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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

Sat, 13 Dec 2008 03:41:47 -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/13/t1229164983yzy4nbtbnausp3a.htm/, Retrieved Sun, 19 May 2024 07:08:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32955, Retrieved Sun, 19 May 2024 07:08:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F   P   [Univariate Data Series] [unemployement] [2008-12-09 14:17:32] [74be16979710d4c4e7c6647856088456]
- RMPD      [(Partial) Autocorrelation Function] [EEEEEE] [2008-12-13 10:41:47] [59094f58b9d90d3694e930ebd2901ecd] [Current]

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Dataseries X:

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Histogram

Boxplots

7.5
7.2
6.9
6.7
6.4
6.3
6.8
7.3
7.1
7.1
6.8
6.5
6.3
6.1
6.1
6.3
6.3
6
6.2
6.4
6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8.0
8.1
8.2
8.3
8.2
8.0
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8.0
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9
6.8

Summary of computational 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 computational 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=32955&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]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=32955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32955&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.927725	9.5064	0
2	0.805896	8.258	0
3	0.697128	7.1434	0
4	0.631351	6.4694	0
5	0.616027	6.3124	0
6	0.614985	6.3017	0
7	0.588635	6.0317	0
8	0.552455	5.661	0
9	0.531413	5.4454	0
10	0.529352	5.4242	0
11	0.540157	5.535	0
12	0.531779	5.4491	0
13	0.457554	4.6885	4e-06
14	0.367953	3.7704	0.000135
15	0.28177	2.8873	0.002359
16	0.211396	2.1662	0.016281
17	0.168813	1.7298	0.043301
18	0.136322	1.3969	0.082696
19	0.091916	0.9419	0.174213
20	0.053573	0.549	0.292098

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927725 & 9.5064 & 0 \tabularnewline
2 & 0.805896 & 8.258 & 0 \tabularnewline
3 & 0.697128 & 7.1434 & 0 \tabularnewline
4 & 0.631351 & 6.4694 & 0 \tabularnewline
5 & 0.616027 & 6.3124 & 0 \tabularnewline
6 & 0.614985 & 6.3017 & 0 \tabularnewline
7 & 0.588635 & 6.0317 & 0 \tabularnewline
8 & 0.552455 & 5.661 & 0 \tabularnewline
9 & 0.531413 & 5.4454 & 0 \tabularnewline
10 & 0.529352 & 5.4242 & 0 \tabularnewline
11 & 0.540157 & 5.535 & 0 \tabularnewline
12 & 0.531779 & 5.4491 & 0 \tabularnewline
13 & 0.457554 & 4.6885 & 4e-06 \tabularnewline
14 & 0.367953 & 3.7704 & 0.000135 \tabularnewline
15 & 0.28177 & 2.8873 & 0.002359 \tabularnewline
16 & 0.211396 & 2.1662 & 0.016281 \tabularnewline
17 & 0.168813 & 1.7298 & 0.043301 \tabularnewline
18 & 0.136322 & 1.3969 & 0.082696 \tabularnewline
19 & 0.091916 & 0.9419 & 0.174213 \tabularnewline
20 & 0.053573 & 0.549 & 0.292098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32955&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]0.927725[/C][C]9.5064[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.805896[/C][C]8.258[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.697128[/C][C]7.1434[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.631351[/C][C]6.4694[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.616027[/C][C]6.3124[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.614985[/C][C]6.3017[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.588635[/C][C]6.0317[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.552455[/C][C]5.661[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.531413[/C][C]5.4454[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.529352[/C][C]5.4242[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.540157[/C][C]5.535[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.531779[/C][C]5.4491[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.457554[/C][C]4.6885[/C][C]4e-06[/C][/ROW]
[ROW][C]14[/C][C]0.367953[/C][C]3.7704[/C][C]0.000135[/C][/ROW]
[ROW][C]15[/C][C]0.28177[/C][C]2.8873[/C][C]0.002359[/C][/ROW]
[ROW][C]16[/C][C]0.211396[/C][C]2.1662[/C][C]0.016281[/C][/ROW]
[ROW][C]17[/C][C]0.168813[/C][C]1.7298[/C][C]0.043301[/C][/ROW]
[ROW][C]18[/C][C]0.136322[/C][C]1.3969[/C][C]0.082696[/C][/ROW]
[ROW][C]19[/C][C]0.091916[/C][C]0.9419[/C][C]0.174213[/C][/ROW]
[ROW][C]20[/C][C]0.053573[/C][C]0.549[/C][C]0.292098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32955&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	0.927725	9.5064	0
2	0.805896	8.258	0
3	0.697128	7.1434	0
4	0.631351	6.4694	0
5	0.616027	6.3124	0
6	0.614985	6.3017	0
7	0.588635	6.0317	0
8	0.552455	5.661	0
9	0.531413	5.4454	0
10	0.529352	5.4242	0
11	0.540157	5.535	0
12	0.531779	5.4491	0
13	0.457554	4.6885	4e-06
14	0.367953	3.7704	0.000135
15	0.28177	2.8873	0.002359
16	0.211396	2.1662	0.016281
17	0.168813	1.7298	0.043301
18	0.136322	1.3969	0.082696
19	0.091916	0.9419	0.174213
20	0.053573	0.549	0.292098

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.927725	9.5064	0
2	-0.393162	-4.0287	5.3e-05
3	0.172144	1.7639	0.040325
4	0.171488	1.7572	0.040897
5	0.195347	2.0017	0.023947
6	-0.059947	-0.6143	0.270182
7	-0.131135	-1.3437	0.090965
8	0.164848	1.6892	0.047075
9	0.159743	1.6369	0.052324
10	0.010721	0.1099	0.456367
11	-0.007305	-0.0749	0.470238
12	-0.123759	-1.2682	0.103773
13	-0.361514	-3.7044	0.00017
14	0.216422	2.2177	0.014366
15	-0.210877	-2.1608	0.01649
16	-0.131514	-1.3476	0.090341
17	-0.055808	-0.5719	0.28432
18	-0.028293	-0.2899	0.386227
19	-0.041395	-0.4242	0.336153
20	0.03984	0.4082	0.341966

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927725 & 9.5064 & 0 \tabularnewline
2 & -0.393162 & -4.0287 & 5.3e-05 \tabularnewline
3 & 0.172144 & 1.7639 & 0.040325 \tabularnewline
4 & 0.171488 & 1.7572 & 0.040897 \tabularnewline
5 & 0.195347 & 2.0017 & 0.023947 \tabularnewline
6 & -0.059947 & -0.6143 & 0.270182 \tabularnewline
7 & -0.131135 & -1.3437 & 0.090965 \tabularnewline
8 & 0.164848 & 1.6892 & 0.047075 \tabularnewline
9 & 0.159743 & 1.6369 & 0.052324 \tabularnewline
10 & 0.010721 & 0.1099 & 0.456367 \tabularnewline
11 & -0.007305 & -0.0749 & 0.470238 \tabularnewline
12 & -0.123759 & -1.2682 & 0.103773 \tabularnewline
13 & -0.361514 & -3.7044 & 0.00017 \tabularnewline
14 & 0.216422 & 2.2177 & 0.014366 \tabularnewline
15 & -0.210877 & -2.1608 & 0.01649 \tabularnewline
16 & -0.131514 & -1.3476 & 0.090341 \tabularnewline
17 & -0.055808 & -0.5719 & 0.28432 \tabularnewline
18 & -0.028293 & -0.2899 & 0.386227 \tabularnewline
19 & -0.041395 & -0.4242 & 0.336153 \tabularnewline
20 & 0.03984 & 0.4082 & 0.341966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32955&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]0.927725[/C][C]9.5064[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.393162[/C][C]-4.0287[/C][C]5.3e-05[/C][/ROW]
[ROW][C]3[/C][C]0.172144[/C][C]1.7639[/C][C]0.040325[/C][/ROW]
[ROW][C]4[/C][C]0.171488[/C][C]1.7572[/C][C]0.040897[/C][/ROW]
[ROW][C]5[/C][C]0.195347[/C][C]2.0017[/C][C]0.023947[/C][/ROW]
[ROW][C]6[/C][C]-0.059947[/C][C]-0.6143[/C][C]0.270182[/C][/ROW]
[ROW][C]7[/C][C]-0.131135[/C][C]-1.3437[/C][C]0.090965[/C][/ROW]
[ROW][C]8[/C][C]0.164848[/C][C]1.6892[/C][C]0.047075[/C][/ROW]
[ROW][C]9[/C][C]0.159743[/C][C]1.6369[/C][C]0.052324[/C][/ROW]
[ROW][C]10[/C][C]0.010721[/C][C]0.1099[/C][C]0.456367[/C][/ROW]
[ROW][C]11[/C][C]-0.007305[/C][C]-0.0749[/C][C]0.470238[/C][/ROW]
[ROW][C]12[/C][C]-0.123759[/C][C]-1.2682[/C][C]0.103773[/C][/ROW]
[ROW][C]13[/C][C]-0.361514[/C][C]-3.7044[/C][C]0.00017[/C][/ROW]
[ROW][C]14[/C][C]0.216422[/C][C]2.2177[/C][C]0.014366[/C][/ROW]
[ROW][C]15[/C][C]-0.210877[/C][C]-2.1608[/C][C]0.01649[/C][/ROW]
[ROW][C]16[/C][C]-0.131514[/C][C]-1.3476[/C][C]0.090341[/C][/ROW]
[ROW][C]17[/C][C]-0.055808[/C][C]-0.5719[/C][C]0.28432[/C][/ROW]
[ROW][C]18[/C][C]-0.028293[/C][C]-0.2899[/C][C]0.386227[/C][/ROW]
[ROW][C]19[/C][C]-0.041395[/C][C]-0.4242[/C][C]0.336153[/C][/ROW]
[ROW][C]20[/C][C]0.03984[/C][C]0.4082[/C][C]0.341966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32955&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	0.927725	9.5064	0
2	-0.393162	-4.0287	5.3e-05
3	0.172144	1.7639	0.040325
4	0.171488	1.7572	0.040897
5	0.195347	2.0017	0.023947
6	-0.059947	-0.6143	0.270182
7	-0.131135	-1.3437	0.090965
8	0.164848	1.6892	0.047075
9	0.159743	1.6369	0.052324
10	0.010721	0.1099	0.456367
11	-0.007305	-0.0749	0.470238
12	-0.123759	-1.2682	0.103773
13	-0.361514	-3.7044	0.00017
14	0.216422	2.2177	0.014366
15	-0.210877	-2.1608	0.01649
16	-0.131514	-1.3476	0.090341
17	-0.055808	-0.5719	0.28432
18	-0.028293	-0.2899	0.386227
19	-0.041395	-0.4242	0.336153
20	0.03984	0.4082	0.341966

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code