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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 30 Nov 2007 08:45:00 -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/30/t119643684317s6aqmxirgu04v.htm/, Retrieved Sat, 27 Apr 2024 16:51:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7742, Retrieved Sat, 27 Apr 2024 16:51:03 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

191

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

-       [(Partial) Autocorrelation Function] [Workshop8_q1c] [2007-11-30 15:45:00] [1ea0754dc57274996703e6220e342fe8] [Current]

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Dataseries X:

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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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7742&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]2 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=7742&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7742&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.798	0
1	0.947915	9.2876	0
2	0.881906	8.6409	0
3	0.804256	7.8801	0
4	0.724532	7.0989	0
5	0.658856	6.4554	0
6	0.59129	5.7934	0
7	0.529876	5.1917	1e-06
8	0.475876	4.6626	5e-06
9	0.425211	4.1662	3.4e-05
10	0.388688	3.8083	0.000123
11	0.354303	3.4714	0.000389
12	0.308005	3.0178	0.00163
13	0.254538	2.494	0.007171
14	0.199774	1.9574	0.026603
15	0.136853	1.3409	0.091562
16	0.089399	0.8759	0.191627
17	0.045585	0.4466	0.328069
18	0.004611	0.0452	0.48203
19	-0.029372	-0.2878	0.612935
20	-0.064291	-0.6299	0.734877
21	-0.086601	-0.8485	0.800867
22	-0.099772	-0.9776	0.834627
23	-0.109182	-1.0698	0.856296

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.798 & 0 \tabularnewline
1 & 0.947915 & 9.2876 & 0 \tabularnewline
2 & 0.881906 & 8.6409 & 0 \tabularnewline
3 & 0.804256 & 7.8801 & 0 \tabularnewline
4 & 0.724532 & 7.0989 & 0 \tabularnewline
5 & 0.658856 & 6.4554 & 0 \tabularnewline
6 & 0.59129 & 5.7934 & 0 \tabularnewline
7 & 0.529876 & 5.1917 & 1e-06 \tabularnewline
8 & 0.475876 & 4.6626 & 5e-06 \tabularnewline
9 & 0.425211 & 4.1662 & 3.4e-05 \tabularnewline
10 & 0.388688 & 3.8083 & 0.000123 \tabularnewline
11 & 0.354303 & 3.4714 & 0.000389 \tabularnewline
12 & 0.308005 & 3.0178 & 0.00163 \tabularnewline
13 & 0.254538 & 2.494 & 0.007171 \tabularnewline
14 & 0.199774 & 1.9574 & 0.026603 \tabularnewline
15 & 0.136853 & 1.3409 & 0.091562 \tabularnewline
16 & 0.089399 & 0.8759 & 0.191627 \tabularnewline
17 & 0.045585 & 0.4466 & 0.328069 \tabularnewline
18 & 0.004611 & 0.0452 & 0.48203 \tabularnewline
19 & -0.029372 & -0.2878 & 0.612935 \tabularnewline
20 & -0.064291 & -0.6299 & 0.734877 \tabularnewline
21 & -0.086601 & -0.8485 & 0.800867 \tabularnewline
22 & -0.099772 & -0.9776 & 0.834627 \tabularnewline
23 & -0.109182 & -1.0698 & 0.856296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7742&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]9.798[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.947915[/C][C]9.2876[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.881906[/C][C]8.6409[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.804256[/C][C]7.8801[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.724532[/C][C]7.0989[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.658856[/C][C]6.4554[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.59129[/C][C]5.7934[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.529876[/C][C]5.1917[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.475876[/C][C]4.6626[/C][C]5e-06[/C][/ROW]
[ROW][C]9[/C][C]0.425211[/C][C]4.1662[/C][C]3.4e-05[/C][/ROW]
[ROW][C]10[/C][C]0.388688[/C][C]3.8083[/C][C]0.000123[/C][/ROW]
[ROW][C]11[/C][C]0.354303[/C][C]3.4714[/C][C]0.000389[/C][/ROW]
[ROW][C]12[/C][C]0.308005[/C][C]3.0178[/C][C]0.00163[/C][/ROW]
[ROW][C]13[/C][C]0.254538[/C][C]2.494[/C][C]0.007171[/C][/ROW]
[ROW][C]14[/C][C]0.199774[/C][C]1.9574[/C][C]0.026603[/C][/ROW]
[ROW][C]15[/C][C]0.136853[/C][C]1.3409[/C][C]0.091562[/C][/ROW]
[ROW][C]16[/C][C]0.089399[/C][C]0.8759[/C][C]0.191627[/C][/ROW]
[ROW][C]17[/C][C]0.045585[/C][C]0.4466[/C][C]0.328069[/C][/ROW]
[ROW][C]18[/C][C]0.004611[/C][C]0.0452[/C][C]0.48203[/C][/ROW]
[ROW][C]19[/C][C]-0.029372[/C][C]-0.2878[/C][C]0.612935[/C][/ROW]
[ROW][C]20[/C][C]-0.064291[/C][C]-0.6299[/C][C]0.734877[/C][/ROW]
[ROW][C]21[/C][C]-0.086601[/C][C]-0.8485[/C][C]0.800867[/C][/ROW]
[ROW][C]22[/C][C]-0.099772[/C][C]-0.9776[/C][C]0.834627[/C][/ROW]
[ROW][C]23[/C][C]-0.109182[/C][C]-1.0698[/C][C]0.856296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7742&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7742&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	9.798	0
1	0.947915	9.2876	0
2	0.881906	8.6409	0
3	0.804256	7.8801	0
4	0.724532	7.0989	0
5	0.658856	6.4554	0
6	0.59129	5.7934	0
7	0.529876	5.1917	1e-06
8	0.475876	4.6626	5e-06
9	0.425211	4.1662	3.4e-05
10	0.388688	3.8083	0.000123
11	0.354303	3.4714	0.000389
12	0.308005	3.0178	0.00163
13	0.254538	2.494	0.007171
14	0.199774	1.9574	0.026603
15	0.136853	1.3409	0.091562
16	0.089399	0.8759	0.191627
17	0.045585	0.4466	0.328069
18	0.004611	0.0452	0.48203
19	-0.029372	-0.2878	0.612935
20	-0.064291	-0.6299	0.734877
21	-0.086601	-0.8485	0.800867
22	-0.099772	-0.9776	0.834627
23	-0.109182	-1.0698	0.856296

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.947915	9.2876	0
1	-0.163981	-1.6067	0.944295
2	-0.135326	-1.3259	0.905993
3	-0.039071	-0.3828	0.648649
4	0.110919	1.0868	0.139927
5	-0.091965	-0.9011	0.815096
6	-0.002341	-0.0229	0.509127
7	0.028576	0.28	0.390047
8	-0.008041	-0.0788	0.531315
9	0.075293	0.7377	0.231243
10	-0.032966	-0.323	0.626302
11	-0.172938	-1.6944	0.953289
12	-0.086332	-0.8459	0.800138
13	0.028293	0.2772	0.391105
14	-0.123993	-1.2149	0.886305
15	0.106397	1.0425	0.149906
16	-0.014398	-0.1411	0.555946
17	-0.049854	-0.4885	0.686834
18	-0.004577	-0.0448	0.517839
19	-0.021366	-0.2093	0.582688
20	0.033874	0.3319	0.370345
21	0.025683	0.2516	0.400928
22	0.015269	0.1496	0.440694
23	0.016374	0.1604	0.43644

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.947915 & 9.2876 & 0 \tabularnewline
1 & -0.163981 & -1.6067 & 0.944295 \tabularnewline
2 & -0.135326 & -1.3259 & 0.905993 \tabularnewline
3 & -0.039071 & -0.3828 & 0.648649 \tabularnewline
4 & 0.110919 & 1.0868 & 0.139927 \tabularnewline
5 & -0.091965 & -0.9011 & 0.815096 \tabularnewline
6 & -0.002341 & -0.0229 & 0.509127 \tabularnewline
7 & 0.028576 & 0.28 & 0.390047 \tabularnewline
8 & -0.008041 & -0.0788 & 0.531315 \tabularnewline
9 & 0.075293 & 0.7377 & 0.231243 \tabularnewline
10 & -0.032966 & -0.323 & 0.626302 \tabularnewline
11 & -0.172938 & -1.6944 & 0.953289 \tabularnewline
12 & -0.086332 & -0.8459 & 0.800138 \tabularnewline
13 & 0.028293 & 0.2772 & 0.391105 \tabularnewline
14 & -0.123993 & -1.2149 & 0.886305 \tabularnewline
15 & 0.106397 & 1.0425 & 0.149906 \tabularnewline
16 & -0.014398 & -0.1411 & 0.555946 \tabularnewline
17 & -0.049854 & -0.4885 & 0.686834 \tabularnewline
18 & -0.004577 & -0.0448 & 0.517839 \tabularnewline
19 & -0.021366 & -0.2093 & 0.582688 \tabularnewline
20 & 0.033874 & 0.3319 & 0.370345 \tabularnewline
21 & 0.025683 & 0.2516 & 0.400928 \tabularnewline
22 & 0.015269 & 0.1496 & 0.440694 \tabularnewline
23 & 0.016374 & 0.1604 & 0.43644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7742&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]0.947915[/C][C]9.2876[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.163981[/C][C]-1.6067[/C][C]0.944295[/C][/ROW]
[ROW][C]2[/C][C]-0.135326[/C][C]-1.3259[/C][C]0.905993[/C][/ROW]
[ROW][C]3[/C][C]-0.039071[/C][C]-0.3828[/C][C]0.648649[/C][/ROW]
[ROW][C]4[/C][C]0.110919[/C][C]1.0868[/C][C]0.139927[/C][/ROW]
[ROW][C]5[/C][C]-0.091965[/C][C]-0.9011[/C][C]0.815096[/C][/ROW]
[ROW][C]6[/C][C]-0.002341[/C][C]-0.0229[/C][C]0.509127[/C][/ROW]
[ROW][C]7[/C][C]0.028576[/C][C]0.28[/C][C]0.390047[/C][/ROW]
[ROW][C]8[/C][C]-0.008041[/C][C]-0.0788[/C][C]0.531315[/C][/ROW]
[ROW][C]9[/C][C]0.075293[/C][C]0.7377[/C][C]0.231243[/C][/ROW]
[ROW][C]10[/C][C]-0.032966[/C][C]-0.323[/C][C]0.626302[/C][/ROW]
[ROW][C]11[/C][C]-0.172938[/C][C]-1.6944[/C][C]0.953289[/C][/ROW]
[ROW][C]12[/C][C]-0.086332[/C][C]-0.8459[/C][C]0.800138[/C][/ROW]
[ROW][C]13[/C][C]0.028293[/C][C]0.2772[/C][C]0.391105[/C][/ROW]
[ROW][C]14[/C][C]-0.123993[/C][C]-1.2149[/C][C]0.886305[/C][/ROW]
[ROW][C]15[/C][C]0.106397[/C][C]1.0425[/C][C]0.149906[/C][/ROW]
[ROW][C]16[/C][C]-0.014398[/C][C]-0.1411[/C][C]0.555946[/C][/ROW]
[ROW][C]17[/C][C]-0.049854[/C][C]-0.4885[/C][C]0.686834[/C][/ROW]
[ROW][C]18[/C][C]-0.004577[/C][C]-0.0448[/C][C]0.517839[/C][/ROW]
[ROW][C]19[/C][C]-0.021366[/C][C]-0.2093[/C][C]0.582688[/C][/ROW]
[ROW][C]20[/C][C]0.033874[/C][C]0.3319[/C][C]0.370345[/C][/ROW]
[ROW][C]21[/C][C]0.025683[/C][C]0.2516[/C][C]0.400928[/C][/ROW]
[ROW][C]22[/C][C]0.015269[/C][C]0.1496[/C][C]0.440694[/C][/ROW]
[ROW][C]23[/C][C]0.016374[/C][C]0.1604[/C][C]0.43644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7742&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7742&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	0.947915	9.2876	0
1	-0.163981	-1.6067	0.944295
2	-0.135326	-1.3259	0.905993
3	-0.039071	-0.3828	0.648649
4	0.110919	1.0868	0.139927
5	-0.091965	-0.9011	0.815096
6	-0.002341	-0.0229	0.509127
7	0.028576	0.28	0.390047
8	-0.008041	-0.0788	0.531315
9	0.075293	0.7377	0.231243
10	-0.032966	-0.323	0.626302
11	-0.172938	-1.6944	0.953289
12	-0.086332	-0.8459	0.800138
13	0.028293	0.2772	0.391105
14	-0.123993	-1.2149	0.886305
15	0.106397	1.0425	0.149906
16	-0.014398	-0.1411	0.555946
17	-0.049854	-0.4885	0.686834
18	-0.004577	-0.0448	0.517839
19	-0.021366	-0.2093	0.582688
20	0.033874	0.3319	0.370345
21	0.025683	0.2516	0.400928
22	0.015269	0.1496	0.440694
23	0.016374	0.1604	0.43644

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 24 ; 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 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code