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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

Sat, 23 Jan 2010 12:23:21 -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/2010/Jan/23/t1264274648t3jycoyn1dmjq6f.htm/, Retrieved Sat, 04 May 2024 21:23:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72388, Retrieved Sat, 04 May 2024 21:23:59 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

206

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

-     [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-14 13:47:12] [379d6c32f73e3218fd773d79e4063d07]
-    D  [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-14 14:18:58] [379d6c32f73e3218fd773d79e4063d07]
-   P     [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-17 11:25:15] [379d6c32f73e3218fd773d79e4063d07]
-   P       [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-23 15:15:29] [379d6c32f73e3218fd773d79e4063d07]
-  MP           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-01-23 19:23:21] [f32a893c5a60da9308cd5d37e6977c4f] [Current]

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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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72388&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72388&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72388&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.273045	1.6154	0.057607
2	-0.217334	-1.2858	0.103484
3	-0.437634	-2.5891	0.006963
4	-0.199727	-1.1816	0.122666
5	0.312162	1.8468	0.036624
6	0.299748	1.7733	0.042438
7	0.090109	0.5331	0.29867
8	-0.296624	-1.7549	0.044018
9	-0.171121	-1.0124	0.159155
10	0.089831	0.5314	0.299233
11	0.136553	0.8079	0.212314
12	-0.067755	-0.4008	0.345486
13	-0.249137	-1.4739	0.074721
14	-0.10597	-0.6269	0.267387
15	0.054326	0.3214	0.374911
16	0.168128	0.9947	0.163364
17	0.031308	0.1852	0.427063
18	-0.20205	-1.1953	0.119994
19	-0.16368	-0.9683	0.169758
20	-0.055481	-0.3282	0.372346
21	0.119801	0.7088	0.241586
22	0.092651	0.5481	0.293541
23	0.034103	0.2018	0.420637
24	0.013699	0.081	0.467934

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.273045 & 1.6154 & 0.057607 \tabularnewline
2 & -0.217334 & -1.2858 & 0.103484 \tabularnewline
3 & -0.437634 & -2.5891 & 0.006963 \tabularnewline
4 & -0.199727 & -1.1816 & 0.122666 \tabularnewline
5 & 0.312162 & 1.8468 & 0.036624 \tabularnewline
6 & 0.299748 & 1.7733 & 0.042438 \tabularnewline
7 & 0.090109 & 0.5331 & 0.29867 \tabularnewline
8 & -0.296624 & -1.7549 & 0.044018 \tabularnewline
9 & -0.171121 & -1.0124 & 0.159155 \tabularnewline
10 & 0.089831 & 0.5314 & 0.299233 \tabularnewline
11 & 0.136553 & 0.8079 & 0.212314 \tabularnewline
12 & -0.067755 & -0.4008 & 0.345486 \tabularnewline
13 & -0.249137 & -1.4739 & 0.074721 \tabularnewline
14 & -0.10597 & -0.6269 & 0.267387 \tabularnewline
15 & 0.054326 & 0.3214 & 0.374911 \tabularnewline
16 & 0.168128 & 0.9947 & 0.163364 \tabularnewline
17 & 0.031308 & 0.1852 & 0.427063 \tabularnewline
18 & -0.20205 & -1.1953 & 0.119994 \tabularnewline
19 & -0.16368 & -0.9683 & 0.169758 \tabularnewline
20 & -0.055481 & -0.3282 & 0.372346 \tabularnewline
21 & 0.119801 & 0.7088 & 0.241586 \tabularnewline
22 & 0.092651 & 0.5481 & 0.293541 \tabularnewline
23 & 0.034103 & 0.2018 & 0.420637 \tabularnewline
24 & 0.013699 & 0.081 & 0.467934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72388&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]0.273045[/C][C]1.6154[/C][C]0.057607[/C][/ROW]
[ROW][C]2[/C][C]-0.217334[/C][C]-1.2858[/C][C]0.103484[/C][/ROW]
[ROW][C]3[/C][C]-0.437634[/C][C]-2.5891[/C][C]0.006963[/C][/ROW]
[ROW][C]4[/C][C]-0.199727[/C][C]-1.1816[/C][C]0.122666[/C][/ROW]
[ROW][C]5[/C][C]0.312162[/C][C]1.8468[/C][C]0.036624[/C][/ROW]
[ROW][C]6[/C][C]0.299748[/C][C]1.7733[/C][C]0.042438[/C][/ROW]
[ROW][C]7[/C][C]0.090109[/C][C]0.5331[/C][C]0.29867[/C][/ROW]
[ROW][C]8[/C][C]-0.296624[/C][C]-1.7549[/C][C]0.044018[/C][/ROW]
[ROW][C]9[/C][C]-0.171121[/C][C]-1.0124[/C][C]0.159155[/C][/ROW]
[ROW][C]10[/C][C]0.089831[/C][C]0.5314[/C][C]0.299233[/C][/ROW]
[ROW][C]11[/C][C]0.136553[/C][C]0.8079[/C][C]0.212314[/C][/ROW]
[ROW][C]12[/C][C]-0.067755[/C][C]-0.4008[/C][C]0.345486[/C][/ROW]
[ROW][C]13[/C][C]-0.249137[/C][C]-1.4739[/C][C]0.074721[/C][/ROW]
[ROW][C]14[/C][C]-0.10597[/C][C]-0.6269[/C][C]0.267387[/C][/ROW]
[ROW][C]15[/C][C]0.054326[/C][C]0.3214[/C][C]0.374911[/C][/ROW]
[ROW][C]16[/C][C]0.168128[/C][C]0.9947[/C][C]0.163364[/C][/ROW]
[ROW][C]17[/C][C]0.031308[/C][C]0.1852[/C][C]0.427063[/C][/ROW]
[ROW][C]18[/C][C]-0.20205[/C][C]-1.1953[/C][C]0.119994[/C][/ROW]
[ROW][C]19[/C][C]-0.16368[/C][C]-0.9683[/C][C]0.169758[/C][/ROW]
[ROW][C]20[/C][C]-0.055481[/C][C]-0.3282[/C][C]0.372346[/C][/ROW]
[ROW][C]21[/C][C]0.119801[/C][C]0.7088[/C][C]0.241586[/C][/ROW]
[ROW][C]22[/C][C]0.092651[/C][C]0.5481[/C][C]0.293541[/C][/ROW]
[ROW][C]23[/C][C]0.034103[/C][C]0.2018[/C][C]0.420637[/C][/ROW]
[ROW][C]24[/C][C]0.013699[/C][C]0.081[/C][C]0.467934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72388&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72388&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	0.273045	1.6154	0.057607
2	-0.217334	-1.2858	0.103484
3	-0.437634	-2.5891	0.006963
4	-0.199727	-1.1816	0.122666
5	0.312162	1.8468	0.036624
6	0.299748	1.7733	0.042438
7	0.090109	0.5331	0.29867
8	-0.296624	-1.7549	0.044018
9	-0.171121	-1.0124	0.159155
10	0.089831	0.5314	0.299233
11	0.136553	0.8079	0.212314
12	-0.067755	-0.4008	0.345486
13	-0.249137	-1.4739	0.074721
14	-0.10597	-0.6269	0.267387
15	0.054326	0.3214	0.374911
16	0.168128	0.9947	0.163364
17	0.031308	0.1852	0.427063
18	-0.20205	-1.1953	0.119994
19	-0.16368	-0.9683	0.169758
20	-0.055481	-0.3282	0.372346
21	0.119801	0.7088	0.241586
22	0.092651	0.5481	0.293541
23	0.034103	0.2018	0.420637
24	0.013699	0.081	0.467934

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.273045	1.6154	0.057607
2	-0.315402	-1.8659	0.035224
3	-0.328127	-1.9412	0.030158
4	-0.05537	-0.3276	0.372592
5	0.290323	1.7176	0.047356
6	-0.029534	-0.1747	0.43115
7	0.020718	0.1226	0.451574
8	-0.159033	-0.9408	0.176615
9	0.169134	1.0006	0.161941
10	0.039834	0.2357	0.407536
11	-0.123101	-0.7283	0.235644
12	-0.27486	-1.6261	0.056451
13	-0.028825	-0.1705	0.432788
14	0.059324	0.351	0.36386
15	-0.089035	-0.5267	0.300849
16	-0.118658	-0.702	0.243664
17	0.012424	0.0735	0.470912
18	-0.02994	-0.1771	0.430214
19	0.000181	0.0011	0.499576
20	-0.187411	-1.1087	0.137552
21	-0.049676	-0.2939	0.38529
22	0.024671	0.146	0.442396
23	0.118132	0.6989	0.244623
24	-0.001061	-0.0063	0.497515

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.273045 & 1.6154 & 0.057607 \tabularnewline
2 & -0.315402 & -1.8659 & 0.035224 \tabularnewline
3 & -0.328127 & -1.9412 & 0.030158 \tabularnewline
4 & -0.05537 & -0.3276 & 0.372592 \tabularnewline
5 & 0.290323 & 1.7176 & 0.047356 \tabularnewline
6 & -0.029534 & -0.1747 & 0.43115 \tabularnewline
7 & 0.020718 & 0.1226 & 0.451574 \tabularnewline
8 & -0.159033 & -0.9408 & 0.176615 \tabularnewline
9 & 0.169134 & 1.0006 & 0.161941 \tabularnewline
10 & 0.039834 & 0.2357 & 0.407536 \tabularnewline
11 & -0.123101 & -0.7283 & 0.235644 \tabularnewline
12 & -0.27486 & -1.6261 & 0.056451 \tabularnewline
13 & -0.028825 & -0.1705 & 0.432788 \tabularnewline
14 & 0.059324 & 0.351 & 0.36386 \tabularnewline
15 & -0.089035 & -0.5267 & 0.300849 \tabularnewline
16 & -0.118658 & -0.702 & 0.243664 \tabularnewline
17 & 0.012424 & 0.0735 & 0.470912 \tabularnewline
18 & -0.02994 & -0.1771 & 0.430214 \tabularnewline
19 & 0.000181 & 0.0011 & 0.499576 \tabularnewline
20 & -0.187411 & -1.1087 & 0.137552 \tabularnewline
21 & -0.049676 & -0.2939 & 0.38529 \tabularnewline
22 & 0.024671 & 0.146 & 0.442396 \tabularnewline
23 & 0.118132 & 0.6989 & 0.244623 \tabularnewline
24 & -0.001061 & -0.0063 & 0.497515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72388&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]0.273045[/C][C]1.6154[/C][C]0.057607[/C][/ROW]
[ROW][C]2[/C][C]-0.315402[/C][C]-1.8659[/C][C]0.035224[/C][/ROW]
[ROW][C]3[/C][C]-0.328127[/C][C]-1.9412[/C][C]0.030158[/C][/ROW]
[ROW][C]4[/C][C]-0.05537[/C][C]-0.3276[/C][C]0.372592[/C][/ROW]
[ROW][C]5[/C][C]0.290323[/C][C]1.7176[/C][C]0.047356[/C][/ROW]
[ROW][C]6[/C][C]-0.029534[/C][C]-0.1747[/C][C]0.43115[/C][/ROW]
[ROW][C]7[/C][C]0.020718[/C][C]0.1226[/C][C]0.451574[/C][/ROW]
[ROW][C]8[/C][C]-0.159033[/C][C]-0.9408[/C][C]0.176615[/C][/ROW]
[ROW][C]9[/C][C]0.169134[/C][C]1.0006[/C][C]0.161941[/C][/ROW]
[ROW][C]10[/C][C]0.039834[/C][C]0.2357[/C][C]0.407536[/C][/ROW]
[ROW][C]11[/C][C]-0.123101[/C][C]-0.7283[/C][C]0.235644[/C][/ROW]
[ROW][C]12[/C][C]-0.27486[/C][C]-1.6261[/C][C]0.056451[/C][/ROW]
[ROW][C]13[/C][C]-0.028825[/C][C]-0.1705[/C][C]0.432788[/C][/ROW]
[ROW][C]14[/C][C]0.059324[/C][C]0.351[/C][C]0.36386[/C][/ROW]
[ROW][C]15[/C][C]-0.089035[/C][C]-0.5267[/C][C]0.300849[/C][/ROW]
[ROW][C]16[/C][C]-0.118658[/C][C]-0.702[/C][C]0.243664[/C][/ROW]
[ROW][C]17[/C][C]0.012424[/C][C]0.0735[/C][C]0.470912[/C][/ROW]
[ROW][C]18[/C][C]-0.02994[/C][C]-0.1771[/C][C]0.430214[/C][/ROW]
[ROW][C]19[/C][C]0.000181[/C][C]0.0011[/C][C]0.499576[/C][/ROW]
[ROW][C]20[/C][C]-0.187411[/C][C]-1.1087[/C][C]0.137552[/C][/ROW]
[ROW][C]21[/C][C]-0.049676[/C][C]-0.2939[/C][C]0.38529[/C][/ROW]
[ROW][C]22[/C][C]0.024671[/C][C]0.146[/C][C]0.442396[/C][/ROW]
[ROW][C]23[/C][C]0.118132[/C][C]0.6989[/C][C]0.244623[/C][/ROW]
[ROW][C]24[/C][C]-0.001061[/C][C]-0.0063[/C][C]0.497515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72388&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72388&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	0.273045	1.6154	0.057607
2	-0.315402	-1.8659	0.035224
3	-0.328127	-1.9412	0.030158
4	-0.05537	-0.3276	0.372592
5	0.290323	1.7176	0.047356
6	-0.029534	-0.1747	0.43115
7	0.020718	0.1226	0.451574
8	-0.159033	-0.9408	0.176615
9	0.169134	1.0006	0.161941
10	0.039834	0.2357	0.407536
11	-0.123101	-0.7283	0.235644
12	-0.27486	-1.6261	0.056451
13	-0.028825	-0.1705	0.432788
14	0.059324	0.351	0.36386
15	-0.089035	-0.5267	0.300849
16	-0.118658	-0.702	0.243664
17	0.012424	0.0735	0.470912
18	-0.02994	-0.1771	0.430214
19	0.000181	0.0011	0.499576
20	-0.187411	-1.1087	0.137552
21	-0.049676	-0.2939	0.38529
22	0.024671	0.146	0.442396
23	0.118132	0.6989	0.244623
24	-0.001061	-0.0063	0.497515

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 0.1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ;

Parameters (R input):

par1 = 24 ; par2 = 0.1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = ;

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