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Author's title

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

Mon, 05 Dec 2011 13:35:17 -0500

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/2011/Dec/05/t1323110131mmqgsxv8dnaxjmc.htm/, Retrieved Fri, 03 May 2024 11:20:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151152, Retrieved Fri, 03 May 2024 11:20:34 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
- R  D            [(Partial) Autocorrelation Function] [ws9-2] [2011-12-05 18:26:48] [f7a862281046b7153543b12c78921b36]
-   P                 [(Partial) Autocorrelation Function] [ws9-3] [2011-12-05 18:35:17] [47995d3a8fac585eeb070a274b466f8c] [Current]
-   P                   [(Partial) Autocorrelation Function] [ws9-4] [2011-12-05 18:43:50] [f7a862281046b7153543b12c78921b36] 
-   P                     [(Partial) Autocorrelation Function] [ws9-4] [2011-12-05 18:46:25] [f7a862281046b7153543b12c78921b36] 
-   P                       [(Partial) Autocorrelation Function] [ws9-4] [2011-12-05 19:34:03] [f7a862281046b7153543b12c78921b36] 
-                             [(Partial) Autocorrelation Function] [ws9-4] [2011-12-05 19:35:13] [f7a862281046b7153543b12c78921b36] 
-  MP                           [(Partial) Autocorrelation Function] [paper2-3] [2011-12-21 20:49:59] [f7a862281046b7153543b12c78921b36] 
-   P                   [(Partial) Autocorrelation Function] [ws9-3] [2011-12-05 19:28:00] [f7a862281046b7153543b12c78921b36] 
-  MP                     [(Partial) Autocorrelation Function] [paper2-2] [2011-12-21 20:48:46] [f7a862281046b7153543b12c78921b36] 

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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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151152&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151152&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151152&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.653944	-5.023	3e-06
2	0.211141	1.6218	0.055089
3	0.091677	0.7042	0.242044
4	-0.298158	-2.2902	0.012801
5	0.438647	3.3693	0.000666
6	-0.487321	-3.7432	0.000207
7	0.217344	1.6694	0.050163
8	-0.007017	-0.0539	0.4786
9	-0.09759	-0.7496	0.228235
10	0.198338	1.5235	0.066492
11	-0.402832	-3.0942	0.001507
12	0.584233	4.4876	1.7e-05
13	-0.372211	-2.859	0.002933
14	0.1271	0.9763	0.166458
15	0.083385	0.6405	0.262165
16	-0.277818	-2.134	0.018507
17	0.428167	3.2888	0.00085

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.653944 & -5.023 & 3e-06 \tabularnewline
2 & 0.211141 & 1.6218 & 0.055089 \tabularnewline
3 & 0.091677 & 0.7042 & 0.242044 \tabularnewline
4 & -0.298158 & -2.2902 & 0.012801 \tabularnewline
5 & 0.438647 & 3.3693 & 0.000666 \tabularnewline
6 & -0.487321 & -3.7432 & 0.000207 \tabularnewline
7 & 0.217344 & 1.6694 & 0.050163 \tabularnewline
8 & -0.007017 & -0.0539 & 0.4786 \tabularnewline
9 & -0.09759 & -0.7496 & 0.228235 \tabularnewline
10 & 0.198338 & 1.5235 & 0.066492 \tabularnewline
11 & -0.402832 & -3.0942 & 0.001507 \tabularnewline
12 & 0.584233 & 4.4876 & 1.7e-05 \tabularnewline
13 & -0.372211 & -2.859 & 0.002933 \tabularnewline
14 & 0.1271 & 0.9763 & 0.166458 \tabularnewline
15 & 0.083385 & 0.6405 & 0.262165 \tabularnewline
16 & -0.277818 & -2.134 & 0.018507 \tabularnewline
17 & 0.428167 & 3.2888 & 0.00085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151152&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]-0.653944[/C][C]-5.023[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.211141[/C][C]1.6218[/C][C]0.055089[/C][/ROW]
[ROW][C]3[/C][C]0.091677[/C][C]0.7042[/C][C]0.242044[/C][/ROW]
[ROW][C]4[/C][C]-0.298158[/C][C]-2.2902[/C][C]0.012801[/C][/ROW]
[ROW][C]5[/C][C]0.438647[/C][C]3.3693[/C][C]0.000666[/C][/ROW]
[ROW][C]6[/C][C]-0.487321[/C][C]-3.7432[/C][C]0.000207[/C][/ROW]
[ROW][C]7[/C][C]0.217344[/C][C]1.6694[/C][C]0.050163[/C][/ROW]
[ROW][C]8[/C][C]-0.007017[/C][C]-0.0539[/C][C]0.4786[/C][/ROW]
[ROW][C]9[/C][C]-0.09759[/C][C]-0.7496[/C][C]0.228235[/C][/ROW]
[ROW][C]10[/C][C]0.198338[/C][C]1.5235[/C][C]0.066492[/C][/ROW]
[ROW][C]11[/C][C]-0.402832[/C][C]-3.0942[/C][C]0.001507[/C][/ROW]
[ROW][C]12[/C][C]0.584233[/C][C]4.4876[/C][C]1.7e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.372211[/C][C]-2.859[/C][C]0.002933[/C][/ROW]
[ROW][C]14[/C][C]0.1271[/C][C]0.9763[/C][C]0.166458[/C][/ROW]
[ROW][C]15[/C][C]0.083385[/C][C]0.6405[/C][C]0.262165[/C][/ROW]
[ROW][C]16[/C][C]-0.277818[/C][C]-2.134[/C][C]0.018507[/C][/ROW]
[ROW][C]17[/C][C]0.428167[/C][C]3.2888[/C][C]0.00085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151152&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151152&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	-0.653944	-5.023	3e-06
2	0.211141	1.6218	0.055089
3	0.091677	0.7042	0.242044
4	-0.298158	-2.2902	0.012801
5	0.438647	3.3693	0.000666
6	-0.487321	-3.7432	0.000207
7	0.217344	1.6694	0.050163
8	-0.007017	-0.0539	0.4786
9	-0.09759	-0.7496	0.228235
10	0.198338	1.5235	0.066492
11	-0.402832	-3.0942	0.001507
12	0.584233	4.4876	1.7e-05
13	-0.372211	-2.859	0.002933
14	0.1271	0.9763	0.166458
15	0.083385	0.6405	0.262165
16	-0.277818	-2.134	0.018507
17	0.428167	3.2888	0.00085

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.653944	-5.023	3e-06
2	-0.378263	-2.9055	0.002578
3	0.070581	0.5421	0.294881
4	-0.215946	-1.6587	0.051241
5	0.217627	1.6716	0.049947
6	-0.193448	-1.4859	0.071315
7	-0.332353	-2.5529	0.006646
8	-0.290211	-2.2292	0.014812
9	-0.072682	-0.5583	0.289383
10	0.045783	0.3517	0.363171
11	-0.440768	-3.3856	0.000634
12	0.209212	1.607	0.056698
13	0.185516	1.425	0.079717
14	0.153265	1.1773	0.121911
15	0.078276	0.6013	0.274988
16	0.002441	0.0187	0.492552
17	0.016082	0.1235	0.451053

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.653944 & -5.023 & 3e-06 \tabularnewline
2 & -0.378263 & -2.9055 & 0.002578 \tabularnewline
3 & 0.070581 & 0.5421 & 0.294881 \tabularnewline
4 & -0.215946 & -1.6587 & 0.051241 \tabularnewline
5 & 0.217627 & 1.6716 & 0.049947 \tabularnewline
6 & -0.193448 & -1.4859 & 0.071315 \tabularnewline
7 & -0.332353 & -2.5529 & 0.006646 \tabularnewline
8 & -0.290211 & -2.2292 & 0.014812 \tabularnewline
9 & -0.072682 & -0.5583 & 0.289383 \tabularnewline
10 & 0.045783 & 0.3517 & 0.363171 \tabularnewline
11 & -0.440768 & -3.3856 & 0.000634 \tabularnewline
12 & 0.209212 & 1.607 & 0.056698 \tabularnewline
13 & 0.185516 & 1.425 & 0.079717 \tabularnewline
14 & 0.153265 & 1.1773 & 0.121911 \tabularnewline
15 & 0.078276 & 0.6013 & 0.274988 \tabularnewline
16 & 0.002441 & 0.0187 & 0.492552 \tabularnewline
17 & 0.016082 & 0.1235 & 0.451053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151152&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]-0.653944[/C][C]-5.023[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.378263[/C][C]-2.9055[/C][C]0.002578[/C][/ROW]
[ROW][C]3[/C][C]0.070581[/C][C]0.5421[/C][C]0.294881[/C][/ROW]
[ROW][C]4[/C][C]-0.215946[/C][C]-1.6587[/C][C]0.051241[/C][/ROW]
[ROW][C]5[/C][C]0.217627[/C][C]1.6716[/C][C]0.049947[/C][/ROW]
[ROW][C]6[/C][C]-0.193448[/C][C]-1.4859[/C][C]0.071315[/C][/ROW]
[ROW][C]7[/C][C]-0.332353[/C][C]-2.5529[/C][C]0.006646[/C][/ROW]
[ROW][C]8[/C][C]-0.290211[/C][C]-2.2292[/C][C]0.014812[/C][/ROW]
[ROW][C]9[/C][C]-0.072682[/C][C]-0.5583[/C][C]0.289383[/C][/ROW]
[ROW][C]10[/C][C]0.045783[/C][C]0.3517[/C][C]0.363171[/C][/ROW]
[ROW][C]11[/C][C]-0.440768[/C][C]-3.3856[/C][C]0.000634[/C][/ROW]
[ROW][C]12[/C][C]0.209212[/C][C]1.607[/C][C]0.056698[/C][/ROW]
[ROW][C]13[/C][C]0.185516[/C][C]1.425[/C][C]0.079717[/C][/ROW]
[ROW][C]14[/C][C]0.153265[/C][C]1.1773[/C][C]0.121911[/C][/ROW]
[ROW][C]15[/C][C]0.078276[/C][C]0.6013[/C][C]0.274988[/C][/ROW]
[ROW][C]16[/C][C]0.002441[/C][C]0.0187[/C][C]0.492552[/C][/ROW]
[ROW][C]17[/C][C]0.016082[/C][C]0.1235[/C][C]0.451053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151152&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151152&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	-0.653944	-5.023	3e-06
2	-0.378263	-2.9055	0.002578
3	0.070581	0.5421	0.294881
4	-0.215946	-1.6587	0.051241
5	0.217627	1.6716	0.049947
6	-0.193448	-1.4859	0.071315
7	-0.332353	-2.5529	0.006646
8	-0.290211	-2.2292	0.014812
9	-0.072682	-0.5583	0.289383
10	0.045783	0.3517	0.363171
11	-0.440768	-3.3856	0.000634
12	0.209212	1.607	0.056698
13	0.185516	1.425	0.079717
14	0.153265	1.1773	0.121911
15	0.078276	0.6013	0.274988
16	0.002441	0.0187	0.492552
17	0.016082	0.1235	0.451053

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code