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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

Sun, 06 Jan 2008 13:51:21 -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/Jan/06/t11996526560lcjcx1zuw388gk.htm/, Retrieved Sun, 05 May 2024 03:59:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7896, Retrieved Sun, 05 May 2024 03:59:13 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

inducing time seris Q2b TI

Estimated Impact

155

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

-     [Central Tendency] [WS2 - Robustness ...] [2007-10-20 13:06:37] [5343e105a400b9e32bf6f011133bbaf4]
- RM D    [(Partial) Autocorrelation Function] [CVWS7TIQ2b] [2008-01-06 20:51:21] [b523c8d839cc24a05ea912c062a47207] [Current]

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Dataseries X:

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Histogram

Boxplots

-12.7
-2.4
7.1
-3.9
9.5
5
-16.1
-10.8
7
13.6
8.1
-8.1
4.9
-0.8
4.3
4
1.5
5.4
-11.3
-16.4
-2
8.9
-7.2
-18
1.3
6.3
-6
2.8
2
5.1
-7.6
-18.6
5.8
20.3
0.7
-11.2
-5.7
-0.1
3.4
3.3
-1.2
4.2
-8.8
-25.3
8.5
14.5
-3.1
-10.4
-2.9
0.3
22.6
15.4
9
29.1
2.8
-3.8
27.7
28.9
26.5
19.8
13.2
14.1
34.1
30
21.8
32.1
5.3
3
17.1
26.3
38.1
19.5
38
35.5
78.6
62.2
76.9
104.9
32.2
42.5
64.3
74.9
75.4
43
58.7
55.4
76.6
63.3
78.9
82.7

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=7896&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=7896&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7896&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	8.775	0
1	-0.332411	-2.9169	0.997685
2	-0.089278	-0.7834	0.782106
3	0.288894	2.535	0.006636
4	-0.079556	-0.6981	0.75639
5	0.097959	0.8596	0.196343
6	-0.056749	-0.498	0.690039
7	0.034969	0.3069	0.379893
8	0.02089	0.1833	0.427519
9	-0.109519	-0.961	0.830226
10	-0.061026	-0.5355	0.703077
11	0.064947	0.5699	0.285199
12	-0.148787	-1.3056	0.902212
13	-0.067309	-0.5906	0.721754
14	0.016677	0.1463	0.442016
15	-0.01817	-0.1594	0.563132
16	-0.113305	-0.9942	0.838391
17	0.032524	0.2854	0.388052
18	0.077586	0.6808	0.249015

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.775 & 0 \tabularnewline
1 & -0.332411 & -2.9169 & 0.997685 \tabularnewline
2 & -0.089278 & -0.7834 & 0.782106 \tabularnewline
3 & 0.288894 & 2.535 & 0.006636 \tabularnewline
4 & -0.079556 & -0.6981 & 0.75639 \tabularnewline
5 & 0.097959 & 0.8596 & 0.196343 \tabularnewline
6 & -0.056749 & -0.498 & 0.690039 \tabularnewline
7 & 0.034969 & 0.3069 & 0.379893 \tabularnewline
8 & 0.02089 & 0.1833 & 0.427519 \tabularnewline
9 & -0.109519 & -0.961 & 0.830226 \tabularnewline
10 & -0.061026 & -0.5355 & 0.703077 \tabularnewline
11 & 0.064947 & 0.5699 & 0.285199 \tabularnewline
12 & -0.148787 & -1.3056 & 0.902212 \tabularnewline
13 & -0.067309 & -0.5906 & 0.721754 \tabularnewline
14 & 0.016677 & 0.1463 & 0.442016 \tabularnewline
15 & -0.01817 & -0.1594 & 0.563132 \tabularnewline
16 & -0.113305 & -0.9942 & 0.838391 \tabularnewline
17 & 0.032524 & 0.2854 & 0.388052 \tabularnewline
18 & 0.077586 & 0.6808 & 0.249015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7896&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]8.775[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.332411[/C][C]-2.9169[/C][C]0.997685[/C][/ROW]
[ROW][C]2[/C][C]-0.089278[/C][C]-0.7834[/C][C]0.782106[/C][/ROW]
[ROW][C]3[/C][C]0.288894[/C][C]2.535[/C][C]0.006636[/C][/ROW]
[ROW][C]4[/C][C]-0.079556[/C][C]-0.6981[/C][C]0.75639[/C][/ROW]
[ROW][C]5[/C][C]0.097959[/C][C]0.8596[/C][C]0.196343[/C][/ROW]
[ROW][C]6[/C][C]-0.056749[/C][C]-0.498[/C][C]0.690039[/C][/ROW]
[ROW][C]7[/C][C]0.034969[/C][C]0.3069[/C][C]0.379893[/C][/ROW]
[ROW][C]8[/C][C]0.02089[/C][C]0.1833[/C][C]0.427519[/C][/ROW]
[ROW][C]9[/C][C]-0.109519[/C][C]-0.961[/C][C]0.830226[/C][/ROW]
[ROW][C]10[/C][C]-0.061026[/C][C]-0.5355[/C][C]0.703077[/C][/ROW]
[ROW][C]11[/C][C]0.064947[/C][C]0.5699[/C][C]0.285199[/C][/ROW]
[ROW][C]12[/C][C]-0.148787[/C][C]-1.3056[/C][C]0.902212[/C][/ROW]
[ROW][C]13[/C][C]-0.067309[/C][C]-0.5906[/C][C]0.721754[/C][/ROW]
[ROW][C]14[/C][C]0.016677[/C][C]0.1463[/C][C]0.442016[/C][/ROW]
[ROW][C]15[/C][C]-0.01817[/C][C]-0.1594[/C][C]0.563132[/C][/ROW]
[ROW][C]16[/C][C]-0.113305[/C][C]-0.9942[/C][C]0.838391[/C][/ROW]
[ROW][C]17[/C][C]0.032524[/C][C]0.2854[/C][C]0.388052[/C][/ROW]
[ROW][C]18[/C][C]0.077586[/C][C]0.6808[/C][C]0.249015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7896&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7896&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	8.775	0
1	-0.332411	-2.9169	0.997685
2	-0.089278	-0.7834	0.782106
3	0.288894	2.535	0.006636
4	-0.079556	-0.6981	0.75639
5	0.097959	0.8596	0.196343
6	-0.056749	-0.498	0.690039
7	0.034969	0.3069	0.379893
8	0.02089	0.1833	0.427519
9	-0.109519	-0.961	0.830226
10	-0.061026	-0.5355	0.703077
11	0.064947	0.5699	0.285199
12	-0.148787	-1.3056	0.902212
13	-0.067309	-0.5906	0.721754
14	0.016677	0.1463	0.442016
15	-0.01817	-0.1594	0.563132
16	-0.113305	-0.9942	0.838391
17	0.032524	0.2854	0.388052
18	0.077586	0.6808	0.249015

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.332411	-2.9169	0.997685
1	-0.224592	-1.9708	0.973829
2	0.210618	1.8482	0.034209
3	0.101581	0.8914	0.187753
4	0.199675	1.7521	0.041865
5	-0.036034	-0.3162	0.623645
6	0.008465	0.0743	0.470489
7	-0.05612	-0.4925	0.688099
8	-0.115096	-1.01	0.842161
9	-0.212341	-1.8633	0.966883
10	-0.040893	-0.3588	0.639651
11	-0.141734	-1.2437	0.89131
12	-0.101214	-0.8881	0.811386
13	-0.072905	-0.6397	0.73788
14	0.063066	0.5534	0.290797
15	-0.065213	-0.5722	0.715587
16	0.045179	0.3964	0.346436
17	0.096624	0.8479	0.199567
18	0.089744	0.7875	0.216702

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.332411 & -2.9169 & 0.997685 \tabularnewline
1 & -0.224592 & -1.9708 & 0.973829 \tabularnewline
2 & 0.210618 & 1.8482 & 0.034209 \tabularnewline
3 & 0.101581 & 0.8914 & 0.187753 \tabularnewline
4 & 0.199675 & 1.7521 & 0.041865 \tabularnewline
5 & -0.036034 & -0.3162 & 0.623645 \tabularnewline
6 & 0.008465 & 0.0743 & 0.470489 \tabularnewline
7 & -0.05612 & -0.4925 & 0.688099 \tabularnewline
8 & -0.115096 & -1.01 & 0.842161 \tabularnewline
9 & -0.212341 & -1.8633 & 0.966883 \tabularnewline
10 & -0.040893 & -0.3588 & 0.639651 \tabularnewline
11 & -0.141734 & -1.2437 & 0.89131 \tabularnewline
12 & -0.101214 & -0.8881 & 0.811386 \tabularnewline
13 & -0.072905 & -0.6397 & 0.73788 \tabularnewline
14 & 0.063066 & 0.5534 & 0.290797 \tabularnewline
15 & -0.065213 & -0.5722 & 0.715587 \tabularnewline
16 & 0.045179 & 0.3964 & 0.346436 \tabularnewline
17 & 0.096624 & 0.8479 & 0.199567 \tabularnewline
18 & 0.089744 & 0.7875 & 0.216702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7896&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]-0.332411[/C][C]-2.9169[/C][C]0.997685[/C][/ROW]
[ROW][C]1[/C][C]-0.224592[/C][C]-1.9708[/C][C]0.973829[/C][/ROW]
[ROW][C]2[/C][C]0.210618[/C][C]1.8482[/C][C]0.034209[/C][/ROW]
[ROW][C]3[/C][C]0.101581[/C][C]0.8914[/C][C]0.187753[/C][/ROW]
[ROW][C]4[/C][C]0.199675[/C][C]1.7521[/C][C]0.041865[/C][/ROW]
[ROW][C]5[/C][C]-0.036034[/C][C]-0.3162[/C][C]0.623645[/C][/ROW]
[ROW][C]6[/C][C]0.008465[/C][C]0.0743[/C][C]0.470489[/C][/ROW]
[ROW][C]7[/C][C]-0.05612[/C][C]-0.4925[/C][C]0.688099[/C][/ROW]
[ROW][C]8[/C][C]-0.115096[/C][C]-1.01[/C][C]0.842161[/C][/ROW]
[ROW][C]9[/C][C]-0.212341[/C][C]-1.8633[/C][C]0.966883[/C][/ROW]
[ROW][C]10[/C][C]-0.040893[/C][C]-0.3588[/C][C]0.639651[/C][/ROW]
[ROW][C]11[/C][C]-0.141734[/C][C]-1.2437[/C][C]0.89131[/C][/ROW]
[ROW][C]12[/C][C]-0.101214[/C][C]-0.8881[/C][C]0.811386[/C][/ROW]
[ROW][C]13[/C][C]-0.072905[/C][C]-0.6397[/C][C]0.73788[/C][/ROW]
[ROW][C]14[/C][C]0.063066[/C][C]0.5534[/C][C]0.290797[/C][/ROW]
[ROW][C]15[/C][C]-0.065213[/C][C]-0.5722[/C][C]0.715587[/C][/ROW]
[ROW][C]16[/C][C]0.045179[/C][C]0.3964[/C][C]0.346436[/C][/ROW]
[ROW][C]17[/C][C]0.096624[/C][C]0.8479[/C][C]0.199567[/C][/ROW]
[ROW][C]18[/C][C]0.089744[/C][C]0.7875[/C][C]0.216702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7896&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7896&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	-0.332411	-2.9169	0.997685
1	-0.224592	-1.9708	0.973829
2	0.210618	1.8482	0.034209
3	0.101581	0.8914	0.187753
4	0.199675	1.7521	0.041865
5	-0.036034	-0.3162	0.623645
6	0.008465	0.0743	0.470489
7	-0.05612	-0.4925	0.688099
8	-0.115096	-1.01	0.842161
9	-0.212341	-1.8633	0.966883
10	-0.040893	-0.3588	0.639651
11	-0.141734	-1.2437	0.89131
12	-0.101214	-0.8881	0.811386
13	-0.072905	-0.6397	0.73788
14	0.063066	0.5534	0.290797
15	-0.065213	-0.5722	0.715587
16	0.045179	0.3964	0.346436
17	0.096624	0.8479	0.199567
18	0.089744	0.7875	0.216702

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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