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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, 03 Dec 2008 06:16:51 -0700

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/2008/Dec/03/t1228310229o952uj0afco32jm.htm/, Retrieved Sun, 19 May 2024 05:57:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28688, Retrieved Sun, 19 May 2024 05:57:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

205

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [q5] [2008-12-03 13:15:06] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RMPD      [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:16:51] [962e6c9020896982bc8283b8971710a9] [Current]
-   P         [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:23:01] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-   P           [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:25:43] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RMP             [Spectral Analysis] [q8] [2008-12-03 13:33:46] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RMP         [Variance Reduction Matrix] [q8] [2008-12-03 13:29:02] [3ffd109c9e040b1ae7e5dbe576d4698c] 
-    D          [Variance Reduction Matrix] [q8] [2008-12-03 13:37:20] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM              [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:40:14] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM                [Spectral Analysis] [q8] [2008-12-03 13:42:10] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM D              [Cross Correlation Function] [q9] [2008-12-03 13:45:45] [3ffd109c9e040b1ae7e5dbe576d4698c] 

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28688&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28688&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28688&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.883771	6.9025	0
2	0.74754	5.8385	0
3	0.646842	5.052	2e-06
4	0.592945	4.6311	1e-05
5	0.562487	4.3932	2.3e-05
6	0.515982	4.0299	7.9e-05
7	0.445455	3.4791	0.000467
8	0.351375	2.7443	0.003976
9	0.318711	2.4892	0.007773
10	0.330926	2.5846	0.006078
11	0.373207	2.9148	0.002485
12	0.376561	2.941	0.002309
13	0.246609	1.9261	0.029379
14	0.117433	0.9172	0.18133
15	0.018965	0.1481	0.441366
16	-0.038115	-0.2977	0.383476
17	-0.08569	-0.6693	0.252928

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.883771 & 6.9025 & 0 \tabularnewline
2 & 0.74754 & 5.8385 & 0 \tabularnewline
3 & 0.646842 & 5.052 & 2e-06 \tabularnewline
4 & 0.592945 & 4.6311 & 1e-05 \tabularnewline
5 & 0.562487 & 4.3932 & 2.3e-05 \tabularnewline
6 & 0.515982 & 4.0299 & 7.9e-05 \tabularnewline
7 & 0.445455 & 3.4791 & 0.000467 \tabularnewline
8 & 0.351375 & 2.7443 & 0.003976 \tabularnewline
9 & 0.318711 & 2.4892 & 0.007773 \tabularnewline
10 & 0.330926 & 2.5846 & 0.006078 \tabularnewline
11 & 0.373207 & 2.9148 & 0.002485 \tabularnewline
12 & 0.376561 & 2.941 & 0.002309 \tabularnewline
13 & 0.246609 & 1.9261 & 0.029379 \tabularnewline
14 & 0.117433 & 0.9172 & 0.18133 \tabularnewline
15 & 0.018965 & 0.1481 & 0.441366 \tabularnewline
16 & -0.038115 & -0.2977 & 0.383476 \tabularnewline
17 & -0.08569 & -0.6693 & 0.252928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28688&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]0.883771[/C][C]6.9025[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.74754[/C][C]5.8385[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.646842[/C][C]5.052[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.592945[/C][C]4.6311[/C][C]1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.562487[/C][C]4.3932[/C][C]2.3e-05[/C][/ROW]
[ROW][C]6[/C][C]0.515982[/C][C]4.0299[/C][C]7.9e-05[/C][/ROW]
[ROW][C]7[/C][C]0.445455[/C][C]3.4791[/C][C]0.000467[/C][/ROW]
[ROW][C]8[/C][C]0.351375[/C][C]2.7443[/C][C]0.003976[/C][/ROW]
[ROW][C]9[/C][C]0.318711[/C][C]2.4892[/C][C]0.007773[/C][/ROW]
[ROW][C]10[/C][C]0.330926[/C][C]2.5846[/C][C]0.006078[/C][/ROW]
[ROW][C]11[/C][C]0.373207[/C][C]2.9148[/C][C]0.002485[/C][/ROW]
[ROW][C]12[/C][C]0.376561[/C][C]2.941[/C][C]0.002309[/C][/ROW]
[ROW][C]13[/C][C]0.246609[/C][C]1.9261[/C][C]0.029379[/C][/ROW]
[ROW][C]14[/C][C]0.117433[/C][C]0.9172[/C][C]0.18133[/C][/ROW]
[ROW][C]15[/C][C]0.018965[/C][C]0.1481[/C][C]0.441366[/C][/ROW]
[ROW][C]16[/C][C]-0.038115[/C][C]-0.2977[/C][C]0.383476[/C][/ROW]
[ROW][C]17[/C][C]-0.08569[/C][C]-0.6693[/C][C]0.252928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28688&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28688&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	0.883771	6.9025	0
2	0.74754	5.8385	0
3	0.646842	5.052	2e-06
4	0.592945	4.6311	1e-05
5	0.562487	4.3932	2.3e-05
6	0.515982	4.0299	7.9e-05
7	0.445455	3.4791	0.000467
8	0.351375	2.7443	0.003976
9	0.318711	2.4892	0.007773
10	0.330926	2.5846	0.006078
11	0.373207	2.9148	0.002485
12	0.376561	2.941	0.002309
13	0.246609	1.9261	0.029379
14	0.117433	0.9172	0.18133
15	0.018965	0.1481	0.441366
16	-0.038115	-0.2977	0.383476
17	-0.08569	-0.6693	0.252928

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.883771	6.9025	0
2	-0.153056	-1.1954	0.118278
3	0.095111	0.7428	0.230214
4	0.128298	1.002	0.160141
5	0.059751	0.4667	0.321198
6	-0.06553	-0.5118	0.305316
7	-0.077955	-0.6089	0.272442
8	-0.12692	-0.9913	0.162732
9	0.225908	1.7644	0.041336
10	0.090095	0.7037	0.24216
11	0.151635	1.1843	0.120443
12	-0.09871	-0.7709	0.221857
13	-0.548598	-4.2847	3.3e-05
14	0.008955	0.0699	0.472234
15	-0.095791	-0.7482	0.228621
16	-0.072083	-0.563	0.287755
17	-0.001581	-0.0123	0.495094

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.883771 & 6.9025 & 0 \tabularnewline
2 & -0.153056 & -1.1954 & 0.118278 \tabularnewline
3 & 0.095111 & 0.7428 & 0.230214 \tabularnewline
4 & 0.128298 & 1.002 & 0.160141 \tabularnewline
5 & 0.059751 & 0.4667 & 0.321198 \tabularnewline
6 & -0.06553 & -0.5118 & 0.305316 \tabularnewline
7 & -0.077955 & -0.6089 & 0.272442 \tabularnewline
8 & -0.12692 & -0.9913 & 0.162732 \tabularnewline
9 & 0.225908 & 1.7644 & 0.041336 \tabularnewline
10 & 0.090095 & 0.7037 & 0.24216 \tabularnewline
11 & 0.151635 & 1.1843 & 0.120443 \tabularnewline
12 & -0.09871 & -0.7709 & 0.221857 \tabularnewline
13 & -0.548598 & -4.2847 & 3.3e-05 \tabularnewline
14 & 0.008955 & 0.0699 & 0.472234 \tabularnewline
15 & -0.095791 & -0.7482 & 0.228621 \tabularnewline
16 & -0.072083 & -0.563 & 0.287755 \tabularnewline
17 & -0.001581 & -0.0123 & 0.495094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28688&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]0.883771[/C][C]6.9025[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.153056[/C][C]-1.1954[/C][C]0.118278[/C][/ROW]
[ROW][C]3[/C][C]0.095111[/C][C]0.7428[/C][C]0.230214[/C][/ROW]
[ROW][C]4[/C][C]0.128298[/C][C]1.002[/C][C]0.160141[/C][/ROW]
[ROW][C]5[/C][C]0.059751[/C][C]0.4667[/C][C]0.321198[/C][/ROW]
[ROW][C]6[/C][C]-0.06553[/C][C]-0.5118[/C][C]0.305316[/C][/ROW]
[ROW][C]7[/C][C]-0.077955[/C][C]-0.6089[/C][C]0.272442[/C][/ROW]
[ROW][C]8[/C][C]-0.12692[/C][C]-0.9913[/C][C]0.162732[/C][/ROW]
[ROW][C]9[/C][C]0.225908[/C][C]1.7644[/C][C]0.041336[/C][/ROW]
[ROW][C]10[/C][C]0.090095[/C][C]0.7037[/C][C]0.24216[/C][/ROW]
[ROW][C]11[/C][C]0.151635[/C][C]1.1843[/C][C]0.120443[/C][/ROW]
[ROW][C]12[/C][C]-0.09871[/C][C]-0.7709[/C][C]0.221857[/C][/ROW]
[ROW][C]13[/C][C]-0.548598[/C][C]-4.2847[/C][C]3.3e-05[/C][/ROW]
[ROW][C]14[/C][C]0.008955[/C][C]0.0699[/C][C]0.472234[/C][/ROW]
[ROW][C]15[/C][C]-0.095791[/C][C]-0.7482[/C][C]0.228621[/C][/ROW]
[ROW][C]16[/C][C]-0.072083[/C][C]-0.563[/C][C]0.287755[/C][/ROW]
[ROW][C]17[/C][C]-0.001581[/C][C]-0.0123[/C][C]0.495094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28688&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28688&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	0.883771	6.9025	0
2	-0.153056	-1.1954	0.118278
3	0.095111	0.7428	0.230214
4	0.128298	1.002	0.160141
5	0.059751	0.4667	0.321198
6	-0.06553	-0.5118	0.305316
7	-0.077955	-0.6089	0.272442
8	-0.12692	-0.9913	0.162732
9	0.225908	1.7644	0.041336
10	0.090095	0.7037	0.24216
11	0.151635	1.1843	0.120443
12	-0.09871	-0.7709	0.221857
13	-0.548598	-4.2847	3.3e-05
14	0.008955	0.0699	0.472234
15	-0.095791	-0.7482	0.228621
16	-0.072083	-0.563	0.287755
17	-0.001581	-0.0123	0.495094

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code