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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

Sun, 03 Dec 2017 15:13:18 +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/03/t15123104787039liq6fmqzvvj.htm/, Retrieved Tue, 14 May 2024 03:47:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308457, Retrieved Tue, 14 May 2024 03:47:53 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

105

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

-       [(Partial) Autocorrelation Function] [] [2017-12-03 14:13:18] [834c75312b1a933b06457deba9c9b5e8] [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=308457&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=308457&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308457&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	-0.426635	-6.1972	0
2	-0.170348	-2.4744	0.007066
3	0.334147	4.8538	1e-06
4	-0.42838	-6.2226	0
5	0.062077	0.9017	0.184117
6	0.34408	4.9981	1e-06
7	-0.154314	-2.2415	0.013016
8	-0.181128	-2.631	0.00457
9	0.276251	4.0128	4.2e-05
10	-0.346291	-5.0302	1e-06
11	-0.03299	-0.4792	0.316146
12	0.570708	8.29	0
13	-0.364791	-5.2989	0
14	0.096172	1.397	0.081945
15	0.089168	1.2952	0.098326
16	-0.421226	-6.1187	0
17	0.240342	3.4912	0.000293
18	0.180533	2.6224	0.004684
19	-0.172184	-2.5011	0.00657
20	0.030426	0.442	0.329483
21	0.035536	0.5162	0.30313
22	-0.310103	-4.5045	6e-06
23	0.210271	3.0544	0.001273

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.426635 & -6.1972 & 0 \tabularnewline
2 & -0.170348 & -2.4744 & 0.007066 \tabularnewline
3 & 0.334147 & 4.8538 & 1e-06 \tabularnewline
4 & -0.42838 & -6.2226 & 0 \tabularnewline
5 & 0.062077 & 0.9017 & 0.184117 \tabularnewline
6 & 0.34408 & 4.9981 & 1e-06 \tabularnewline
7 & -0.154314 & -2.2415 & 0.013016 \tabularnewline
8 & -0.181128 & -2.631 & 0.00457 \tabularnewline
9 & 0.276251 & 4.0128 & 4.2e-05 \tabularnewline
10 & -0.346291 & -5.0302 & 1e-06 \tabularnewline
11 & -0.03299 & -0.4792 & 0.316146 \tabularnewline
12 & 0.570708 & 8.29 & 0 \tabularnewline
13 & -0.364791 & -5.2989 & 0 \tabularnewline
14 & 0.096172 & 1.397 & 0.081945 \tabularnewline
15 & 0.089168 & 1.2952 & 0.098326 \tabularnewline
16 & -0.421226 & -6.1187 & 0 \tabularnewline
17 & 0.240342 & 3.4912 & 0.000293 \tabularnewline
18 & 0.180533 & 2.6224 & 0.004684 \tabularnewline
19 & -0.172184 & -2.5011 & 0.00657 \tabularnewline
20 & 0.030426 & 0.442 & 0.329483 \tabularnewline
21 & 0.035536 & 0.5162 & 0.30313 \tabularnewline
22 & -0.310103 & -4.5045 & 6e-06 \tabularnewline
23 & 0.210271 & 3.0544 & 0.001273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308457&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]-0.426635[/C][C]-6.1972[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.170348[/C][C]-2.4744[/C][C]0.007066[/C][/ROW]
[ROW][C]3[/C][C]0.334147[/C][C]4.8538[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.42838[/C][C]-6.2226[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.062077[/C][C]0.9017[/C][C]0.184117[/C][/ROW]
[ROW][C]6[/C][C]0.34408[/C][C]4.9981[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.154314[/C][C]-2.2415[/C][C]0.013016[/C][/ROW]
[ROW][C]8[/C][C]-0.181128[/C][C]-2.631[/C][C]0.00457[/C][/ROW]
[ROW][C]9[/C][C]0.276251[/C][C]4.0128[/C][C]4.2e-05[/C][/ROW]
[ROW][C]10[/C][C]-0.346291[/C][C]-5.0302[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]-0.03299[/C][C]-0.4792[/C][C]0.316146[/C][/ROW]
[ROW][C]12[/C][C]0.570708[/C][C]8.29[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.364791[/C][C]-5.2989[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.096172[/C][C]1.397[/C][C]0.081945[/C][/ROW]
[ROW][C]15[/C][C]0.089168[/C][C]1.2952[/C][C]0.098326[/C][/ROW]
[ROW][C]16[/C][C]-0.421226[/C][C]-6.1187[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.240342[/C][C]3.4912[/C][C]0.000293[/C][/ROW]
[ROW][C]18[/C][C]0.180533[/C][C]2.6224[/C][C]0.004684[/C][/ROW]
[ROW][C]19[/C][C]-0.172184[/C][C]-2.5011[/C][C]0.00657[/C][/ROW]
[ROW][C]20[/C][C]0.030426[/C][C]0.442[/C][C]0.329483[/C][/ROW]
[ROW][C]21[/C][C]0.035536[/C][C]0.5162[/C][C]0.30313[/C][/ROW]
[ROW][C]22[/C][C]-0.310103[/C][C]-4.5045[/C][C]6e-06[/C][/ROW]
[ROW][C]23[/C][C]0.210271[/C][C]3.0544[/C][C]0.001273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308457&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308457&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	-0.426635	-6.1972	0
2	-0.170348	-2.4744	0.007066
3	0.334147	4.8538	1e-06
4	-0.42838	-6.2226	0
5	0.062077	0.9017	0.184117
6	0.34408	4.9981	1e-06
7	-0.154314	-2.2415	0.013016
8	-0.181128	-2.631	0.00457
9	0.276251	4.0128	4.2e-05
10	-0.346291	-5.0302	1e-06
11	-0.03299	-0.4792	0.316146
12	0.570708	8.29	0
13	-0.364791	-5.2989	0
14	0.096172	1.397	0.081945
15	0.089168	1.2952	0.098326
16	-0.421226	-6.1187	0
17	0.240342	3.4912	0.000293
18	0.180533	2.6224	0.004684
19	-0.172184	-2.5011	0.00657
20	0.030426	0.442	0.329483
21	0.035536	0.5162	0.30313
22	-0.310103	-4.5045	6e-06
23	0.210271	3.0544	0.001273

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.426635	-6.1972	0
2	-0.430773	-6.2573	0
3	0.06962	1.0113	0.156519
4	-0.408577	-5.9349	0
5	-0.352137	-5.1151	0
6	-0.010118	-0.147	0.441645
7	0.220207	3.1987	0.000797
8	-0.269932	-3.921	6e-05
9	-0.0149	-0.2164	0.41443
10	-0.272356	-3.9562	5.2e-05
11	-0.372546	-5.4115	0
12	0.139636	2.0283	0.021891
13	0.169276	2.4589	0.007371
14	0.308301	4.4783	6e-06
15	0.123457	1.7933	0.037177
16	-0.058926	-0.8559	0.1965
17	-0.000741	-0.0108	0.495711
18	0.020849	0.3028	0.381154
19	0.047348	0.6878	0.246178
20	-0.000218	-0.0032	0.498737
21	-0.097426	-1.4152	0.079244
22	-0.177536	-2.5789	0.005296
23	-0.067881	-0.986	0.162625

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.426635 & -6.1972 & 0 \tabularnewline
2 & -0.430773 & -6.2573 & 0 \tabularnewline
3 & 0.06962 & 1.0113 & 0.156519 \tabularnewline
4 & -0.408577 & -5.9349 & 0 \tabularnewline
5 & -0.352137 & -5.1151 & 0 \tabularnewline
6 & -0.010118 & -0.147 & 0.441645 \tabularnewline
7 & 0.220207 & 3.1987 & 0.000797 \tabularnewline
8 & -0.269932 & -3.921 & 6e-05 \tabularnewline
9 & -0.0149 & -0.2164 & 0.41443 \tabularnewline
10 & -0.272356 & -3.9562 & 5.2e-05 \tabularnewline
11 & -0.372546 & -5.4115 & 0 \tabularnewline
12 & 0.139636 & 2.0283 & 0.021891 \tabularnewline
13 & 0.169276 & 2.4589 & 0.007371 \tabularnewline
14 & 0.308301 & 4.4783 & 6e-06 \tabularnewline
15 & 0.123457 & 1.7933 & 0.037177 \tabularnewline
16 & -0.058926 & -0.8559 & 0.1965 \tabularnewline
17 & -0.000741 & -0.0108 & 0.495711 \tabularnewline
18 & 0.020849 & 0.3028 & 0.381154 \tabularnewline
19 & 0.047348 & 0.6878 & 0.246178 \tabularnewline
20 & -0.000218 & -0.0032 & 0.498737 \tabularnewline
21 & -0.097426 & -1.4152 & 0.079244 \tabularnewline
22 & -0.177536 & -2.5789 & 0.005296 \tabularnewline
23 & -0.067881 & -0.986 & 0.162625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308457&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]-0.426635[/C][C]-6.1972[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.430773[/C][C]-6.2573[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.06962[/C][C]1.0113[/C][C]0.156519[/C][/ROW]
[ROW][C]4[/C][C]-0.408577[/C][C]-5.9349[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.352137[/C][C]-5.1151[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.010118[/C][C]-0.147[/C][C]0.441645[/C][/ROW]
[ROW][C]7[/C][C]0.220207[/C][C]3.1987[/C][C]0.000797[/C][/ROW]
[ROW][C]8[/C][C]-0.269932[/C][C]-3.921[/C][C]6e-05[/C][/ROW]
[ROW][C]9[/C][C]-0.0149[/C][C]-0.2164[/C][C]0.41443[/C][/ROW]
[ROW][C]10[/C][C]-0.272356[/C][C]-3.9562[/C][C]5.2e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.372546[/C][C]-5.4115[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.139636[/C][C]2.0283[/C][C]0.021891[/C][/ROW]
[ROW][C]13[/C][C]0.169276[/C][C]2.4589[/C][C]0.007371[/C][/ROW]
[ROW][C]14[/C][C]0.308301[/C][C]4.4783[/C][C]6e-06[/C][/ROW]
[ROW][C]15[/C][C]0.123457[/C][C]1.7933[/C][C]0.037177[/C][/ROW]
[ROW][C]16[/C][C]-0.058926[/C][C]-0.8559[/C][C]0.1965[/C][/ROW]
[ROW][C]17[/C][C]-0.000741[/C][C]-0.0108[/C][C]0.495711[/C][/ROW]
[ROW][C]18[/C][C]0.020849[/C][C]0.3028[/C][C]0.381154[/C][/ROW]
[ROW][C]19[/C][C]0.047348[/C][C]0.6878[/C][C]0.246178[/C][/ROW]
[ROW][C]20[/C][C]-0.000218[/C][C]-0.0032[/C][C]0.498737[/C][/ROW]
[ROW][C]21[/C][C]-0.097426[/C][C]-1.4152[/C][C]0.079244[/C][/ROW]
[ROW][C]22[/C][C]-0.177536[/C][C]-2.5789[/C][C]0.005296[/C][/ROW]
[ROW][C]23[/C][C]-0.067881[/C][C]-0.986[/C][C]0.162625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308457&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308457&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	-0.426635	-6.1972	0
2	-0.430773	-6.2573	0
3	0.06962	1.0113	0.156519
4	-0.408577	-5.9349	0
5	-0.352137	-5.1151	0
6	-0.010118	-0.147	0.441645
7	0.220207	3.1987	0.000797
8	-0.269932	-3.921	6e-05
9	-0.0149	-0.2164	0.41443
10	-0.272356	-3.9562	5.2e-05
11	-0.372546	-5.4115	0
12	0.139636	2.0283	0.021891
13	0.169276	2.4589	0.007371
14	0.308301	4.4783	6e-06
15	0.123457	1.7933	0.037177
16	-0.058926	-0.8559	0.1965
17	-0.000741	-0.0108	0.495711
18	0.020849	0.3028	0.381154
19	0.047348	0.6878	0.246178
20	-0.000218	-0.0032	0.498737
21	-0.097426	-1.4152	0.079244
22	-0.177536	-2.5789	0.005296
23	-0.067881	-0.986	0.162625

Figure 1

PNG link

Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

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):

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