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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 Dec 2017 11:42:37 +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/2017/Dec/21/t15138530545ghbpg11jo3fng9.htm/, Retrieved Tue, 14 May 2024 05:27:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310611, Retrieved Tue, 14 May 2024 05:27:36 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

108

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

-     [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2017-12-13 13:12:41] [a481bee26174c184b67ebb747724ca60]
- R PD    [(Partial) Autocorrelation Function] [autocorrelation] [2017-12-21 10:42:37] [bd83e7d2022b632a928e3cc7dd68d98c] [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=310611&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=310611&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310611&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	0.912258	13.2827	0
2	0.885534	12.8936	0
3	0.876743	12.7656	0
4	0.826536	12.0345	0
5	0.847624	12.3416	0
6	0.844541	12.2967	0
7	0.804544	11.7143	0
8	0.78443	11.4215	0
9	0.79001	11.5027	0
10	0.773458	11.2617	0
11	0.794841	11.5731	0
12	0.819314	11.9294	0
13	0.756532	11.0153	0
14	0.741333	10.794	0
15	0.712813	10.3787	0
16	0.672947	9.7983	0
17	0.697669	10.1582	0
18	0.683131	9.9465	0
19	0.650309	9.4686	0
20	0.642928	9.3612	0
21	0.63281	9.2139	0
22	0.628114	9.1455	0
23	0.654562	9.5306	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.912258 & 13.2827 & 0 \tabularnewline
2 & 0.885534 & 12.8936 & 0 \tabularnewline
3 & 0.876743 & 12.7656 & 0 \tabularnewline
4 & 0.826536 & 12.0345 & 0 \tabularnewline
5 & 0.847624 & 12.3416 & 0 \tabularnewline
6 & 0.844541 & 12.2967 & 0 \tabularnewline
7 & 0.804544 & 11.7143 & 0 \tabularnewline
8 & 0.78443 & 11.4215 & 0 \tabularnewline
9 & 0.79001 & 11.5027 & 0 \tabularnewline
10 & 0.773458 & 11.2617 & 0 \tabularnewline
11 & 0.794841 & 11.5731 & 0 \tabularnewline
12 & 0.819314 & 11.9294 & 0 \tabularnewline
13 & 0.756532 & 11.0153 & 0 \tabularnewline
14 & 0.741333 & 10.794 & 0 \tabularnewline
15 & 0.712813 & 10.3787 & 0 \tabularnewline
16 & 0.672947 & 9.7983 & 0 \tabularnewline
17 & 0.697669 & 10.1582 & 0 \tabularnewline
18 & 0.683131 & 9.9465 & 0 \tabularnewline
19 & 0.650309 & 9.4686 & 0 \tabularnewline
20 & 0.642928 & 9.3612 & 0 \tabularnewline
21 & 0.63281 & 9.2139 & 0 \tabularnewline
22 & 0.628114 & 9.1455 & 0 \tabularnewline
23 & 0.654562 & 9.5306 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310611&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]0.912258[/C][C]13.2827[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.885534[/C][C]12.8936[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.876743[/C][C]12.7656[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.826536[/C][C]12.0345[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.847624[/C][C]12.3416[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.844541[/C][C]12.2967[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.804544[/C][C]11.7143[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.78443[/C][C]11.4215[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.79001[/C][C]11.5027[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.773458[/C][C]11.2617[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.794841[/C][C]11.5731[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.819314[/C][C]11.9294[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.756532[/C][C]11.0153[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.741333[/C][C]10.794[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.712813[/C][C]10.3787[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.672947[/C][C]9.7983[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.697669[/C][C]10.1582[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.683131[/C][C]9.9465[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.650309[/C][C]9.4686[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.642928[/C][C]9.3612[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.63281[/C][C]9.2139[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.628114[/C][C]9.1455[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.654562[/C][C]9.5306[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310611&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310611&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	0.912258	13.2827	0
2	0.885534	12.8936	0
3	0.876743	12.7656	0
4	0.826536	12.0345	0
5	0.847624	12.3416	0
6	0.844541	12.2967	0
7	0.804544	11.7143	0
8	0.78443	11.4215	0
9	0.79001	11.5027	0
10	0.773458	11.2617	0
11	0.794841	11.5731	0
12	0.819314	11.9294	0
13	0.756532	11.0153	0
14	0.741333	10.794	0
15	0.712813	10.3787	0
16	0.672947	9.7983	0
17	0.697669	10.1582	0
18	0.683131	9.9465	0
19	0.650309	9.4686	0
20	0.642928	9.3612	0
21	0.63281	9.2139	0
22	0.628114	9.1455	0
23	0.654562	9.5306	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.912258	13.2827	0
2	0.31778	4.6269	3e-06
3	0.23683	3.4483	0.00034
4	-0.140921	-2.0518	0.020707
5	0.343712	5.0045	1e-06
6	0.091251	1.3286	0.092699
7	-0.137358	-2	0.023391
8	-0.164163	-2.3902	0.008856
9	0.311538	4.5361	5e-06
10	0.0306	0.4455	0.328191
11	0.148549	2.1629	0.015834
12	0.148933	2.1685	0.015617
13	-0.332671	-4.8438	1e-06
14	-0.157923	-2.2994	0.011228
15	-0.130498	-1.9001	0.02939
16	0.008139	0.1185	0.452889
17	0.091862	1.3375	0.091241
18	0.065091	0.9477	0.17217
19	0.002633	0.0383	0.484727
20	0.024326	0.3542	0.361776
21	0.056011	0.8155	0.207843
22	0.044925	0.6541	0.256872
23	0.015797	0.23	0.409152

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.912258 & 13.2827 & 0 \tabularnewline
2 & 0.31778 & 4.6269 & 3e-06 \tabularnewline
3 & 0.23683 & 3.4483 & 0.00034 \tabularnewline
4 & -0.140921 & -2.0518 & 0.020707 \tabularnewline
5 & 0.343712 & 5.0045 & 1e-06 \tabularnewline
6 & 0.091251 & 1.3286 & 0.092699 \tabularnewline
7 & -0.137358 & -2 & 0.023391 \tabularnewline
8 & -0.164163 & -2.3902 & 0.008856 \tabularnewline
9 & 0.311538 & 4.5361 & 5e-06 \tabularnewline
10 & 0.0306 & 0.4455 & 0.328191 \tabularnewline
11 & 0.148549 & 2.1629 & 0.015834 \tabularnewline
12 & 0.148933 & 2.1685 & 0.015617 \tabularnewline
13 & -0.332671 & -4.8438 & 1e-06 \tabularnewline
14 & -0.157923 & -2.2994 & 0.011228 \tabularnewline
15 & -0.130498 & -1.9001 & 0.02939 \tabularnewline
16 & 0.008139 & 0.1185 & 0.452889 \tabularnewline
17 & 0.091862 & 1.3375 & 0.091241 \tabularnewline
18 & 0.065091 & 0.9477 & 0.17217 \tabularnewline
19 & 0.002633 & 0.0383 & 0.484727 \tabularnewline
20 & 0.024326 & 0.3542 & 0.361776 \tabularnewline
21 & 0.056011 & 0.8155 & 0.207843 \tabularnewline
22 & 0.044925 & 0.6541 & 0.256872 \tabularnewline
23 & 0.015797 & 0.23 & 0.409152 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310611&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]0.912258[/C][C]13.2827[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.31778[/C][C]4.6269[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.23683[/C][C]3.4483[/C][C]0.00034[/C][/ROW]
[ROW][C]4[/C][C]-0.140921[/C][C]-2.0518[/C][C]0.020707[/C][/ROW]
[ROW][C]5[/C][C]0.343712[/C][C]5.0045[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.091251[/C][C]1.3286[/C][C]0.092699[/C][/ROW]
[ROW][C]7[/C][C]-0.137358[/C][C]-2[/C][C]0.023391[/C][/ROW]
[ROW][C]8[/C][C]-0.164163[/C][C]-2.3902[/C][C]0.008856[/C][/ROW]
[ROW][C]9[/C][C]0.311538[/C][C]4.5361[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.0306[/C][C]0.4455[/C][C]0.328191[/C][/ROW]
[ROW][C]11[/C][C]0.148549[/C][C]2.1629[/C][C]0.015834[/C][/ROW]
[ROW][C]12[/C][C]0.148933[/C][C]2.1685[/C][C]0.015617[/C][/ROW]
[ROW][C]13[/C][C]-0.332671[/C][C]-4.8438[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.157923[/C][C]-2.2994[/C][C]0.011228[/C][/ROW]
[ROW][C]15[/C][C]-0.130498[/C][C]-1.9001[/C][C]0.02939[/C][/ROW]
[ROW][C]16[/C][C]0.008139[/C][C]0.1185[/C][C]0.452889[/C][/ROW]
[ROW][C]17[/C][C]0.091862[/C][C]1.3375[/C][C]0.091241[/C][/ROW]
[ROW][C]18[/C][C]0.065091[/C][C]0.9477[/C][C]0.17217[/C][/ROW]
[ROW][C]19[/C][C]0.002633[/C][C]0.0383[/C][C]0.484727[/C][/ROW]
[ROW][C]20[/C][C]0.024326[/C][C]0.3542[/C][C]0.361776[/C][/ROW]
[ROW][C]21[/C][C]0.056011[/C][C]0.8155[/C][C]0.207843[/C][/ROW]
[ROW][C]22[/C][C]0.044925[/C][C]0.6541[/C][C]0.256872[/C][/ROW]
[ROW][C]23[/C][C]0.015797[/C][C]0.23[/C][C]0.409152[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310611&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310611&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	0.912258	13.2827	0
2	0.31778	4.6269	3e-06
3	0.23683	3.4483	0.00034
4	-0.140921	-2.0518	0.020707
5	0.343712	5.0045	1e-06
6	0.091251	1.3286	0.092699
7	-0.137358	-2	0.023391
8	-0.164163	-2.3902	0.008856
9	0.311538	4.5361	5e-06
10	0.0306	0.4455	0.328191
11	0.148549	2.1629	0.015834
12	0.148933	2.1685	0.015617
13	-0.332671	-4.8438	1e-06
14	-0.157923	-2.2994	0.011228
15	-0.130498	-1.9001	0.02939
16	0.008139	0.1185	0.452889
17	0.091862	1.3375	0.091241
18	0.065091	0.9477	0.17217
19	0.002633	0.0383	0.484727
20	0.024326	0.3542	0.361776
21	0.056011	0.8155	0.207843
22	0.044925	0.6541	0.256872
23	0.015797	0.23	0.409152

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.5 ; 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