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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2016 19:39:28 +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/07/t1481135996fql3myxcx6yvkcc.htm/, Retrieved Tue, 07 May 2024 11:03:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298288, Retrieved Tue, 07 May 2024 11:03:24 +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] [N830] [2016-12-07 18:39:28] [85f5800284aab30c091766186b093bb4] [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=298288&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=298288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298288&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	-0.339226	-2.0069	0.026267
2	-0.097753	-0.5783	0.283378
3	-0.229018	-1.3549	0.092067
4	0.524	3.1	0.001904
5	-0.251062	-1.4853	0.073208
6	-0.007407	-0.0438	0.482648
7	-0.025341	-0.1499	0.440844
8	0.336021	1.9879	0.027343
9	-0.375472	-2.2213	0.016447
10	0.095059	0.5624	0.288722
11	-0.0547	-0.3236	0.374079
12	0.313691	1.8558	0.035957
13	-0.343261	-2.0308	0.024965
14	0.106843	0.6321	0.265716
15	-0.154463	-0.9138	0.183533
16	0.186002	1.1004	0.139334
17	-0.055917	-0.3308	0.371381
18	0.035357	0.2092	0.417763
19	-0.1185	-0.7011	0.243951
20	0.007741	0.0458	0.481866
21	-0.032482	-0.1922	0.424362
22	0.068168	0.4033	0.344595
23	-0.110492	-0.6537	0.258795
24	0.083484	0.4939	0.312231

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.339226 & -2.0069 & 0.026267 \tabularnewline
2 & -0.097753 & -0.5783 & 0.283378 \tabularnewline
3 & -0.229018 & -1.3549 & 0.092067 \tabularnewline
4 & 0.524 & 3.1 & 0.001904 \tabularnewline
5 & -0.251062 & -1.4853 & 0.073208 \tabularnewline
6 & -0.007407 & -0.0438 & 0.482648 \tabularnewline
7 & -0.025341 & -0.1499 & 0.440844 \tabularnewline
8 & 0.336021 & 1.9879 & 0.027343 \tabularnewline
9 & -0.375472 & -2.2213 & 0.016447 \tabularnewline
10 & 0.095059 & 0.5624 & 0.288722 \tabularnewline
11 & -0.0547 & -0.3236 & 0.374079 \tabularnewline
12 & 0.313691 & 1.8558 & 0.035957 \tabularnewline
13 & -0.343261 & -2.0308 & 0.024965 \tabularnewline
14 & 0.106843 & 0.6321 & 0.265716 \tabularnewline
15 & -0.154463 & -0.9138 & 0.183533 \tabularnewline
16 & 0.186002 & 1.1004 & 0.139334 \tabularnewline
17 & -0.055917 & -0.3308 & 0.371381 \tabularnewline
18 & 0.035357 & 0.2092 & 0.417763 \tabularnewline
19 & -0.1185 & -0.7011 & 0.243951 \tabularnewline
20 & 0.007741 & 0.0458 & 0.481866 \tabularnewline
21 & -0.032482 & -0.1922 & 0.424362 \tabularnewline
22 & 0.068168 & 0.4033 & 0.344595 \tabularnewline
23 & -0.110492 & -0.6537 & 0.258795 \tabularnewline
24 & 0.083484 & 0.4939 & 0.312231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298288&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]-0.339226[/C][C]-2.0069[/C][C]0.026267[/C][/ROW]
[ROW][C]2[/C][C]-0.097753[/C][C]-0.5783[/C][C]0.283378[/C][/ROW]
[ROW][C]3[/C][C]-0.229018[/C][C]-1.3549[/C][C]0.092067[/C][/ROW]
[ROW][C]4[/C][C]0.524[/C][C]3.1[/C][C]0.001904[/C][/ROW]
[ROW][C]5[/C][C]-0.251062[/C][C]-1.4853[/C][C]0.073208[/C][/ROW]
[ROW][C]6[/C][C]-0.007407[/C][C]-0.0438[/C][C]0.482648[/C][/ROW]
[ROW][C]7[/C][C]-0.025341[/C][C]-0.1499[/C][C]0.440844[/C][/ROW]
[ROW][C]8[/C][C]0.336021[/C][C]1.9879[/C][C]0.027343[/C][/ROW]
[ROW][C]9[/C][C]-0.375472[/C][C]-2.2213[/C][C]0.016447[/C][/ROW]
[ROW][C]10[/C][C]0.095059[/C][C]0.5624[/C][C]0.288722[/C][/ROW]
[ROW][C]11[/C][C]-0.0547[/C][C]-0.3236[/C][C]0.374079[/C][/ROW]
[ROW][C]12[/C][C]0.313691[/C][C]1.8558[/C][C]0.035957[/C][/ROW]
[ROW][C]13[/C][C]-0.343261[/C][C]-2.0308[/C][C]0.024965[/C][/ROW]
[ROW][C]14[/C][C]0.106843[/C][C]0.6321[/C][C]0.265716[/C][/ROW]
[ROW][C]15[/C][C]-0.154463[/C][C]-0.9138[/C][C]0.183533[/C][/ROW]
[ROW][C]16[/C][C]0.186002[/C][C]1.1004[/C][C]0.139334[/C][/ROW]
[ROW][C]17[/C][C]-0.055917[/C][C]-0.3308[/C][C]0.371381[/C][/ROW]
[ROW][C]18[/C][C]0.035357[/C][C]0.2092[/C][C]0.417763[/C][/ROW]
[ROW][C]19[/C][C]-0.1185[/C][C]-0.7011[/C][C]0.243951[/C][/ROW]
[ROW][C]20[/C][C]0.007741[/C][C]0.0458[/C][C]0.481866[/C][/ROW]
[ROW][C]21[/C][C]-0.032482[/C][C]-0.1922[/C][C]0.424362[/C][/ROW]
[ROW][C]22[/C][C]0.068168[/C][C]0.4033[/C][C]0.344595[/C][/ROW]
[ROW][C]23[/C][C]-0.110492[/C][C]-0.6537[/C][C]0.258795[/C][/ROW]
[ROW][C]24[/C][C]0.083484[/C][C]0.4939[/C][C]0.312231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298288&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	-0.339226	-2.0069	0.026267
2	-0.097753	-0.5783	0.283378
3	-0.229018	-1.3549	0.092067
4	0.524	3.1	0.001904
5	-0.251062	-1.4853	0.073208
6	-0.007407	-0.0438	0.482648
7	-0.025341	-0.1499	0.440844
8	0.336021	1.9879	0.027343
9	-0.375472	-2.2213	0.016447
10	0.095059	0.5624	0.288722
11	-0.0547	-0.3236	0.374079
12	0.313691	1.8558	0.035957
13	-0.343261	-2.0308	0.024965
14	0.106843	0.6321	0.265716
15	-0.154463	-0.9138	0.183533
16	0.186002	1.1004	0.139334
17	-0.055917	-0.3308	0.371381
18	0.035357	0.2092	0.417763
19	-0.1185	-0.7011	0.243951
20	0.007741	0.0458	0.481866
21	-0.032482	-0.1922	0.424362
22	0.068168	0.4033	0.344595
23	-0.110492	-0.6537	0.258795
24	0.083484	0.4939	0.312231

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.339226	-2.0069	0.026267
2	-0.240502	-1.4228	0.081819
3	-0.421879	-2.4959	0.008713
4	0.321609	1.9027	0.032669
5	-0.047451	-0.2807	0.390286
6	0.010759	0.0637	0.474805
7	0.171361	1.0138	0.158821
8	0.214577	1.2695	0.106328
9	-0.158017	-0.9348	0.178137
10	0.055586	0.3289	0.372113
11	-0.119398	-0.7064	0.242318
12	0.057471	0.34	0.367943
13	-0.029515	-0.1746	0.431195
14	-0.040775	-0.2412	0.405392
15	-0.209445	-1.2391	0.111778
16	-0.153121	-0.9059	0.185598
17	0.211216	1.2496	0.109875
18	-0.068673	-0.4063	0.343508
19	0.05259	0.3111	0.378774
20	-0.132131	-0.7817	0.219825
21	-0.077876	-0.4607	0.323925
22	-0.049514	-0.2929	0.385654
23	-0.055651	-0.3292	0.371971
24	-0.074924	-0.4433	0.330155

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.339226 & -2.0069 & 0.026267 \tabularnewline
2 & -0.240502 & -1.4228 & 0.081819 \tabularnewline
3 & -0.421879 & -2.4959 & 0.008713 \tabularnewline
4 & 0.321609 & 1.9027 & 0.032669 \tabularnewline
5 & -0.047451 & -0.2807 & 0.390286 \tabularnewline
6 & 0.010759 & 0.0637 & 0.474805 \tabularnewline
7 & 0.171361 & 1.0138 & 0.158821 \tabularnewline
8 & 0.214577 & 1.2695 & 0.106328 \tabularnewline
9 & -0.158017 & -0.9348 & 0.178137 \tabularnewline
10 & 0.055586 & 0.3289 & 0.372113 \tabularnewline
11 & -0.119398 & -0.7064 & 0.242318 \tabularnewline
12 & 0.057471 & 0.34 & 0.367943 \tabularnewline
13 & -0.029515 & -0.1746 & 0.431195 \tabularnewline
14 & -0.040775 & -0.2412 & 0.405392 \tabularnewline
15 & -0.209445 & -1.2391 & 0.111778 \tabularnewline
16 & -0.153121 & -0.9059 & 0.185598 \tabularnewline
17 & 0.211216 & 1.2496 & 0.109875 \tabularnewline
18 & -0.068673 & -0.4063 & 0.343508 \tabularnewline
19 & 0.05259 & 0.3111 & 0.378774 \tabularnewline
20 & -0.132131 & -0.7817 & 0.219825 \tabularnewline
21 & -0.077876 & -0.4607 & 0.323925 \tabularnewline
22 & -0.049514 & -0.2929 & 0.385654 \tabularnewline
23 & -0.055651 & -0.3292 & 0.371971 \tabularnewline
24 & -0.074924 & -0.4433 & 0.330155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298288&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]-0.339226[/C][C]-2.0069[/C][C]0.026267[/C][/ROW]
[ROW][C]2[/C][C]-0.240502[/C][C]-1.4228[/C][C]0.081819[/C][/ROW]
[ROW][C]3[/C][C]-0.421879[/C][C]-2.4959[/C][C]0.008713[/C][/ROW]
[ROW][C]4[/C][C]0.321609[/C][C]1.9027[/C][C]0.032669[/C][/ROW]
[ROW][C]5[/C][C]-0.047451[/C][C]-0.2807[/C][C]0.390286[/C][/ROW]
[ROW][C]6[/C][C]0.010759[/C][C]0.0637[/C][C]0.474805[/C][/ROW]
[ROW][C]7[/C][C]0.171361[/C][C]1.0138[/C][C]0.158821[/C][/ROW]
[ROW][C]8[/C][C]0.214577[/C][C]1.2695[/C][C]0.106328[/C][/ROW]
[ROW][C]9[/C][C]-0.158017[/C][C]-0.9348[/C][C]0.178137[/C][/ROW]
[ROW][C]10[/C][C]0.055586[/C][C]0.3289[/C][C]0.372113[/C][/ROW]
[ROW][C]11[/C][C]-0.119398[/C][C]-0.7064[/C][C]0.242318[/C][/ROW]
[ROW][C]12[/C][C]0.057471[/C][C]0.34[/C][C]0.367943[/C][/ROW]
[ROW][C]13[/C][C]-0.029515[/C][C]-0.1746[/C][C]0.431195[/C][/ROW]
[ROW][C]14[/C][C]-0.040775[/C][C]-0.2412[/C][C]0.405392[/C][/ROW]
[ROW][C]15[/C][C]-0.209445[/C][C]-1.2391[/C][C]0.111778[/C][/ROW]
[ROW][C]16[/C][C]-0.153121[/C][C]-0.9059[/C][C]0.185598[/C][/ROW]
[ROW][C]17[/C][C]0.211216[/C][C]1.2496[/C][C]0.109875[/C][/ROW]
[ROW][C]18[/C][C]-0.068673[/C][C]-0.4063[/C][C]0.343508[/C][/ROW]
[ROW][C]19[/C][C]0.05259[/C][C]0.3111[/C][C]0.378774[/C][/ROW]
[ROW][C]20[/C][C]-0.132131[/C][C]-0.7817[/C][C]0.219825[/C][/ROW]
[ROW][C]21[/C][C]-0.077876[/C][C]-0.4607[/C][C]0.323925[/C][/ROW]
[ROW][C]22[/C][C]-0.049514[/C][C]-0.2929[/C][C]0.385654[/C][/ROW]
[ROW][C]23[/C][C]-0.055651[/C][C]-0.3292[/C][C]0.371971[/C][/ROW]
[ROW][C]24[/C][C]-0.074924[/C][C]-0.4433[/C][C]0.330155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298288&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298288&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	-0.339226	-2.0069	0.026267
2	-0.240502	-1.4228	0.081819
3	-0.421879	-2.4959	0.008713
4	0.321609	1.9027	0.032669
5	-0.047451	-0.2807	0.390286
6	0.010759	0.0637	0.474805
7	0.171361	1.0138	0.158821
8	0.214577	1.2695	0.106328
9	-0.158017	-0.9348	0.178137
10	0.055586	0.3289	0.372113
11	-0.119398	-0.7064	0.242318
12	0.057471	0.34	0.367943
13	-0.029515	-0.1746	0.431195
14	-0.040775	-0.2412	0.405392
15	-0.209445	-1.2391	0.111778
16	-0.153121	-0.9059	0.185598
17	0.211216	1.2496	0.109875
18	-0.068673	-0.4063	0.343508
19	0.05259	0.3111	0.378774
20	-0.132131	-0.7817	0.219825
21	-0.077876	-0.4607	0.323925
22	-0.049514	-0.2929	0.385654
23	-0.055651	-0.3292	0.371971
24	-0.074924	-0.4433	0.330155

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 = -1.0 ; par2 = 1 ; par3 = 0 ; par4 = 1 ;

Parameters (R input):

par1 = 24 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '0.0'
par1 <- 'Default'
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