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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 06:09:46 -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/22/t11957364977iv2t9a6mism26m.htm/, Retrieved Thu, 02 May 2024 17:34:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5972, Retrieved Thu, 02 May 2024 17:34:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

WS10 G29 Q2

Estimated Impact

178

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

-       [(Partial) Autocorrelation Function] [Partial auto corr] [2007-11-22 13:09:46] [7a600ca82a81f1b71fd92dcbb183f5b4] [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	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=5972&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=5972&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5972&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	11.8743	0
1	0.953128	11.3178	0
2	0.90308	10.7235	0
3	0.850189	10.0954	0
4	0.790178	9.3828	0
5	0.739611	8.7824	0
6	0.705892	8.382	0
7	0.674964	8.0147	0
8	0.646369	7.6752	0
9	0.625314	7.4252	0
10	0.606784	7.2052	0
11	0.586197	6.9607	0
12	0.567557	6.7394	0
13	0.546592	6.4904	0
14	0.514167	6.1054	0
15	0.471099	5.594	0
16	0.433659	5.1494	0
17	0.390215	4.6335	4e-06
18	0.354409	4.2084	2.3e-05
19	0.322793	3.833	9.5e-05
20	0.28596	3.3956	0.000445

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 11.8743 & 0 \tabularnewline
1 & 0.953128 & 11.3178 & 0 \tabularnewline
2 & 0.90308 & 10.7235 & 0 \tabularnewline
3 & 0.850189 & 10.0954 & 0 \tabularnewline
4 & 0.790178 & 9.3828 & 0 \tabularnewline
5 & 0.739611 & 8.7824 & 0 \tabularnewline
6 & 0.705892 & 8.382 & 0 \tabularnewline
7 & 0.674964 & 8.0147 & 0 \tabularnewline
8 & 0.646369 & 7.6752 & 0 \tabularnewline
9 & 0.625314 & 7.4252 & 0 \tabularnewline
10 & 0.606784 & 7.2052 & 0 \tabularnewline
11 & 0.586197 & 6.9607 & 0 \tabularnewline
12 & 0.567557 & 6.7394 & 0 \tabularnewline
13 & 0.546592 & 6.4904 & 0 \tabularnewline
14 & 0.514167 & 6.1054 & 0 \tabularnewline
15 & 0.471099 & 5.594 & 0 \tabularnewline
16 & 0.433659 & 5.1494 & 0 \tabularnewline
17 & 0.390215 & 4.6335 & 4e-06 \tabularnewline
18 & 0.354409 & 4.2084 & 2.3e-05 \tabularnewline
19 & 0.322793 & 3.833 & 9.5e-05 \tabularnewline
20 & 0.28596 & 3.3956 & 0.000445 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5972&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]11.8743[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.953128[/C][C]11.3178[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.90308[/C][C]10.7235[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.850189[/C][C]10.0954[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.790178[/C][C]9.3828[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.739611[/C][C]8.7824[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.705892[/C][C]8.382[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.674964[/C][C]8.0147[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.646369[/C][C]7.6752[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.625314[/C][C]7.4252[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.606784[/C][C]7.2052[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.586197[/C][C]6.9607[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.567557[/C][C]6.7394[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.546592[/C][C]6.4904[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.514167[/C][C]6.1054[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.471099[/C][C]5.594[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.433659[/C][C]5.1494[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.390215[/C][C]4.6335[/C][C]4e-06[/C][/ROW]
[ROW][C]18[/C][C]0.354409[/C][C]4.2084[/C][C]2.3e-05[/C][/ROW]
[ROW][C]19[/C][C]0.322793[/C][C]3.833[/C][C]9.5e-05[/C][/ROW]
[ROW][C]20[/C][C]0.28596[/C][C]3.3956[/C][C]0.000445[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5972&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5972&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	11.8743	0
1	0.953128	11.3178	0
2	0.90308	10.7235	0
3	0.850189	10.0954	0
4	0.790178	9.3828	0
5	0.739611	8.7824	0
6	0.705892	8.382	0
7	0.674964	8.0147	0
8	0.646369	7.6752	0
9	0.625314	7.4252	0
10	0.606784	7.2052	0
11	0.586197	6.9607	0
12	0.567557	6.7394	0
13	0.546592	6.4904	0
14	0.514167	6.1054	0
15	0.471099	5.594	0
16	0.433659	5.1494	0
17	0.390215	4.6335	4e-06
18	0.354409	4.2084	2.3e-05
19	0.322793	3.833	9.5e-05
20	0.28596	3.3956	0.000445

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.953128	11.3178	0
1	-0.058699	-0.697	0.756527
2	-0.056335	-0.6689	0.747687
3	-0.104993	-1.2467	0.892717
4	0.076403	0.9072	0.182916
5	0.156741	1.8612	0.032399
6	0.000171	0.002	0.499191
7	-0.025486	-0.3026	0.618692
8	0.043443	0.5159	0.303382
9	0.041746	0.4957	0.310436
10	-0.00944	-0.1121	0.544544
11	0.001959	0.0233	0.490737
12	-0.029496	-0.3502	0.63666
13	-0.111551	-1.3246	0.906275
14	-0.12596	-1.4957	0.931515
15	0.059465	0.7061	0.240643
16	-0.058664	-0.6966	0.756399
17	0.052363	0.6218	0.267545
18	-0.048558	-0.5766	0.717433
19	-0.112692	-1.3381	0.908498
20	-0.078743	-0.935	0.824313

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.953128 & 11.3178 & 0 \tabularnewline
1 & -0.058699 & -0.697 & 0.756527 \tabularnewline
2 & -0.056335 & -0.6689 & 0.747687 \tabularnewline
3 & -0.104993 & -1.2467 & 0.892717 \tabularnewline
4 & 0.076403 & 0.9072 & 0.182916 \tabularnewline
5 & 0.156741 & 1.8612 & 0.032399 \tabularnewline
6 & 0.000171 & 0.002 & 0.499191 \tabularnewline
7 & -0.025486 & -0.3026 & 0.618692 \tabularnewline
8 & 0.043443 & 0.5159 & 0.303382 \tabularnewline
9 & 0.041746 & 0.4957 & 0.310436 \tabularnewline
10 & -0.00944 & -0.1121 & 0.544544 \tabularnewline
11 & 0.001959 & 0.0233 & 0.490737 \tabularnewline
12 & -0.029496 & -0.3502 & 0.63666 \tabularnewline
13 & -0.111551 & -1.3246 & 0.906275 \tabularnewline
14 & -0.12596 & -1.4957 & 0.931515 \tabularnewline
15 & 0.059465 & 0.7061 & 0.240643 \tabularnewline
16 & -0.058664 & -0.6966 & 0.756399 \tabularnewline
17 & 0.052363 & 0.6218 & 0.267545 \tabularnewline
18 & -0.048558 & -0.5766 & 0.717433 \tabularnewline
19 & -0.112692 & -1.3381 & 0.908498 \tabularnewline
20 & -0.078743 & -0.935 & 0.824313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5972&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]0.953128[/C][C]11.3178[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.058699[/C][C]-0.697[/C][C]0.756527[/C][/ROW]
[ROW][C]2[/C][C]-0.056335[/C][C]-0.6689[/C][C]0.747687[/C][/ROW]
[ROW][C]3[/C][C]-0.104993[/C][C]-1.2467[/C][C]0.892717[/C][/ROW]
[ROW][C]4[/C][C]0.076403[/C][C]0.9072[/C][C]0.182916[/C][/ROW]
[ROW][C]5[/C][C]0.156741[/C][C]1.8612[/C][C]0.032399[/C][/ROW]
[ROW][C]6[/C][C]0.000171[/C][C]0.002[/C][C]0.499191[/C][/ROW]
[ROW][C]7[/C][C]-0.025486[/C][C]-0.3026[/C][C]0.618692[/C][/ROW]
[ROW][C]8[/C][C]0.043443[/C][C]0.5159[/C][C]0.303382[/C][/ROW]
[ROW][C]9[/C][C]0.041746[/C][C]0.4957[/C][C]0.310436[/C][/ROW]
[ROW][C]10[/C][C]-0.00944[/C][C]-0.1121[/C][C]0.544544[/C][/ROW]
[ROW][C]11[/C][C]0.001959[/C][C]0.0233[/C][C]0.490737[/C][/ROW]
[ROW][C]12[/C][C]-0.029496[/C][C]-0.3502[/C][C]0.63666[/C][/ROW]
[ROW][C]13[/C][C]-0.111551[/C][C]-1.3246[/C][C]0.906275[/C][/ROW]
[ROW][C]14[/C][C]-0.12596[/C][C]-1.4957[/C][C]0.931515[/C][/ROW]
[ROW][C]15[/C][C]0.059465[/C][C]0.7061[/C][C]0.240643[/C][/ROW]
[ROW][C]16[/C][C]-0.058664[/C][C]-0.6966[/C][C]0.756399[/C][/ROW]
[ROW][C]17[/C][C]0.052363[/C][C]0.6218[/C][C]0.267545[/C][/ROW]
[ROW][C]18[/C][C]-0.048558[/C][C]-0.5766[/C][C]0.717433[/C][/ROW]
[ROW][C]19[/C][C]-0.112692[/C][C]-1.3381[/C][C]0.908498[/C][/ROW]
[ROW][C]20[/C][C]-0.078743[/C][C]-0.935[/C][C]0.824313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5972&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5972&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	0.953128	11.3178	0
1	-0.058699	-0.697	0.756527
2	-0.056335	-0.6689	0.747687
3	-0.104993	-1.2467	0.892717
4	0.076403	0.9072	0.182916
5	0.156741	1.8612	0.032399
6	0.000171	0.002	0.499191
7	-0.025486	-0.3026	0.618692
8	0.043443	0.5159	0.303382
9	0.041746	0.4957	0.310436
10	-0.00944	-0.1121	0.544544
11	0.001959	0.0233	0.490737
12	-0.029496	-0.3502	0.63666
13	-0.111551	-1.3246	0.906275
14	-0.12596	-1.4957	0.931515
15	0.059465	0.7061	0.240643
16	-0.058664	-0.6966	0.756399
17	0.052363	0.6218	0.267545
18	-0.048558	-0.5766	0.717433
19	-0.112692	-1.3381	0.908498
20	-0.078743	-0.935	0.824313

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 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code