0.0383	0.484754
3	0.032364	0.3154	0.376559
4	-0.3714	-3.62	0.000237
5	-0.208362	-2.0309	0.022532
6	-0.082367	-0.8028	0.212042
7	-0.321003	-3.1287	0.001166
8	-0.504109	-4.9134	2e-06
9	-0.138311	-1.3481	0.090418
10	-0.379235	-3.6963	0.000183
11	-0.032071	-0.3126	0.377638
12	0.123538	1.2041	0.115771
13	0.040991	0.3995	0.345199
14	-0.285084	-2.7787	0.003289
15	0.037161	0.3622	0.359002
16	-0.003625	-0.0353	0.485945
17	-0.128629	-1.2537	0.10651
18	-0.037157	-0.3622	0.359018
19	0.014944	0.1457	0.442251

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