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Author's title

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

Sun, 11 Dec 2016 17:38:45 +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/11/t14814743455ym2kmjkl4dr0w5.htm/, Retrieved Thu, 02 May 2024 06:29:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298826, Retrieved Thu, 02 May 2024 06:29:40 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2016-12-11 16:38:45] [10299735033611e1e2dae6371997f8c9] [Current]
- RMP     [Spectral Analysis] [SA F1] [2016-12-18 16:34:32] [48565d122ad1a5ad6c25b7f5730e03d6] 
- RMP     [ARIMA Backward Selection] [Arima backward] [2016-12-18 16:46:17] [48565d122ad1a5ad6c25b7f5730e03d6] 
-           [ARIMA Backward Selection] [Backward F1] [2016-12-18 17:16:24] [48565d122ad1a5ad6c25b7f5730e03d6] 
- RM        [ARIMA Forecasting] [Arima forecast F1] [2016-12-18 18:48:42] [48565d122ad1a5ad6c25b7f5730e03d6] 
- R P         [ARIMA Forecasting] [ARIMA forecast F1] [2016-12-23 11:21:48] [e37f5c813d0dfcb3787d64bb91655c98] 
- RM        [Standard Deviation-Mean Plot] [SDMP F1] [2016-12-21 09:32:02] [48565d122ad1a5ad6c25b7f5730e03d6] 
-           [ARIMA Backward Selection] [F1 Arima backward...] [2016-12-23 10:56:30] [48565d122ad1a5ad6c25b7f5730e03d6] 

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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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298826&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298826&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.357535	-3.8341	0.000103
2	-0.283527	-3.0405	0.001463
3	0.267482	2.8684	0.002455
4	-0.174491	-1.8712	0.031929
5	-0.284168	-3.0474	0.001432
6	0.685481	7.351	0
7	-0.282679	-3.0314	0.001504
8	-0.143147	-1.5351	0.063756
9	0.244471	2.6217	0.004967
10	-0.283648	-3.0418	0.001457
11	-0.292696	-3.1388	0.001078
12	0.852874	9.1461	0
13	-0.322498	-3.4584	0.000381
14	-0.231555	-2.4831	0.007233
15	0.228703	2.4526	0.007843
16	-0.167818	-1.7996	0.037269
17	-0.242641	-2.602	0.005243
18	0.626657	6.7202	0
19	-0.282062	-3.0248	0.001535
20	-0.104637	-1.1221	0.132077

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.357535 & -3.8341 & 0.000103 \tabularnewline
2 & -0.283527 & -3.0405 & 0.001463 \tabularnewline
3 & 0.267482 & 2.8684 & 0.002455 \tabularnewline
4 & -0.174491 & -1.8712 & 0.031929 \tabularnewline
5 & -0.284168 & -3.0474 & 0.001432 \tabularnewline
6 & 0.685481 & 7.351 & 0 \tabularnewline
7 & -0.282679 & -3.0314 & 0.001504 \tabularnewline
8 & -0.143147 & -1.5351 & 0.063756 \tabularnewline
9 & 0.244471 & 2.6217 & 0.004967 \tabularnewline
10 & -0.283648 & -3.0418 & 0.001457 \tabularnewline
11 & -0.292696 & -3.1388 & 0.001078 \tabularnewline
12 & 0.852874 & 9.1461 & 0 \tabularnewline
13 & -0.322498 & -3.4584 & 0.000381 \tabularnewline
14 & -0.231555 & -2.4831 & 0.007233 \tabularnewline
15 & 0.228703 & 2.4526 & 0.007843 \tabularnewline
16 & -0.167818 & -1.7996 & 0.037269 \tabularnewline
17 & -0.242641 & -2.602 & 0.005243 \tabularnewline
18 & 0.626657 & 6.7202 & 0 \tabularnewline
19 & -0.282062 & -3.0248 & 0.001535 \tabularnewline
20 & -0.104637 & -1.1221 & 0.132077 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298826&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]-0.357535[/C][C]-3.8341[/C][C]0.000103[/C][/ROW]
[ROW][C]2[/C][C]-0.283527[/C][C]-3.0405[/C][C]0.001463[/C][/ROW]
[ROW][C]3[/C][C]0.267482[/C][C]2.8684[/C][C]0.002455[/C][/ROW]
[ROW][C]4[/C][C]-0.174491[/C][C]-1.8712[/C][C]0.031929[/C][/ROW]
[ROW][C]5[/C][C]-0.284168[/C][C]-3.0474[/C][C]0.001432[/C][/ROW]
[ROW][C]6[/C][C]0.685481[/C][C]7.351[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.282679[/C][C]-3.0314[/C][C]0.001504[/C][/ROW]
[ROW][C]8[/C][C]-0.143147[/C][C]-1.5351[/C][C]0.063756[/C][/ROW]
[ROW][C]9[/C][C]0.244471[/C][C]2.6217[/C][C]0.004967[/C][/ROW]
[ROW][C]10[/C][C]-0.283648[/C][C]-3.0418[/C][C]0.001457[/C][/ROW]
[ROW][C]11[/C][C]-0.292696[/C][C]-3.1388[/C][C]0.001078[/C][/ROW]
[ROW][C]12[/C][C]0.852874[/C][C]9.1461[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.322498[/C][C]-3.4584[/C][C]0.000381[/C][/ROW]
[ROW][C]14[/C][C]-0.231555[/C][C]-2.4831[/C][C]0.007233[/C][/ROW]
[ROW][C]15[/C][C]0.228703[/C][C]2.4526[/C][C]0.007843[/C][/ROW]
[ROW][C]16[/C][C]-0.167818[/C][C]-1.7996[/C][C]0.037269[/C][/ROW]
[ROW][C]17[/C][C]-0.242641[/C][C]-2.602[/C][C]0.005243[/C][/ROW]
[ROW][C]18[/C][C]0.626657[/C][C]6.7202[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.282062[/C][C]-3.0248[/C][C]0.001535[/C][/ROW]
[ROW][C]20[/C][C]-0.104637[/C][C]-1.1221[/C][C]0.132077[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298826&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	-0.357535	-3.8341	0.000103
2	-0.283527	-3.0405	0.001463
3	0.267482	2.8684	0.002455
4	-0.174491	-1.8712	0.031929
5	-0.284168	-3.0474	0.001432
6	0.685481	7.351	0
7	-0.282679	-3.0314	0.001504
8	-0.143147	-1.5351	0.063756
9	0.244471	2.6217	0.004967
10	-0.283648	-3.0418	0.001457
11	-0.292696	-3.1388	0.001078
12	0.852874	9.1461	0
13	-0.322498	-3.4584	0.000381
14	-0.231555	-2.4831	0.007233
15	0.228703	2.4526	0.007843
16	-0.167818	-1.7996	0.037269
17	-0.242641	-2.602	0.005243
18	0.626657	6.7202	0
19	-0.282062	-3.0248	0.001535
20	-0.104637	-1.1221	0.132077

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.357535	-3.8341	0.000103
2	-0.47165	-5.0579	1e-06
3	-0.07422	-0.7959	0.213858
4	-0.29021	-3.1122	0.001172
5	-0.616204	-6.608	0
6	0.251174	2.6935	0.004064
7	-0.123374	-1.323	0.094223
8	0.197682	2.1199	0.018082
9	0.171304	1.837	0.034393
10	-0.193989	-2.0803	0.01986
11	-0.491474	-5.2705	0
12	0.442236	4.7424	3e-06
13	0.158045	1.6948	0.046406
14	0.149038	1.5983	0.056365
15	-0.113703	-1.2193	0.112607
16	0.022225	0.2383	0.406024
17	0.102323	1.0973	0.137403
18	0.026386	0.283	0.388858
19	-0.063354	-0.6794	0.249125
20	-0.048521	-0.5203	0.301918

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.357535 & -3.8341 & 0.000103 \tabularnewline
2 & -0.47165 & -5.0579 & 1e-06 \tabularnewline
3 & -0.07422 & -0.7959 & 0.213858 \tabularnewline
4 & -0.29021 & -3.1122 & 0.001172 \tabularnewline
5 & -0.616204 & -6.608 & 0 \tabularnewline
6 & 0.251174 & 2.6935 & 0.004064 \tabularnewline
7 & -0.123374 & -1.323 & 0.094223 \tabularnewline
8 & 0.197682 & 2.1199 & 0.018082 \tabularnewline
9 & 0.171304 & 1.837 & 0.034393 \tabularnewline
10 & -0.193989 & -2.0803 & 0.01986 \tabularnewline
11 & -0.491474 & -5.2705 & 0 \tabularnewline
12 & 0.442236 & 4.7424 & 3e-06 \tabularnewline
13 & 0.158045 & 1.6948 & 0.046406 \tabularnewline
14 & 0.149038 & 1.5983 & 0.056365 \tabularnewline
15 & -0.113703 & -1.2193 & 0.112607 \tabularnewline
16 & 0.022225 & 0.2383 & 0.406024 \tabularnewline
17 & 0.102323 & 1.0973 & 0.137403 \tabularnewline
18 & 0.026386 & 0.283 & 0.388858 \tabularnewline
19 & -0.063354 & -0.6794 & 0.249125 \tabularnewline
20 & -0.048521 & -0.5203 & 0.301918 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298826&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]-0.357535[/C][C]-3.8341[/C][C]0.000103[/C][/ROW]
[ROW][C]2[/C][C]-0.47165[/C][C]-5.0579[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.07422[/C][C]-0.7959[/C][C]0.213858[/C][/ROW]
[ROW][C]4[/C][C]-0.29021[/C][C]-3.1122[/C][C]0.001172[/C][/ROW]
[ROW][C]5[/C][C]-0.616204[/C][C]-6.608[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.251174[/C][C]2.6935[/C][C]0.004064[/C][/ROW]
[ROW][C]7[/C][C]-0.123374[/C][C]-1.323[/C][C]0.094223[/C][/ROW]
[ROW][C]8[/C][C]0.197682[/C][C]2.1199[/C][C]0.018082[/C][/ROW]
[ROW][C]9[/C][C]0.171304[/C][C]1.837[/C][C]0.034393[/C][/ROW]
[ROW][C]10[/C][C]-0.193989[/C][C]-2.0803[/C][C]0.01986[/C][/ROW]
[ROW][C]11[/C][C]-0.491474[/C][C]-5.2705[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.442236[/C][C]4.7424[/C][C]3e-06[/C][/ROW]
[ROW][C]13[/C][C]0.158045[/C][C]1.6948[/C][C]0.046406[/C][/ROW]
[ROW][C]14[/C][C]0.149038[/C][C]1.5983[/C][C]0.056365[/C][/ROW]
[ROW][C]15[/C][C]-0.113703[/C][C]-1.2193[/C][C]0.112607[/C][/ROW]
[ROW][C]16[/C][C]0.022225[/C][C]0.2383[/C][C]0.406024[/C][/ROW]
[ROW][C]17[/C][C]0.102323[/C][C]1.0973[/C][C]0.137403[/C][/ROW]
[ROW][C]18[/C][C]0.026386[/C][C]0.283[/C][C]0.388858[/C][/ROW]
[ROW][C]19[/C][C]-0.063354[/C][C]-0.6794[/C][C]0.249125[/C][/ROW]
[ROW][C]20[/C][C]-0.048521[/C][C]-0.5203[/C][C]0.301918[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298826&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	-0.357535	-3.8341	0.000103
2	-0.47165	-5.0579	1e-06
3	-0.07422	-0.7959	0.213858
4	-0.29021	-3.1122	0.001172
5	-0.616204	-6.608	0
6	0.251174	2.6935	0.004064
7	-0.123374	-1.323	0.094223
8	0.197682	2.1199	0.018082
9	0.171304	1.837	0.034393
10	-0.193989	-2.0803	0.01986
11	-0.491474	-5.2705	0
12	0.442236	4.7424	3e-06
13	0.158045	1.6948	0.046406
14	0.149038	1.5983	0.056365
15	-0.113703	-1.2193	0.112607
16	0.022225	0.2383	0.406024
17	0.102323	1.0973	0.137403
18	0.026386	0.283	0.388858
19	-0.063354	-0.6794	0.249125
20	-0.048521	-0.5203	0.301918

Figure 1

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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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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