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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, 21 Dec 2016 16:00:19 +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/21/t1482332606yzh9vvd74g97sgx.htm/, Retrieved Mon, 06 May 2024 15:08:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302364, Retrieved Mon, 06 May 2024 15:08:14 +0000

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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] [] [2016-12-21 15:00:19] [361c8dad91b3f1ef2e651cd04783c23b] [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	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=302364&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=302364&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302364&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	0.136141	1.0545	0.14793
2	-0.53023	-4.1071	6.2e-05
3	0.140788	1.0905	0.139919
4	0.839107	6.4997	0
5	0.055305	0.4284	0.334951
6	-0.53052	-4.1094	6.1e-05
7	0.103819	0.8042	0.212233
8	0.719535	5.5735	0
9	0.008414	0.0652	0.474125
10	-0.533426	-4.1319	5.7e-05
11	0.04522	0.3503	0.363681
12	0.606912	4.7011	8e-06
13	-0.048607	-0.3765	0.353935
14	-0.530395	-4.1084	6.1e-05
15	-0.007002	-0.0542	0.478462
16	0.485244	3.7587	0.000195
17	-0.103913	-0.8049	0.212025
18	-0.542245	-4.2002	4.5e-05
19	-0.043355	-0.3358	0.369085
20	0.428528	3.3194	0.000769
21	-0.11324	-0.8772	0.19195
22	-0.508319	-3.9374	0.000109
23	-0.054261	-0.4203	0.337882
24	0.357889	2.7722	0.003703

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.136141 & 1.0545 & 0.14793 \tabularnewline
2 & -0.53023 & -4.1071 & 6.2e-05 \tabularnewline
3 & 0.140788 & 1.0905 & 0.139919 \tabularnewline
4 & 0.839107 & 6.4997 & 0 \tabularnewline
5 & 0.055305 & 0.4284 & 0.334951 \tabularnewline
6 & -0.53052 & -4.1094 & 6.1e-05 \tabularnewline
7 & 0.103819 & 0.8042 & 0.212233 \tabularnewline
8 & 0.719535 & 5.5735 & 0 \tabularnewline
9 & 0.008414 & 0.0652 & 0.474125 \tabularnewline
10 & -0.533426 & -4.1319 & 5.7e-05 \tabularnewline
11 & 0.04522 & 0.3503 & 0.363681 \tabularnewline
12 & 0.606912 & 4.7011 & 8e-06 \tabularnewline
13 & -0.048607 & -0.3765 & 0.353935 \tabularnewline
14 & -0.530395 & -4.1084 & 6.1e-05 \tabularnewline
15 & -0.007002 & -0.0542 & 0.478462 \tabularnewline
16 & 0.485244 & 3.7587 & 0.000195 \tabularnewline
17 & -0.103913 & -0.8049 & 0.212025 \tabularnewline
18 & -0.542245 & -4.2002 & 4.5e-05 \tabularnewline
19 & -0.043355 & -0.3358 & 0.369085 \tabularnewline
20 & 0.428528 & 3.3194 & 0.000769 \tabularnewline
21 & -0.11324 & -0.8772 & 0.19195 \tabularnewline
22 & -0.508319 & -3.9374 & 0.000109 \tabularnewline
23 & -0.054261 & -0.4203 & 0.337882 \tabularnewline
24 & 0.357889 & 2.7722 & 0.003703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302364&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]0.136141[/C][C]1.0545[/C][C]0.14793[/C][/ROW]
[ROW][C]2[/C][C]-0.53023[/C][C]-4.1071[/C][C]6.2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.140788[/C][C]1.0905[/C][C]0.139919[/C][/ROW]
[ROW][C]4[/C][C]0.839107[/C][C]6.4997[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.055305[/C][C]0.4284[/C][C]0.334951[/C][/ROW]
[ROW][C]6[/C][C]-0.53052[/C][C]-4.1094[/C][C]6.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.103819[/C][C]0.8042[/C][C]0.212233[/C][/ROW]
[ROW][C]8[/C][C]0.719535[/C][C]5.5735[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.008414[/C][C]0.0652[/C][C]0.474125[/C][/ROW]
[ROW][C]10[/C][C]-0.533426[/C][C]-4.1319[/C][C]5.7e-05[/C][/ROW]
[ROW][C]11[/C][C]0.04522[/C][C]0.3503[/C][C]0.363681[/C][/ROW]
[ROW][C]12[/C][C]0.606912[/C][C]4.7011[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.048607[/C][C]-0.3765[/C][C]0.353935[/C][/ROW]
[ROW][C]14[/C][C]-0.530395[/C][C]-4.1084[/C][C]6.1e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.007002[/C][C]-0.0542[/C][C]0.478462[/C][/ROW]
[ROW][C]16[/C][C]0.485244[/C][C]3.7587[/C][C]0.000195[/C][/ROW]
[ROW][C]17[/C][C]-0.103913[/C][C]-0.8049[/C][C]0.212025[/C][/ROW]
[ROW][C]18[/C][C]-0.542245[/C][C]-4.2002[/C][C]4.5e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.043355[/C][C]-0.3358[/C][C]0.369085[/C][/ROW]
[ROW][C]20[/C][C]0.428528[/C][C]3.3194[/C][C]0.000769[/C][/ROW]
[ROW][C]21[/C][C]-0.11324[/C][C]-0.8772[/C][C]0.19195[/C][/ROW]
[ROW][C]22[/C][C]-0.508319[/C][C]-3.9374[/C][C]0.000109[/C][/ROW]
[ROW][C]23[/C][C]-0.054261[/C][C]-0.4203[/C][C]0.337882[/C][/ROW]
[ROW][C]24[/C][C]0.357889[/C][C]2.7722[/C][C]0.003703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302364&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302364&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	0.136141	1.0545	0.14793
2	-0.53023	-4.1071	6.2e-05
3	0.140788	1.0905	0.139919
4	0.839107	6.4997	0
5	0.055305	0.4284	0.334951
6	-0.53052	-4.1094	6.1e-05
7	0.103819	0.8042	0.212233
8	0.719535	5.5735	0
9	0.008414	0.0652	0.474125
10	-0.533426	-4.1319	5.7e-05
11	0.04522	0.3503	0.363681
12	0.606912	4.7011	8e-06
13	-0.048607	-0.3765	0.353935
14	-0.530395	-4.1084	6.1e-05
15	-0.007002	-0.0542	0.478462
16	0.485244	3.7587	0.000195
17	-0.103913	-0.8049	0.212025
18	-0.542245	-4.2002	4.5e-05
19	-0.043355	-0.3358	0.369085
20	0.428528	3.3194	0.000769
21	-0.11324	-0.8772	0.19195
22	-0.508319	-3.9374	0.000109
23	-0.054261	-0.4203	0.337882
24	0.357889	2.7722	0.003703

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.136141	1.0545	0.14793
2	-0.559127	-4.331	2.9e-05
3	0.488345	3.7827	0.00018
4	0.686853	5.3203	1e-06
5	-0.193696	-1.5004	0.069382
6	-0.028391	-0.2199	0.413341
7	-0.130402	-1.0101	0.158254
8	0.096399	0.7467	0.229078
9	-0.009385	-0.0727	0.471144
10	-0.060491	-0.4686	0.320541
11	-0.134234	-1.0398	0.151308
12	-0.01718	-0.1331	0.447289
13	-0.091726	-0.7105	0.24007
14	0.031594	0.2447	0.403751
15	-0.115529	-0.8949	0.187212
16	-0.096336	-0.7462	0.229226
17	-0.084422	-0.6539	0.257828
18	-0.100656	-0.7797	0.219322
19	0.014047	0.1088	0.456859
20	0.083868	0.6496	0.259202
21	-0.000866	-0.0067	0.497335
22	0.050983	0.3949	0.347153
23	-0.075322	-0.5834	0.280892
24	-0.096943	-0.7509	0.227818

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.136141 & 1.0545 & 0.14793 \tabularnewline
2 & -0.559127 & -4.331 & 2.9e-05 \tabularnewline
3 & 0.488345 & 3.7827 & 0.00018 \tabularnewline
4 & 0.686853 & 5.3203 & 1e-06 \tabularnewline
5 & -0.193696 & -1.5004 & 0.069382 \tabularnewline
6 & -0.028391 & -0.2199 & 0.413341 \tabularnewline
7 & -0.130402 & -1.0101 & 0.158254 \tabularnewline
8 & 0.096399 & 0.7467 & 0.229078 \tabularnewline
9 & -0.009385 & -0.0727 & 0.471144 \tabularnewline
10 & -0.060491 & -0.4686 & 0.320541 \tabularnewline
11 & -0.134234 & -1.0398 & 0.151308 \tabularnewline
12 & -0.01718 & -0.1331 & 0.447289 \tabularnewline
13 & -0.091726 & -0.7105 & 0.24007 \tabularnewline
14 & 0.031594 & 0.2447 & 0.403751 \tabularnewline
15 & -0.115529 & -0.8949 & 0.187212 \tabularnewline
16 & -0.096336 & -0.7462 & 0.229226 \tabularnewline
17 & -0.084422 & -0.6539 & 0.257828 \tabularnewline
18 & -0.100656 & -0.7797 & 0.219322 \tabularnewline
19 & 0.014047 & 0.1088 & 0.456859 \tabularnewline
20 & 0.083868 & 0.6496 & 0.259202 \tabularnewline
21 & -0.000866 & -0.0067 & 0.497335 \tabularnewline
22 & 0.050983 & 0.3949 & 0.347153 \tabularnewline
23 & -0.075322 & -0.5834 & 0.280892 \tabularnewline
24 & -0.096943 & -0.7509 & 0.227818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302364&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]0.136141[/C][C]1.0545[/C][C]0.14793[/C][/ROW]
[ROW][C]2[/C][C]-0.559127[/C][C]-4.331[/C][C]2.9e-05[/C][/ROW]
[ROW][C]3[/C][C]0.488345[/C][C]3.7827[/C][C]0.00018[/C][/ROW]
[ROW][C]4[/C][C]0.686853[/C][C]5.3203[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.193696[/C][C]-1.5004[/C][C]0.069382[/C][/ROW]
[ROW][C]6[/C][C]-0.028391[/C][C]-0.2199[/C][C]0.413341[/C][/ROW]
[ROW][C]7[/C][C]-0.130402[/C][C]-1.0101[/C][C]0.158254[/C][/ROW]
[ROW][C]8[/C][C]0.096399[/C][C]0.7467[/C][C]0.229078[/C][/ROW]
[ROW][C]9[/C][C]-0.009385[/C][C]-0.0727[/C][C]0.471144[/C][/ROW]
[ROW][C]10[/C][C]-0.060491[/C][C]-0.4686[/C][C]0.320541[/C][/ROW]
[ROW][C]11[/C][C]-0.134234[/C][C]-1.0398[/C][C]0.151308[/C][/ROW]
[ROW][C]12[/C][C]-0.01718[/C][C]-0.1331[/C][C]0.447289[/C][/ROW]
[ROW][C]13[/C][C]-0.091726[/C][C]-0.7105[/C][C]0.24007[/C][/ROW]
[ROW][C]14[/C][C]0.031594[/C][C]0.2447[/C][C]0.403751[/C][/ROW]
[ROW][C]15[/C][C]-0.115529[/C][C]-0.8949[/C][C]0.187212[/C][/ROW]
[ROW][C]16[/C][C]-0.096336[/C][C]-0.7462[/C][C]0.229226[/C][/ROW]
[ROW][C]17[/C][C]-0.084422[/C][C]-0.6539[/C][C]0.257828[/C][/ROW]
[ROW][C]18[/C][C]-0.100656[/C][C]-0.7797[/C][C]0.219322[/C][/ROW]
[ROW][C]19[/C][C]0.014047[/C][C]0.1088[/C][C]0.456859[/C][/ROW]
[ROW][C]20[/C][C]0.083868[/C][C]0.6496[/C][C]0.259202[/C][/ROW]
[ROW][C]21[/C][C]-0.000866[/C][C]-0.0067[/C][C]0.497335[/C][/ROW]
[ROW][C]22[/C][C]0.050983[/C][C]0.3949[/C][C]0.347153[/C][/ROW]
[ROW][C]23[/C][C]-0.075322[/C][C]-0.5834[/C][C]0.280892[/C][/ROW]
[ROW][C]24[/C][C]-0.096943[/C][C]-0.7509[/C][C]0.227818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302364&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302364&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	0.136141	1.0545	0.14793
2	-0.559127	-4.331	2.9e-05
3	0.488345	3.7827	0.00018
4	0.686853	5.3203	1e-06
5	-0.193696	-1.5004	0.069382
6	-0.028391	-0.2199	0.413341
7	-0.130402	-1.0101	0.158254
8	0.096399	0.7467	0.229078
9	-0.009385	-0.0727	0.471144
10	-0.060491	-0.4686	0.320541
11	-0.134234	-1.0398	0.151308
12	-0.01718	-0.1331	0.447289
13	-0.091726	-0.7105	0.24007
14	0.031594	0.2447	0.403751
15	-0.115529	-0.8949	0.187212
16	-0.096336	-0.7462	0.229226
17	-0.084422	-0.6539	0.257828
18	-0.100656	-0.7797	0.219322
19	0.014047	0.1088	0.456859
20	0.083868	0.6496	0.259202
21	-0.000866	-0.0067	0.497335
22	0.050983	0.3949	0.347153
23	-0.075322	-0.5834	0.280892
24	-0.096943	-0.7509	0.227818

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

Parameters (R input):

par1 = 24 ; 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):

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