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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

Thu, 15 Jan 2015 18:25:14 +0000

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/2015/Jan/15/t142134634855lqmda4lukjtgu.htm/, Retrieved Mon, 13 May 2024 22:21:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=272906, Retrieved Mon, 13 May 2024 22:21:04 +0000

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Original text written by user:

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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)

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [ARIMA Backward Selection] [] [2011-12-06 19:59:13] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [] [2011-12-06 20:08:12] [b98453cac15ba1066b407e146608df68]
- R         [ARIMA Forecasting] [] [2013-11-22 17:39:30] [0307e7a6407eb638caabc417e3a6b260]
- RM          [ARIMA Forecasting] [] [2014-11-26 18:52:52] [d253a55552bf9917a397def3be261e30]
- RMPD            [(Partial) Autocorrelation Function] [] [2015-01-15 18:25:14] [940a3d9bc049bdd1effc6e8b1116301d] [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	7 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 7 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272906&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272906&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272906&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	7 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.129242	-1.4158	0.079716
2	0.135193	1.481	0.070618
3	0.433028	4.7436	3e-06
4	-0.110575	-1.2113	0.114083
5	0.216939	2.3764	0.009531
6	0.352852	3.8653	9e-05
7	-0.255532	-2.7992	0.002986
8	0.243824	2.671	0.004307
9	0.242456	2.656	0.004491
10	-0.193764	-2.1226	0.017922
11	0.218364	2.3921	0.009153
12	-0.077216	-0.8459	0.199657
13	-0.188532	-2.0653	0.020526
14	0.177836	1.9481	0.026869
15	-0.013352	-0.1463	0.441977
16	-0.217366	-2.3811	0.009417
17	0.170964	1.8728	0.031764
18	-0.09043	-0.9906	0.161935
19	-0.170026	-1.8625	0.032486
20	0.110354	1.2089	0.114544
21	-0.183524	-2.0104	0.023315

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.129242 & -1.4158 & 0.079716 \tabularnewline
2 & 0.135193 & 1.481 & 0.070618 \tabularnewline
3 & 0.433028 & 4.7436 & 3e-06 \tabularnewline
4 & -0.110575 & -1.2113 & 0.114083 \tabularnewline
5 & 0.216939 & 2.3764 & 0.009531 \tabularnewline
6 & 0.352852 & 3.8653 & 9e-05 \tabularnewline
7 & -0.255532 & -2.7992 & 0.002986 \tabularnewline
8 & 0.243824 & 2.671 & 0.004307 \tabularnewline
9 & 0.242456 & 2.656 & 0.004491 \tabularnewline
10 & -0.193764 & -2.1226 & 0.017922 \tabularnewline
11 & 0.218364 & 2.3921 & 0.009153 \tabularnewline
12 & -0.077216 & -0.8459 & 0.199657 \tabularnewline
13 & -0.188532 & -2.0653 & 0.020526 \tabularnewline
14 & 0.177836 & 1.9481 & 0.026869 \tabularnewline
15 & -0.013352 & -0.1463 & 0.441977 \tabularnewline
16 & -0.217366 & -2.3811 & 0.009417 \tabularnewline
17 & 0.170964 & 1.8728 & 0.031764 \tabularnewline
18 & -0.09043 & -0.9906 & 0.161935 \tabularnewline
19 & -0.170026 & -1.8625 & 0.032486 \tabularnewline
20 & 0.110354 & 1.2089 & 0.114544 \tabularnewline
21 & -0.183524 & -2.0104 & 0.023315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272906&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]-0.129242[/C][C]-1.4158[/C][C]0.079716[/C][/ROW]
[ROW][C]2[/C][C]0.135193[/C][C]1.481[/C][C]0.070618[/C][/ROW]
[ROW][C]3[/C][C]0.433028[/C][C]4.7436[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.110575[/C][C]-1.2113[/C][C]0.114083[/C][/ROW]
[ROW][C]5[/C][C]0.216939[/C][C]2.3764[/C][C]0.009531[/C][/ROW]
[ROW][C]6[/C][C]0.352852[/C][C]3.8653[/C][C]9e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.255532[/C][C]-2.7992[/C][C]0.002986[/C][/ROW]
[ROW][C]8[/C][C]0.243824[/C][C]2.671[/C][C]0.004307[/C][/ROW]
[ROW][C]9[/C][C]0.242456[/C][C]2.656[/C][C]0.004491[/C][/ROW]
[ROW][C]10[/C][C]-0.193764[/C][C]-2.1226[/C][C]0.017922[/C][/ROW]
[ROW][C]11[/C][C]0.218364[/C][C]2.3921[/C][C]0.009153[/C][/ROW]
[ROW][C]12[/C][C]-0.077216[/C][C]-0.8459[/C][C]0.199657[/C][/ROW]
[ROW][C]13[/C][C]-0.188532[/C][C]-2.0653[/C][C]0.020526[/C][/ROW]
[ROW][C]14[/C][C]0.177836[/C][C]1.9481[/C][C]0.026869[/C][/ROW]
[ROW][C]15[/C][C]-0.013352[/C][C]-0.1463[/C][C]0.441977[/C][/ROW]
[ROW][C]16[/C][C]-0.217366[/C][C]-2.3811[/C][C]0.009417[/C][/ROW]
[ROW][C]17[/C][C]0.170964[/C][C]1.8728[/C][C]0.031764[/C][/ROW]
[ROW][C]18[/C][C]-0.09043[/C][C]-0.9906[/C][C]0.161935[/C][/ROW]
[ROW][C]19[/C][C]-0.170026[/C][C]-1.8625[/C][C]0.032486[/C][/ROW]
[ROW][C]20[/C][C]0.110354[/C][C]1.2089[/C][C]0.114544[/C][/ROW]
[ROW][C]21[/C][C]-0.183524[/C][C]-2.0104[/C][C]0.023315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272906&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272906&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	-0.129242	-1.4158	0.079716
2	0.135193	1.481	0.070618
3	0.433028	4.7436	3e-06
4	-0.110575	-1.2113	0.114083
5	0.216939	2.3764	0.009531
6	0.352852	3.8653	9e-05
7	-0.255532	-2.7992	0.002986
8	0.243824	2.671	0.004307
9	0.242456	2.656	0.004491
10	-0.193764	-2.1226	0.017922
11	0.218364	2.3921	0.009153
12	-0.077216	-0.8459	0.199657
13	-0.188532	-2.0653	0.020526
14	0.177836	1.9481	0.026869
15	-0.013352	-0.1463	0.441977
16	-0.217366	-2.3811	0.009417
17	0.170964	1.8728	0.031764
18	-0.09043	-0.9906	0.161935
19	-0.170026	-1.8625	0.032486
20	0.110354	1.2089	0.114544
21	-0.183524	-2.0104	0.023315

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.129242	-1.4158	0.079716
2	0.120503	1.32	0.094667
3	0.478803	5.245	0
4	0.002494	0.0273	0.489123
5	0.077433	0.8482	0.198996
6	0.285182	3.124	0.001119
7	-0.218426	-2.3927	0.009137
8	-0.062829	-0.6883	0.24631
9	0.193426	2.1189	0.018081
10	-0.03253	-0.3563	0.361104
11	-0.11008	-1.2059	0.11512
12	-0.225133	-2.4662	0.007534
13	-0.11391	-1.2478	0.107262
14	-0.058782	-0.6439	0.260427
15	0.159063	1.7424	0.041996
16	-0.025322	-0.2774	0.390978
17	0.020856	0.2285	0.409834
18	0.099968	1.0951	0.137834
19	-0.144923	-1.5876	0.057509
20	-0.119287	-1.3067	0.096903
21	0.027035	0.2962	0.383811

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.129242 & -1.4158 & 0.079716 \tabularnewline
2 & 0.120503 & 1.32 & 0.094667 \tabularnewline
3 & 0.478803 & 5.245 & 0 \tabularnewline
4 & 0.002494 & 0.0273 & 0.489123 \tabularnewline
5 & 0.077433 & 0.8482 & 0.198996 \tabularnewline
6 & 0.285182 & 3.124 & 0.001119 \tabularnewline
7 & -0.218426 & -2.3927 & 0.009137 \tabularnewline
8 & -0.062829 & -0.6883 & 0.24631 \tabularnewline
9 & 0.193426 & 2.1189 & 0.018081 \tabularnewline
10 & -0.03253 & -0.3563 & 0.361104 \tabularnewline
11 & -0.11008 & -1.2059 & 0.11512 \tabularnewline
12 & -0.225133 & -2.4662 & 0.007534 \tabularnewline
13 & -0.11391 & -1.2478 & 0.107262 \tabularnewline
14 & -0.058782 & -0.6439 & 0.260427 \tabularnewline
15 & 0.159063 & 1.7424 & 0.041996 \tabularnewline
16 & -0.025322 & -0.2774 & 0.390978 \tabularnewline
17 & 0.020856 & 0.2285 & 0.409834 \tabularnewline
18 & 0.099968 & 1.0951 & 0.137834 \tabularnewline
19 & -0.144923 & -1.5876 & 0.057509 \tabularnewline
20 & -0.119287 & -1.3067 & 0.096903 \tabularnewline
21 & 0.027035 & 0.2962 & 0.383811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=272906&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]-0.129242[/C][C]-1.4158[/C][C]0.079716[/C][/ROW]
[ROW][C]2[/C][C]0.120503[/C][C]1.32[/C][C]0.094667[/C][/ROW]
[ROW][C]3[/C][C]0.478803[/C][C]5.245[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.002494[/C][C]0.0273[/C][C]0.489123[/C][/ROW]
[ROW][C]5[/C][C]0.077433[/C][C]0.8482[/C][C]0.198996[/C][/ROW]
[ROW][C]6[/C][C]0.285182[/C][C]3.124[/C][C]0.001119[/C][/ROW]
[ROW][C]7[/C][C]-0.218426[/C][C]-2.3927[/C][C]0.009137[/C][/ROW]
[ROW][C]8[/C][C]-0.062829[/C][C]-0.6883[/C][C]0.24631[/C][/ROW]
[ROW][C]9[/C][C]0.193426[/C][C]2.1189[/C][C]0.018081[/C][/ROW]
[ROW][C]10[/C][C]-0.03253[/C][C]-0.3563[/C][C]0.361104[/C][/ROW]
[ROW][C]11[/C][C]-0.11008[/C][C]-1.2059[/C][C]0.11512[/C][/ROW]
[ROW][C]12[/C][C]-0.225133[/C][C]-2.4662[/C][C]0.007534[/C][/ROW]
[ROW][C]13[/C][C]-0.11391[/C][C]-1.2478[/C][C]0.107262[/C][/ROW]
[ROW][C]14[/C][C]-0.058782[/C][C]-0.6439[/C][C]0.260427[/C][/ROW]
[ROW][C]15[/C][C]0.159063[/C][C]1.7424[/C][C]0.041996[/C][/ROW]
[ROW][C]16[/C][C]-0.025322[/C][C]-0.2774[/C][C]0.390978[/C][/ROW]
[ROW][C]17[/C][C]0.020856[/C][C]0.2285[/C][C]0.409834[/C][/ROW]
[ROW][C]18[/C][C]0.099968[/C][C]1.0951[/C][C]0.137834[/C][/ROW]
[ROW][C]19[/C][C]-0.144923[/C][C]-1.5876[/C][C]0.057509[/C][/ROW]
[ROW][C]20[/C][C]-0.119287[/C][C]-1.3067[/C][C]0.096903[/C][/ROW]
[ROW][C]21[/C][C]0.027035[/C][C]0.2962[/C][C]0.383811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=272906&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=272906&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	-0.129242	-1.4158	0.079716
2	0.120503	1.32	0.094667
3	0.478803	5.245	0
4	0.002494	0.0273	0.489123
5	0.077433	0.8482	0.198996
6	0.285182	3.124	0.001119
7	-0.218426	-2.3927	0.009137
8	-0.062829	-0.6883	0.24631
9	0.193426	2.1189	0.018081
10	-0.03253	-0.3563	0.361104
11	-0.11008	-1.2059	0.11512
12	-0.225133	-2.4662	0.007534
13	-0.11391	-1.2478	0.107262
14	-0.058782	-0.6439	0.260427
15	0.159063	1.7424	0.041996
16	-0.025322	-0.2774	0.390978
17	0.020856	0.2285	0.409834
18	0.099968	1.0951	0.137834
19	-0.144923	-1.5876	0.057509
20	-0.119287	-1.3067	0.096903
21	0.027035	0.2962	0.383811

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):

Parameters (R input):

par1 = Default ; par2 = -0.1 ; par3 = 0 ; par4 = 1 ; 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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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