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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, 23 Dec 2016 00:00:42 +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/23/t148244772299hc83mz5pq3wp1.htm/, Retrieved Fri, 01 Nov 2024 05:24:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302728, Retrieved Fri, 01 Nov 2024 05:24:46 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

137

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

-       [(Partial) Autocorrelation Function] [Autocorrelation ] [2016-12-22 23:00:42] [36884fbde1107444791dd71ee0072a5a] [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	1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302728&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302728&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.764767	8.5845	0
2	0.759541	8.5258	0
3	0.669066	7.5102	0
4	0.659395	7.4017	0
5	0.526448	5.9094	0
6	0.560075	6.2868	0
7	0.498432	5.5949	0
8	0.518914	5.8248	0
9	0.464154	5.2101	0
10	0.472051	5.2988	0
11	0.450086	5.0522	1e-06
12	0.435462	4.8881	2e-06
13	0.310732	3.488	0.000335
14	0.320078	3.5929	0.000234
15	0.276267	3.1011	0.00119
16	0.244662	2.7463	0.003455
17	0.205284	2.3043	0.011421
18	0.202086	2.2684	0.012503
19	0.114754	1.2881	0.100033
20	0.100265	1.1255	0.131264
21	0.066658	0.7482	0.227857

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.764767 & 8.5845 & 0 \tabularnewline
2 & 0.759541 & 8.5258 & 0 \tabularnewline
3 & 0.669066 & 7.5102 & 0 \tabularnewline
4 & 0.659395 & 7.4017 & 0 \tabularnewline
5 & 0.526448 & 5.9094 & 0 \tabularnewline
6 & 0.560075 & 6.2868 & 0 \tabularnewline
7 & 0.498432 & 5.5949 & 0 \tabularnewline
8 & 0.518914 & 5.8248 & 0 \tabularnewline
9 & 0.464154 & 5.2101 & 0 \tabularnewline
10 & 0.472051 & 5.2988 & 0 \tabularnewline
11 & 0.450086 & 5.0522 & 1e-06 \tabularnewline
12 & 0.435462 & 4.8881 & 2e-06 \tabularnewline
13 & 0.310732 & 3.488 & 0.000335 \tabularnewline
14 & 0.320078 & 3.5929 & 0.000234 \tabularnewline
15 & 0.276267 & 3.1011 & 0.00119 \tabularnewline
16 & 0.244662 & 2.7463 & 0.003455 \tabularnewline
17 & 0.205284 & 2.3043 & 0.011421 \tabularnewline
18 & 0.202086 & 2.2684 & 0.012503 \tabularnewline
19 & 0.114754 & 1.2881 & 0.100033 \tabularnewline
20 & 0.100265 & 1.1255 & 0.131264 \tabularnewline
21 & 0.066658 & 0.7482 & 0.227857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302728&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]0.764767[/C][C]8.5845[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.759541[/C][C]8.5258[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.669066[/C][C]7.5102[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.659395[/C][C]7.4017[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.526448[/C][C]5.9094[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.560075[/C][C]6.2868[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.498432[/C][C]5.5949[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.518914[/C][C]5.8248[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.464154[/C][C]5.2101[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.472051[/C][C]5.2988[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.450086[/C][C]5.0522[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.435462[/C][C]4.8881[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.310732[/C][C]3.488[/C][C]0.000335[/C][/ROW]
[ROW][C]14[/C][C]0.320078[/C][C]3.5929[/C][C]0.000234[/C][/ROW]
[ROW][C]15[/C][C]0.276267[/C][C]3.1011[/C][C]0.00119[/C][/ROW]
[ROW][C]16[/C][C]0.244662[/C][C]2.7463[/C][C]0.003455[/C][/ROW]
[ROW][C]17[/C][C]0.205284[/C][C]2.3043[/C][C]0.011421[/C][/ROW]
[ROW][C]18[/C][C]0.202086[/C][C]2.2684[/C][C]0.012503[/C][/ROW]
[ROW][C]19[/C][C]0.114754[/C][C]1.2881[/C][C]0.100033[/C][/ROW]
[ROW][C]20[/C][C]0.100265[/C][C]1.1255[/C][C]0.131264[/C][/ROW]
[ROW][C]21[/C][C]0.066658[/C][C]0.7482[/C][C]0.227857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302728&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	0.764767	8.5845	0
2	0.759541	8.5258	0
3	0.669066	7.5102	0
4	0.659395	7.4017	0
5	0.526448	5.9094	0
6	0.560075	6.2868	0
7	0.498432	5.5949	0
8	0.518914	5.8248	0
9	0.464154	5.2101	0
10	0.472051	5.2988	0
11	0.450086	5.0522	1e-06
12	0.435462	4.8881	2e-06
13	0.310732	3.488	0.000335
14	0.320078	3.5929	0.000234
15	0.276267	3.1011	0.00119
16	0.244662	2.7463	0.003455
17	0.205284	2.3043	0.011421
18	0.202086	2.2684	0.012503
19	0.114754	1.2881	0.100033
20	0.100265	1.1255	0.131264
21	0.066658	0.7482	0.227857

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.764767	8.5845	0
2	0.420765	4.7231	3e-06
3	0.031662	0.3554	0.36144
4	0.113616	1.2753	0.102269
5	-0.20651	-2.3181	0.011029
6	0.168986	1.8969	0.030068
7	0.052714	0.5917	0.27755
8	0.099759	1.1198	0.132467
9	0.000943	0.0106	0.495787
10	-0.035544	-0.399	0.34529
11	0.085218	0.9566	0.170307
12	-0.037689	-0.4231	0.336489
13	-0.284946	-3.1985	0.000874
14	0.032657	0.3666	0.357274
15	0.059723	0.6704	0.251919
16	-0.005547	-0.0623	0.475226
17	0.016586	0.1862	0.426304
18	-0.107846	-1.2106	0.114163
19	-0.179777	-2.018	0.022858
20	-0.012393	-0.1391	0.444792
21	0.060241	0.6762	0.250075

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.764767 & 8.5845 & 0 \tabularnewline
2 & 0.420765 & 4.7231 & 3e-06 \tabularnewline
3 & 0.031662 & 0.3554 & 0.36144 \tabularnewline
4 & 0.113616 & 1.2753 & 0.102269 \tabularnewline
5 & -0.20651 & -2.3181 & 0.011029 \tabularnewline
6 & 0.168986 & 1.8969 & 0.030068 \tabularnewline
7 & 0.052714 & 0.5917 & 0.27755 \tabularnewline
8 & 0.099759 & 1.1198 & 0.132467 \tabularnewline
9 & 0.000943 & 0.0106 & 0.495787 \tabularnewline
10 & -0.035544 & -0.399 & 0.34529 \tabularnewline
11 & 0.085218 & 0.9566 & 0.170307 \tabularnewline
12 & -0.037689 & -0.4231 & 0.336489 \tabularnewline
13 & -0.284946 & -3.1985 & 0.000874 \tabularnewline
14 & 0.032657 & 0.3666 & 0.357274 \tabularnewline
15 & 0.059723 & 0.6704 & 0.251919 \tabularnewline
16 & -0.005547 & -0.0623 & 0.475226 \tabularnewline
17 & 0.016586 & 0.1862 & 0.426304 \tabularnewline
18 & -0.107846 & -1.2106 & 0.114163 \tabularnewline
19 & -0.179777 & -2.018 & 0.022858 \tabularnewline
20 & -0.012393 & -0.1391 & 0.444792 \tabularnewline
21 & 0.060241 & 0.6762 & 0.250075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302728&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]0.764767[/C][C]8.5845[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.420765[/C][C]4.7231[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.031662[/C][C]0.3554[/C][C]0.36144[/C][/ROW]
[ROW][C]4[/C][C]0.113616[/C][C]1.2753[/C][C]0.102269[/C][/ROW]
[ROW][C]5[/C][C]-0.20651[/C][C]-2.3181[/C][C]0.011029[/C][/ROW]
[ROW][C]6[/C][C]0.168986[/C][C]1.8969[/C][C]0.030068[/C][/ROW]
[ROW][C]7[/C][C]0.052714[/C][C]0.5917[/C][C]0.27755[/C][/ROW]
[ROW][C]8[/C][C]0.099759[/C][C]1.1198[/C][C]0.132467[/C][/ROW]
[ROW][C]9[/C][C]0.000943[/C][C]0.0106[/C][C]0.495787[/C][/ROW]
[ROW][C]10[/C][C]-0.035544[/C][C]-0.399[/C][C]0.34529[/C][/ROW]
[ROW][C]11[/C][C]0.085218[/C][C]0.9566[/C][C]0.170307[/C][/ROW]
[ROW][C]12[/C][C]-0.037689[/C][C]-0.4231[/C][C]0.336489[/C][/ROW]
[ROW][C]13[/C][C]-0.284946[/C][C]-3.1985[/C][C]0.000874[/C][/ROW]
[ROW][C]14[/C][C]0.032657[/C][C]0.3666[/C][C]0.357274[/C][/ROW]
[ROW][C]15[/C][C]0.059723[/C][C]0.6704[/C][C]0.251919[/C][/ROW]
[ROW][C]16[/C][C]-0.005547[/C][C]-0.0623[/C][C]0.475226[/C][/ROW]
[ROW][C]17[/C][C]0.016586[/C][C]0.1862[/C][C]0.426304[/C][/ROW]
[ROW][C]18[/C][C]-0.107846[/C][C]-1.2106[/C][C]0.114163[/C][/ROW]
[ROW][C]19[/C][C]-0.179777[/C][C]-2.018[/C][C]0.022858[/C][/ROW]
[ROW][C]20[/C][C]-0.012393[/C][C]-0.1391[/C][C]0.444792[/C][/ROW]
[ROW][C]21[/C][C]0.060241[/C][C]0.6762[/C][C]0.250075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302728&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302728&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	0.764767	8.5845	0
2	0.420765	4.7231	3e-06
3	0.031662	0.3554	0.36144
4	0.113616	1.2753	0.102269
5	-0.20651	-2.3181	0.011029
6	0.168986	1.8969	0.030068
7	0.052714	0.5917	0.27755
8	0.099759	1.1198	0.132467
9	0.000943	0.0106	0.495787
10	-0.035544	-0.399	0.34529
11	0.085218	0.9566	0.170307
12	-0.037689	-0.4231	0.336489
13	-0.284946	-3.1985	0.000874
14	0.032657	0.3666	0.357274
15	0.059723	0.6704	0.251919
16	-0.005547	-0.0623	0.475226
17	0.016586	0.1862	0.426304
18	-0.107846	-1.2106	0.114163
19	-0.179777	-2.018	0.022858
20	-0.012393	-0.1391	0.444792
21	0.060241	0.6762	0.250075

Figure 1

PNG link

Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

Postscript link

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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)
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