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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 06 Dec 2017 18:11:14 +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/06/t1512580308f4ycpkbq47wy7gi.htm/, Retrieved Tue, 14 May 2024 23:54:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308630, Retrieved Tue, 14 May 2024 23:54:07 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [autocorrelation (...] [2017-12-06 17:11:14] [33956d13de8d8b5d5d1b78ead3554acb] [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=308630&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=308630&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308630&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	-0.517425	-7.2992	0
2	0.019443	0.2743	0.392076
3	0.228283	3.2203	0.000748
4	-0.240396	-3.3912	0.00042
5	0.091347	1.2886	0.099515
6	0.080713	1.1386	0.12812
7	-0.099104	-1.398	0.08183
8	0.063264	0.8924	0.186616
9	-0.016847	-0.2376	0.406199
10	0.008048	0.1135	0.454861
11	0.170714	2.4082	0.008471
12	-0.365171	-5.1514	0
13	0.228614	3.225	0.000736
14	-0.118258	-1.6682	0.048421
15	0.024547	0.3463	0.364751
16	0.06932	0.9779	0.164662
17	-0.106352	-1.5003	0.067563
18	0.041136	0.5803	0.281186
19	-0.0332	-0.4683	0.320028
20	-0.023454	-0.3309	0.370547
21	0.104332	1.4718	0.07133
22	-0.195205	-2.7537	0.003219
23	0.188062	2.6529	0.004312

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.517425 & -7.2992 & 0 \tabularnewline
2 & 0.019443 & 0.2743 & 0.392076 \tabularnewline
3 & 0.228283 & 3.2203 & 0.000748 \tabularnewline
4 & -0.240396 & -3.3912 & 0.00042 \tabularnewline
5 & 0.091347 & 1.2886 & 0.099515 \tabularnewline
6 & 0.080713 & 1.1386 & 0.12812 \tabularnewline
7 & -0.099104 & -1.398 & 0.08183 \tabularnewline
8 & 0.063264 & 0.8924 & 0.186616 \tabularnewline
9 & -0.016847 & -0.2376 & 0.406199 \tabularnewline
10 & 0.008048 & 0.1135 & 0.454861 \tabularnewline
11 & 0.170714 & 2.4082 & 0.008471 \tabularnewline
12 & -0.365171 & -5.1514 & 0 \tabularnewline
13 & 0.228614 & 3.225 & 0.000736 \tabularnewline
14 & -0.118258 & -1.6682 & 0.048421 \tabularnewline
15 & 0.024547 & 0.3463 & 0.364751 \tabularnewline
16 & 0.06932 & 0.9779 & 0.164662 \tabularnewline
17 & -0.106352 & -1.5003 & 0.067563 \tabularnewline
18 & 0.041136 & 0.5803 & 0.281186 \tabularnewline
19 & -0.0332 & -0.4683 & 0.320028 \tabularnewline
20 & -0.023454 & -0.3309 & 0.370547 \tabularnewline
21 & 0.104332 & 1.4718 & 0.07133 \tabularnewline
22 & -0.195205 & -2.7537 & 0.003219 \tabularnewline
23 & 0.188062 & 2.6529 & 0.004312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308630&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]-0.517425[/C][C]-7.2992[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.019443[/C][C]0.2743[/C][C]0.392076[/C][/ROW]
[ROW][C]3[/C][C]0.228283[/C][C]3.2203[/C][C]0.000748[/C][/ROW]
[ROW][C]4[/C][C]-0.240396[/C][C]-3.3912[/C][C]0.00042[/C][/ROW]
[ROW][C]5[/C][C]0.091347[/C][C]1.2886[/C][C]0.099515[/C][/ROW]
[ROW][C]6[/C][C]0.080713[/C][C]1.1386[/C][C]0.12812[/C][/ROW]
[ROW][C]7[/C][C]-0.099104[/C][C]-1.398[/C][C]0.08183[/C][/ROW]
[ROW][C]8[/C][C]0.063264[/C][C]0.8924[/C][C]0.186616[/C][/ROW]
[ROW][C]9[/C][C]-0.016847[/C][C]-0.2376[/C][C]0.406199[/C][/ROW]
[ROW][C]10[/C][C]0.008048[/C][C]0.1135[/C][C]0.454861[/C][/ROW]
[ROW][C]11[/C][C]0.170714[/C][C]2.4082[/C][C]0.008471[/C][/ROW]
[ROW][C]12[/C][C]-0.365171[/C][C]-5.1514[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.228614[/C][C]3.225[/C][C]0.000736[/C][/ROW]
[ROW][C]14[/C][C]-0.118258[/C][C]-1.6682[/C][C]0.048421[/C][/ROW]
[ROW][C]15[/C][C]0.024547[/C][C]0.3463[/C][C]0.364751[/C][/ROW]
[ROW][C]16[/C][C]0.06932[/C][C]0.9779[/C][C]0.164662[/C][/ROW]
[ROW][C]17[/C][C]-0.106352[/C][C]-1.5003[/C][C]0.067563[/C][/ROW]
[ROW][C]18[/C][C]0.041136[/C][C]0.5803[/C][C]0.281186[/C][/ROW]
[ROW][C]19[/C][C]-0.0332[/C][C]-0.4683[/C][C]0.320028[/C][/ROW]
[ROW][C]20[/C][C]-0.023454[/C][C]-0.3309[/C][C]0.370547[/C][/ROW]
[ROW][C]21[/C][C]0.104332[/C][C]1.4718[/C][C]0.07133[/C][/ROW]
[ROW][C]22[/C][C]-0.195205[/C][C]-2.7537[/C][C]0.003219[/C][/ROW]
[ROW][C]23[/C][C]0.188062[/C][C]2.6529[/C][C]0.004312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308630&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308630&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	-0.517425	-7.2992	0
2	0.019443	0.2743	0.392076
3	0.228283	3.2203	0.000748
4	-0.240396	-3.3912	0.00042
5	0.091347	1.2886	0.099515
6	0.080713	1.1386	0.12812
7	-0.099104	-1.398	0.08183
8	0.063264	0.8924	0.186616
9	-0.016847	-0.2376	0.406199
10	0.008048	0.1135	0.454861
11	0.170714	2.4082	0.008471
12	-0.365171	-5.1514	0
13	0.228614	3.225	0.000736
14	-0.118258	-1.6682	0.048421
15	0.024547	0.3463	0.364751
16	0.06932	0.9779	0.164662
17	-0.106352	-1.5003	0.067563
18	0.041136	0.5803	0.281186
19	-0.0332	-0.4683	0.320028
20	-0.023454	-0.3309	0.370547
21	0.104332	1.4718	0.07133
22	-0.195205	-2.7537	0.003219
23	0.188062	2.6529	0.004312

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.517425	-7.2992	0
2	-0.339063	-4.7831	2e-06
3	0.102324	1.4435	0.075232
4	-0.04988	-0.7036	0.241241
5	-0.044609	-0.6293	0.264942
6	0.061233	0.8638	0.194371
7	0.058681	0.8278	0.204387
8	0.039791	0.5613	0.287607
9	-0.008781	-0.1239	0.450771
10	0.04276	0.6032	0.273528
11	0.286063	4.0354	3.9e-05
12	-0.231554	-3.2665	0.000641
13	-0.151775	-2.141	0.016743
14	-0.230209	-3.2475	0.000683
15	0.059161	0.8346	0.202482
16	0.001852	0.0261	0.48959
17	-0.081772	-1.1535	0.125038
18	-0.035769	-0.5046	0.307204
19	-0.04831	-0.6815	0.248174
20	-0.065555	-0.9248	0.178102
21	0.077914	1.0991	0.136524
22	-0.12681	-1.7889	0.037578
23	0.264783	3.7352	0.000122

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.517425 & -7.2992 & 0 \tabularnewline
2 & -0.339063 & -4.7831 & 2e-06 \tabularnewline
3 & 0.102324 & 1.4435 & 0.075232 \tabularnewline
4 & -0.04988 & -0.7036 & 0.241241 \tabularnewline
5 & -0.044609 & -0.6293 & 0.264942 \tabularnewline
6 & 0.061233 & 0.8638 & 0.194371 \tabularnewline
7 & 0.058681 & 0.8278 & 0.204387 \tabularnewline
8 & 0.039791 & 0.5613 & 0.287607 \tabularnewline
9 & -0.008781 & -0.1239 & 0.450771 \tabularnewline
10 & 0.04276 & 0.6032 & 0.273528 \tabularnewline
11 & 0.286063 & 4.0354 & 3.9e-05 \tabularnewline
12 & -0.231554 & -3.2665 & 0.000641 \tabularnewline
13 & -0.151775 & -2.141 & 0.016743 \tabularnewline
14 & -0.230209 & -3.2475 & 0.000683 \tabularnewline
15 & 0.059161 & 0.8346 & 0.202482 \tabularnewline
16 & 0.001852 & 0.0261 & 0.48959 \tabularnewline
17 & -0.081772 & -1.1535 & 0.125038 \tabularnewline
18 & -0.035769 & -0.5046 & 0.307204 \tabularnewline
19 & -0.04831 & -0.6815 & 0.248174 \tabularnewline
20 & -0.065555 & -0.9248 & 0.178102 \tabularnewline
21 & 0.077914 & 1.0991 & 0.136524 \tabularnewline
22 & -0.12681 & -1.7889 & 0.037578 \tabularnewline
23 & 0.264783 & 3.7352 & 0.000122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308630&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]-0.517425[/C][C]-7.2992[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.339063[/C][C]-4.7831[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.102324[/C][C]1.4435[/C][C]0.075232[/C][/ROW]
[ROW][C]4[/C][C]-0.04988[/C][C]-0.7036[/C][C]0.241241[/C][/ROW]
[ROW][C]5[/C][C]-0.044609[/C][C]-0.6293[/C][C]0.264942[/C][/ROW]
[ROW][C]6[/C][C]0.061233[/C][C]0.8638[/C][C]0.194371[/C][/ROW]
[ROW][C]7[/C][C]0.058681[/C][C]0.8278[/C][C]0.204387[/C][/ROW]
[ROW][C]8[/C][C]0.039791[/C][C]0.5613[/C][C]0.287607[/C][/ROW]
[ROW][C]9[/C][C]-0.008781[/C][C]-0.1239[/C][C]0.450771[/C][/ROW]
[ROW][C]10[/C][C]0.04276[/C][C]0.6032[/C][C]0.273528[/C][/ROW]
[ROW][C]11[/C][C]0.286063[/C][C]4.0354[/C][C]3.9e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.231554[/C][C]-3.2665[/C][C]0.000641[/C][/ROW]
[ROW][C]13[/C][C]-0.151775[/C][C]-2.141[/C][C]0.016743[/C][/ROW]
[ROW][C]14[/C][C]-0.230209[/C][C]-3.2475[/C][C]0.000683[/C][/ROW]
[ROW][C]15[/C][C]0.059161[/C][C]0.8346[/C][C]0.202482[/C][/ROW]
[ROW][C]16[/C][C]0.001852[/C][C]0.0261[/C][C]0.48959[/C][/ROW]
[ROW][C]17[/C][C]-0.081772[/C][C]-1.1535[/C][C]0.125038[/C][/ROW]
[ROW][C]18[/C][C]-0.035769[/C][C]-0.5046[/C][C]0.307204[/C][/ROW]
[ROW][C]19[/C][C]-0.04831[/C][C]-0.6815[/C][C]0.248174[/C][/ROW]
[ROW][C]20[/C][C]-0.065555[/C][C]-0.9248[/C][C]0.178102[/C][/ROW]
[ROW][C]21[/C][C]0.077914[/C][C]1.0991[/C][C]0.136524[/C][/ROW]
[ROW][C]22[/C][C]-0.12681[/C][C]-1.7889[/C][C]0.037578[/C][/ROW]
[ROW][C]23[/C][C]0.264783[/C][C]3.7352[/C][C]0.000122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308630&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308630&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	-0.517425	-7.2992	0
2	-0.339063	-4.7831	2e-06
3	0.102324	1.4435	0.075232
4	-0.04988	-0.7036	0.241241
5	-0.044609	-0.6293	0.264942
6	0.061233	0.8638	0.194371
7	0.058681	0.8278	0.204387
8	0.039791	0.5613	0.287607
9	-0.008781	-0.1239	0.450771
10	0.04276	0.6032	0.273528
11	0.286063	4.0354	3.9e-05
12	-0.231554	-3.2665	0.000641
13	-0.151775	-2.141	0.016743
14	-0.230209	-3.2475	0.000683
15	0.059161	0.8346	0.202482
16	0.001852	0.0261	0.48959
17	-0.081772	-1.1535	0.125038
18	-0.035769	-0.5046	0.307204
19	-0.04831	-0.6815	0.248174
20	-0.065555	-0.9248	0.178102
21	0.077914	1.0991	0.136524
22	-0.12681	-1.7889	0.037578
23	0.264783	3.7352	0.000122

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par1 = Default ; par2 = 0.1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.1 ; par3 = 1 ; par4 = 1 ; 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