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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 05 Nov 2021 16:51:09 +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/2021/Nov/05/t1636127657k6tos7y4zotmsh0.htm/, Retrieved Thu, 09 May 2024 04:43:27 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 09 May 2024 04:43:27 +0200

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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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.885392	17.9497	0
2	0.859668	17.4282	0
3	0.855757	17.3489	0
4	0.855278	17.3392	0
5	0.829494	16.8165	0
6	0.865712	17.5507	0
7	0.883213	17.9055	0
8	0.838802	17.0051	0
9	0.794987	16.1169	0
10	0.800355	16.2257	0
11	0.781341	15.8402	0
12	0.78775	15.9702	0
13	0.778128	15.7751	0
14	0.796264	16.1428	0
15	0.74917	15.188	0
16	0.712293	14.4404	0
17	0.696828	14.1269	0
18	0.685885	13.905	0
19	0.679723	13.7801	0
20	0.676816	13.7212	0
21	0.667784	13.5381	0
22	0.637841	12.931	0
23	0.603873	12.2424	0
24	0.581551	11.7899	0
25	0.562077	11.3951	0
26	0.562455	11.4027	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.885392 & 17.9497 & 0 \tabularnewline
2 & 0.859668 & 17.4282 & 0 \tabularnewline
3 & 0.855757 & 17.3489 & 0 \tabularnewline
4 & 0.855278 & 17.3392 & 0 \tabularnewline
5 & 0.829494 & 16.8165 & 0 \tabularnewline
6 & 0.865712 & 17.5507 & 0 \tabularnewline
7 & 0.883213 & 17.9055 & 0 \tabularnewline
8 & 0.838802 & 17.0051 & 0 \tabularnewline
9 & 0.794987 & 16.1169 & 0 \tabularnewline
10 & 0.800355 & 16.2257 & 0 \tabularnewline
11 & 0.781341 & 15.8402 & 0 \tabularnewline
12 & 0.78775 & 15.9702 & 0 \tabularnewline
13 & 0.778128 & 15.7751 & 0 \tabularnewline
14 & 0.796264 & 16.1428 & 0 \tabularnewline
15 & 0.74917 & 15.188 & 0 \tabularnewline
16 & 0.712293 & 14.4404 & 0 \tabularnewline
17 & 0.696828 & 14.1269 & 0 \tabularnewline
18 & 0.685885 & 13.905 & 0 \tabularnewline
19 & 0.679723 & 13.7801 & 0 \tabularnewline
20 & 0.676816 & 13.7212 & 0 \tabularnewline
21 & 0.667784 & 13.5381 & 0 \tabularnewline
22 & 0.637841 & 12.931 & 0 \tabularnewline
23 & 0.603873 & 12.2424 & 0 \tabularnewline
24 & 0.581551 & 11.7899 & 0 \tabularnewline
25 & 0.562077 & 11.3951 & 0 \tabularnewline
26 & 0.562455 & 11.4027 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.885392[/C][C]17.9497[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.859668[/C][C]17.4282[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.855757[/C][C]17.3489[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.855278[/C][C]17.3392[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.829494[/C][C]16.8165[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.865712[/C][C]17.5507[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.883213[/C][C]17.9055[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.838802[/C][C]17.0051[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.794987[/C][C]16.1169[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.800355[/C][C]16.2257[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.781341[/C][C]15.8402[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.78775[/C][C]15.9702[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.778128[/C][C]15.7751[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.796264[/C][C]16.1428[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.74917[/C][C]15.188[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.712293[/C][C]14.4404[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.696828[/C][C]14.1269[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.685885[/C][C]13.905[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.679723[/C][C]13.7801[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.676816[/C][C]13.7212[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.667784[/C][C]13.5381[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.637841[/C][C]12.931[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.603873[/C][C]12.2424[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.581551[/C][C]11.7899[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.562077[/C][C]11.3951[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]0.562455[/C][C]11.4027[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.885392	17.9497	0
2	0.859668	17.4282	0
3	0.855757	17.3489	0
4	0.855278	17.3392	0
5	0.829494	16.8165	0
6	0.865712	17.5507	0
7	0.883213	17.9055	0
8	0.838802	17.0051	0
9	0.794987	16.1169	0
10	0.800355	16.2257	0
11	0.781341	15.8402	0
12	0.78775	15.9702	0
13	0.778128	15.7751	0
14	0.796264	16.1428	0
15	0.74917	15.188	0
16	0.712293	14.4404	0
17	0.696828	14.1269	0
18	0.685885	13.905	0
19	0.679723	13.7801	0
20	0.676816	13.7212	0
21	0.667784	13.5381	0
22	0.637841	12.931	0
23	0.603873	12.2424	0
24	0.581551	11.7899	0
25	0.562077	11.3951	0
26	0.562455	11.4027	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.885392	17.9497	0
2	0.35056	7.107	0
3	0.269393	5.4614	0
4	0.212252	4.303	1.1e-05
5	0.021769	0.4413	0.329603
6	0.330484	6.6999	0
7	0.269475	5.4631	0
8	-0.118328	-2.3989	0.008445
9	-0.246282	-4.9929	0
10	-0.051323	-1.0405	0.149364
11	-0.072132	-1.4623	0.072206
12	0.118376	2.3998	0.008423
13	-0.120747	-2.4479	0.007393
14	0.058014	1.1761	0.120112
15	-0.087213	-1.7681	0.038895
16	-0.138137	-2.8005	0.002672
17	-0.064797	-1.3136	0.094852
18	-0.113573	-2.3025	0.010903
19	0.021632	0.4385	0.330613
20	0.001018	0.0206	0.491771
21	-0.021756	-0.4411	0.3297
22	-0.014798	-0.3	0.382162
23	0.017138	0.3474	0.364219
24	-0.07599	-1.5406	0.062097
25	-0.054972	-1.1145	0.132866
26	-0.009853	-0.1998	0.420884

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.885392 & 17.9497 & 0 \tabularnewline
2 & 0.35056 & 7.107 & 0 \tabularnewline
3 & 0.269393 & 5.4614 & 0 \tabularnewline
4 & 0.212252 & 4.303 & 1.1e-05 \tabularnewline
5 & 0.021769 & 0.4413 & 0.329603 \tabularnewline
6 & 0.330484 & 6.6999 & 0 \tabularnewline
7 & 0.269475 & 5.4631 & 0 \tabularnewline
8 & -0.118328 & -2.3989 & 0.008445 \tabularnewline
9 & -0.246282 & -4.9929 & 0 \tabularnewline
10 & -0.051323 & -1.0405 & 0.149364 \tabularnewline
11 & -0.072132 & -1.4623 & 0.072206 \tabularnewline
12 & 0.118376 & 2.3998 & 0.008423 \tabularnewline
13 & -0.120747 & -2.4479 & 0.007393 \tabularnewline
14 & 0.058014 & 1.1761 & 0.120112 \tabularnewline
15 & -0.087213 & -1.7681 & 0.038895 \tabularnewline
16 & -0.138137 & -2.8005 & 0.002672 \tabularnewline
17 & -0.064797 & -1.3136 & 0.094852 \tabularnewline
18 & -0.113573 & -2.3025 & 0.010903 \tabularnewline
19 & 0.021632 & 0.4385 & 0.330613 \tabularnewline
20 & 0.001018 & 0.0206 & 0.491771 \tabularnewline
21 & -0.021756 & -0.4411 & 0.3297 \tabularnewline
22 & -0.014798 & -0.3 & 0.382162 \tabularnewline
23 & 0.017138 & 0.3474 & 0.364219 \tabularnewline
24 & -0.07599 & -1.5406 & 0.062097 \tabularnewline
25 & -0.054972 & -1.1145 & 0.132866 \tabularnewline
26 & -0.009853 & -0.1998 & 0.420884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.885392[/C][C]17.9497[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.35056[/C][C]7.107[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.269393[/C][C]5.4614[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.212252[/C][C]4.303[/C][C]1.1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.021769[/C][C]0.4413[/C][C]0.329603[/C][/ROW]
[ROW][C]6[/C][C]0.330484[/C][C]6.6999[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.269475[/C][C]5.4631[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.118328[/C][C]-2.3989[/C][C]0.008445[/C][/ROW]
[ROW][C]9[/C][C]-0.246282[/C][C]-4.9929[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]-0.051323[/C][C]-1.0405[/C][C]0.149364[/C][/ROW]
[ROW][C]11[/C][C]-0.072132[/C][C]-1.4623[/C][C]0.072206[/C][/ROW]
[ROW][C]12[/C][C]0.118376[/C][C]2.3998[/C][C]0.008423[/C][/ROW]
[ROW][C]13[/C][C]-0.120747[/C][C]-2.4479[/C][C]0.007393[/C][/ROW]
[ROW][C]14[/C][C]0.058014[/C][C]1.1761[/C][C]0.120112[/C][/ROW]
[ROW][C]15[/C][C]-0.087213[/C][C]-1.7681[/C][C]0.038895[/C][/ROW]
[ROW][C]16[/C][C]-0.138137[/C][C]-2.8005[/C][C]0.002672[/C][/ROW]
[ROW][C]17[/C][C]-0.064797[/C][C]-1.3136[/C][C]0.094852[/C][/ROW]
[ROW][C]18[/C][C]-0.113573[/C][C]-2.3025[/C][C]0.010903[/C][/ROW]
[ROW][C]19[/C][C]0.021632[/C][C]0.4385[/C][C]0.330613[/C][/ROW]
[ROW][C]20[/C][C]0.001018[/C][C]0.0206[/C][C]0.491771[/C][/ROW]
[ROW][C]21[/C][C]-0.021756[/C][C]-0.4411[/C][C]0.3297[/C][/ROW]
[ROW][C]22[/C][C]-0.014798[/C][C]-0.3[/C][C]0.382162[/C][/ROW]
[ROW][C]23[/C][C]0.017138[/C][C]0.3474[/C][C]0.364219[/C][/ROW]
[ROW][C]24[/C][C]-0.07599[/C][C]-1.5406[/C][C]0.062097[/C][/ROW]
[ROW][C]25[/C][C]-0.054972[/C][C]-1.1145[/C][C]0.132866[/C][/ROW]
[ROW][C]26[/C][C]-0.009853[/C][C]-0.1998[/C][C]0.420884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.885392	17.9497	0
2	0.35056	7.107	0
3	0.269393	5.4614	0
4	0.212252	4.303	1.1e-05
5	0.021769	0.4413	0.329603
6	0.330484	6.6999	0
7	0.269475	5.4631	0
8	-0.118328	-2.3989	0.008445
9	-0.246282	-4.9929	0
10	-0.051323	-1.0405	0.149364
11	-0.072132	-1.4623	0.072206
12	0.118376	2.3998	0.008423
13	-0.120747	-2.4479	0.007393
14	0.058014	1.1761	0.120112
15	-0.087213	-1.7681	0.038895
16	-0.138137	-2.8005	0.002672
17	-0.064797	-1.3136	0.094852
18	-0.113573	-2.3025	0.010903
19	0.021632	0.4385	0.330613
20	0.001018	0.0206	0.491771
21	-0.021756	-0.4411	0.3297
22	-0.014798	-0.3	0.382162
23	0.017138	0.3474	0.364219
24	-0.07599	-1.5406	0.062097
25	-0.054972	-1.1145	0.132866
26	-0.009853	-0.1998	0.420884

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 = 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