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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 16:19:42 -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/2007/Nov/27/t1196118609k7k86497m5upifv.htm/, Retrieved Sun, 05 May 2024 16:43:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6737, Retrieved Sun, 05 May 2024 16:43:51 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

219

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

-       [(Partial) Autocorrelation Function] [Inducing Stationa...] [2007-11-26 23:19:42] [640491d00f3c9cca22cbf779aa38ac16] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6737&T=0

[TABLE]
[ROW][C]Summary of compuational 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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6737&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6737&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.9443	0
1	0.973268	8.7052	0
2	0.940197	8.4094	0
3	0.905732	8.1011	0
4	0.8689	7.7717	0
5	0.830363	7.427	0
6	0.790618	7.0715	0
7	0.74878	6.6973	0
8	0.706539	6.3195	0
9	0.663722	5.9365	0
10	0.617065	5.5192	0
11	0.565968	5.0622	1e-06
12	0.519308	4.6448	7e-06
13	0.472942	4.2301	3.1e-05
14	0.423474	3.7877	0.000146
15	0.375292	3.3567	0.000605
16	0.322821	2.8874	0.002497
17	0.272763	2.4397	0.008456
18	0.232775	2.082	0.020269

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.973268 & 8.7052 & 0 \tabularnewline
2 & 0.940197 & 8.4094 & 0 \tabularnewline
3 & 0.905732 & 8.1011 & 0 \tabularnewline
4 & 0.8689 & 7.7717 & 0 \tabularnewline
5 & 0.830363 & 7.427 & 0 \tabularnewline
6 & 0.790618 & 7.0715 & 0 \tabularnewline
7 & 0.74878 & 6.6973 & 0 \tabularnewline
8 & 0.706539 & 6.3195 & 0 \tabularnewline
9 & 0.663722 & 5.9365 & 0 \tabularnewline
10 & 0.617065 & 5.5192 & 0 \tabularnewline
11 & 0.565968 & 5.0622 & 1e-06 \tabularnewline
12 & 0.519308 & 4.6448 & 7e-06 \tabularnewline
13 & 0.472942 & 4.2301 & 3.1e-05 \tabularnewline
14 & 0.423474 & 3.7877 & 0.000146 \tabularnewline
15 & 0.375292 & 3.3567 & 0.000605 \tabularnewline
16 & 0.322821 & 2.8874 & 0.002497 \tabularnewline
17 & 0.272763 & 2.4397 & 0.008456 \tabularnewline
18 & 0.232775 & 2.082 & 0.020269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6737&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]0[/C][C]1[/C][C]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.973268[/C][C]8.7052[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.940197[/C][C]8.4094[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.905732[/C][C]8.1011[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.8689[/C][C]7.7717[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.830363[/C][C]7.427[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.790618[/C][C]7.0715[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.74878[/C][C]6.6973[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.706539[/C][C]6.3195[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.663722[/C][C]5.9365[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.617065[/C][C]5.5192[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.565968[/C][C]5.0622[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.519308[/C][C]4.6448[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]0.472942[/C][C]4.2301[/C][C]3.1e-05[/C][/ROW]
[ROW][C]14[/C][C]0.423474[/C][C]3.7877[/C][C]0.000146[/C][/ROW]
[ROW][C]15[/C][C]0.375292[/C][C]3.3567[/C][C]0.000605[/C][/ROW]
[ROW][C]16[/C][C]0.322821[/C][C]2.8874[/C][C]0.002497[/C][/ROW]
[ROW][C]17[/C][C]0.272763[/C][C]2.4397[/C][C]0.008456[/C][/ROW]
[ROW][C]18[/C][C]0.232775[/C][C]2.082[/C][C]0.020269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6737&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6737&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
0	1	8.9443	0
1	0.973268	8.7052	0
2	0.940197	8.4094	0
3	0.905732	8.1011	0
4	0.8689	7.7717	0
5	0.830363	7.427	0
6	0.790618	7.0715	0
7	0.74878	6.6973	0
8	0.706539	6.3195	0
9	0.663722	5.9365	0
10	0.617065	5.5192	0
11	0.565968	5.0622	1e-06
12	0.519308	4.6448	7e-06
13	0.472942	4.2301	3.1e-05
14	0.423474	3.7877	0.000146
15	0.375292	3.3567	0.000605
16	0.322821	2.8874	0.002497
17	0.272763	2.4397	0.008456
18	0.232775	2.082	0.020269

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.973268	8.7052	0
1	-0.133718	-1.196	0.882387
2	-0.029895	-0.2674	0.605072
3	-0.059329	-0.5307	0.701434
4	-0.042724	-0.3821	0.648314
5	-0.037117	-0.332	0.629615
6	-0.056318	-0.5037	0.69208
7	-0.0214	-0.1914	0.575655
8	-0.032862	-0.2939	0.615212
9	-0.095433	-0.8536	0.802058
10	-0.099411	-0.8892	0.811707
11	0.0731	0.6538	0.257548
12	-0.038343	-0.3429	0.633731
13	-0.087895	-0.7862	0.782952
14	0.001825	0.0163	0.493507
15	-0.124734	-1.1157	0.866045
16	0.031835	0.2847	0.388289
17	0.149364	1.336	0.092677
18	0.053722	0.4805	0.316089

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.973268 & 8.7052 & 0 \tabularnewline
1 & -0.133718 & -1.196 & 0.882387 \tabularnewline
2 & -0.029895 & -0.2674 & 0.605072 \tabularnewline
3 & -0.059329 & -0.5307 & 0.701434 \tabularnewline
4 & -0.042724 & -0.3821 & 0.648314 \tabularnewline
5 & -0.037117 & -0.332 & 0.629615 \tabularnewline
6 & -0.056318 & -0.5037 & 0.69208 \tabularnewline
7 & -0.0214 & -0.1914 & 0.575655 \tabularnewline
8 & -0.032862 & -0.2939 & 0.615212 \tabularnewline
9 & -0.095433 & -0.8536 & 0.802058 \tabularnewline
10 & -0.099411 & -0.8892 & 0.811707 \tabularnewline
11 & 0.0731 & 0.6538 & 0.257548 \tabularnewline
12 & -0.038343 & -0.3429 & 0.633731 \tabularnewline
13 & -0.087895 & -0.7862 & 0.782952 \tabularnewline
14 & 0.001825 & 0.0163 & 0.493507 \tabularnewline
15 & -0.124734 & -1.1157 & 0.866045 \tabularnewline
16 & 0.031835 & 0.2847 & 0.388289 \tabularnewline
17 & 0.149364 & 1.336 & 0.092677 \tabularnewline
18 & 0.053722 & 0.4805 & 0.316089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6737&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]0[/C][C]0.973268[/C][C]8.7052[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.133718[/C][C]-1.196[/C][C]0.882387[/C][/ROW]
[ROW][C]2[/C][C]-0.029895[/C][C]-0.2674[/C][C]0.605072[/C][/ROW]
[ROW][C]3[/C][C]-0.059329[/C][C]-0.5307[/C][C]0.701434[/C][/ROW]
[ROW][C]4[/C][C]-0.042724[/C][C]-0.3821[/C][C]0.648314[/C][/ROW]
[ROW][C]5[/C][C]-0.037117[/C][C]-0.332[/C][C]0.629615[/C][/ROW]
[ROW][C]6[/C][C]-0.056318[/C][C]-0.5037[/C][C]0.69208[/C][/ROW]
[ROW][C]7[/C][C]-0.0214[/C][C]-0.1914[/C][C]0.575655[/C][/ROW]
[ROW][C]8[/C][C]-0.032862[/C][C]-0.2939[/C][C]0.615212[/C][/ROW]
[ROW][C]9[/C][C]-0.095433[/C][C]-0.8536[/C][C]0.802058[/C][/ROW]
[ROW][C]10[/C][C]-0.099411[/C][C]-0.8892[/C][C]0.811707[/C][/ROW]
[ROW][C]11[/C][C]0.0731[/C][C]0.6538[/C][C]0.257548[/C][/ROW]
[ROW][C]12[/C][C]-0.038343[/C][C]-0.3429[/C][C]0.633731[/C][/ROW]
[ROW][C]13[/C][C]-0.087895[/C][C]-0.7862[/C][C]0.782952[/C][/ROW]
[ROW][C]14[/C][C]0.001825[/C][C]0.0163[/C][C]0.493507[/C][/ROW]
[ROW][C]15[/C][C]-0.124734[/C][C]-1.1157[/C][C]0.866045[/C][/ROW]
[ROW][C]16[/C][C]0.031835[/C][C]0.2847[/C][C]0.388289[/C][/ROW]
[ROW][C]17[/C][C]0.149364[/C][C]1.336[/C][C]0.092677[/C][/ROW]
[ROW][C]18[/C][C]0.053722[/C][C]0.4805[/C][C]0.316089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6737&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6737&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
0	0.973268	8.7052	0
1	-0.133718	-1.196	0.882387
2	-0.029895	-0.2674	0.605072
3	-0.059329	-0.5307	0.701434
4	-0.042724	-0.3821	0.648314
5	-0.037117	-0.332	0.629615
6	-0.056318	-0.5037	0.69208
7	-0.0214	-0.1914	0.575655
8	-0.032862	-0.2939	0.615212
9	-0.095433	-0.8536	0.802058
10	-0.099411	-0.8892	0.811707
11	0.0731	0.6538	0.257548
12	-0.038343	-0.3429	0.633731
13	-0.087895	-0.7862	0.782952
14	0.001825	0.0163	0.493507
15	-0.124734	-1.1157	0.866045
16	0.031835	0.2847	0.388289
17	0.149364	1.336	0.092677
18	0.053722	0.4805	0.316089

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.9 ; 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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