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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

Thu, 29 Nov 2007 13:44:44 -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/29/t1196368783liwk5376pgzvlko.htm/, Retrieved Fri, 03 May 2024 14:28:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7602, Retrieved Fri, 03 May 2024 14:28:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

177

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

-       [(Partial) Autocorrelation Function] [Q1 estimate arma] [2007-11-29 20:44:44] [1dd4e56f2879fe34e71a5ad240ab3149] [Current]

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Dataseries X:

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Histogram

Boxplots

0.18
-0.15
0.40
0.44
-0.09
0.22
-0.34
-0.04
0.02
-0.02
-0.07
0.30
0.20
0.07
0.35
0.16
-0.18
0.14
-0.11
0.20
0.12
0.19
0.29
0.17
0.34
0.35
0.18
0.26
0.35
0.18
-0.03
0.64
-0.23
0.31
-0.25
-0.09
0.40
0.21
0.81
0.60
0.16
-0.07
-0.01
0.27
-0.15
0.11
-0.20
0.57
0.16
0.25
0.03
0.15
-0.27
0.31
-0.03
0.27
-0.11
-0.08
0.05
0.43
0.67
0.28
-0.25
-0.27
0.28
0.19
0.27
0.28
-0.32
0.18
-0.06
0.29
0.37
0.14
0.53
0.39
-0.05
0.34
0.12
0.07
0.49
-0.12
-0.33
0.28
0.68
0.65
0.23
0.15
0.31
0.62
0.10
0.12
-0.19
-0.03
-0.02
0.03
0.45
-0.04
0.51
0.39
-0.02
0.36
0.13
-0.30
-0.21
0.26
0.14
0.05
0.57
0.01
0.48
-0.13
-0.01
0.45
-0.13
0.10

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=7602&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=7602&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7602&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	10.7703	0
1	0.026225	0.2825	0.389049
2	0.012272	0.1322	0.447538
3	-0.109861	-1.1832	0.880434
4	-0.204273	-2.2001	0.985109
5	0.023115	0.249	0.401917
6	-0.044197	-0.476	0.68252
7	-0.113697	-1.2246	0.888388
8	-0.071764	-0.7729	0.779429
9	0.014491	0.1561	0.438124
10	0.078117	0.8414	0.200941
11	0.175242	1.8874	0.030802
12	0.204554	2.2031	0.014781
13	-0.06357	-0.6847	0.752541
14	0.121013	1.3033	0.097518
15	-0.166424	-1.7924	0.962166
16	-0.035683	-0.3843	0.649275
17	-0.023808	-0.2564	0.600959
18	-0.12007	-1.2932	0.900743
19	-0.037136	-0.4	0.655041

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.7703 & 0 \tabularnewline
1 & 0.026225 & 0.2825 & 0.389049 \tabularnewline
2 & 0.012272 & 0.1322 & 0.447538 \tabularnewline
3 & -0.109861 & -1.1832 & 0.880434 \tabularnewline
4 & -0.204273 & -2.2001 & 0.985109 \tabularnewline
5 & 0.023115 & 0.249 & 0.401917 \tabularnewline
6 & -0.044197 & -0.476 & 0.68252 \tabularnewline
7 & -0.113697 & -1.2246 & 0.888388 \tabularnewline
8 & -0.071764 & -0.7729 & 0.779429 \tabularnewline
9 & 0.014491 & 0.1561 & 0.438124 \tabularnewline
10 & 0.078117 & 0.8414 & 0.200941 \tabularnewline
11 & 0.175242 & 1.8874 & 0.030802 \tabularnewline
12 & 0.204554 & 2.2031 & 0.014781 \tabularnewline
13 & -0.06357 & -0.6847 & 0.752541 \tabularnewline
14 & 0.121013 & 1.3033 & 0.097518 \tabularnewline
15 & -0.166424 & -1.7924 & 0.962166 \tabularnewline
16 & -0.035683 & -0.3843 & 0.649275 \tabularnewline
17 & -0.023808 & -0.2564 & 0.600959 \tabularnewline
18 & -0.12007 & -1.2932 & 0.900743 \tabularnewline
19 & -0.037136 & -0.4 & 0.655041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7602&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]10.7703[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.026225[/C][C]0.2825[/C][C]0.389049[/C][/ROW]
[ROW][C]2[/C][C]0.012272[/C][C]0.1322[/C][C]0.447538[/C][/ROW]
[ROW][C]3[/C][C]-0.109861[/C][C]-1.1832[/C][C]0.880434[/C][/ROW]
[ROW][C]4[/C][C]-0.204273[/C][C]-2.2001[/C][C]0.985109[/C][/ROW]
[ROW][C]5[/C][C]0.023115[/C][C]0.249[/C][C]0.401917[/C][/ROW]
[ROW][C]6[/C][C]-0.044197[/C][C]-0.476[/C][C]0.68252[/C][/ROW]
[ROW][C]7[/C][C]-0.113697[/C][C]-1.2246[/C][C]0.888388[/C][/ROW]
[ROW][C]8[/C][C]-0.071764[/C][C]-0.7729[/C][C]0.779429[/C][/ROW]
[ROW][C]9[/C][C]0.014491[/C][C]0.1561[/C][C]0.438124[/C][/ROW]
[ROW][C]10[/C][C]0.078117[/C][C]0.8414[/C][C]0.200941[/C][/ROW]
[ROW][C]11[/C][C]0.175242[/C][C]1.8874[/C][C]0.030802[/C][/ROW]
[ROW][C]12[/C][C]0.204554[/C][C]2.2031[/C][C]0.014781[/C][/ROW]
[ROW][C]13[/C][C]-0.06357[/C][C]-0.6847[/C][C]0.752541[/C][/ROW]
[ROW][C]14[/C][C]0.121013[/C][C]1.3033[/C][C]0.097518[/C][/ROW]
[ROW][C]15[/C][C]-0.166424[/C][C]-1.7924[/C][C]0.962166[/C][/ROW]
[ROW][C]16[/C][C]-0.035683[/C][C]-0.3843[/C][C]0.649275[/C][/ROW]
[ROW][C]17[/C][C]-0.023808[/C][C]-0.2564[/C][C]0.600959[/C][/ROW]
[ROW][C]18[/C][C]-0.12007[/C][C]-1.2932[/C][C]0.900743[/C][/ROW]
[ROW][C]19[/C][C]-0.037136[/C][C]-0.4[/C][C]0.655041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7602&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7602&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	10.7703	0
1	0.026225	0.2825	0.389049
2	0.012272	0.1322	0.447538
3	-0.109861	-1.1832	0.880434
4	-0.204273	-2.2001	0.985109
5	0.023115	0.249	0.401917
6	-0.044197	-0.476	0.68252
7	-0.113697	-1.2246	0.888388
8	-0.071764	-0.7729	0.779429
9	0.014491	0.1561	0.438124
10	0.078117	0.8414	0.200941
11	0.175242	1.8874	0.030802
12	0.204554	2.2031	0.014781
13	-0.06357	-0.6847	0.752541
14	0.121013	1.3033	0.097518
15	-0.166424	-1.7924	0.962166
16	-0.035683	-0.3843	0.649275
17	-0.023808	-0.2564	0.600959
18	-0.12007	-1.2932	0.900743
19	-0.037136	-0.4	0.655041

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.026225	0.2825	0.389049
1	0.011592	0.1249	0.450428
2	-0.110574	-1.1909	0.881942
3	-0.201185	-2.1668	0.983854
4	0.034426	0.3708	0.35574
5	-0.053102	-0.5719	0.715761
6	-0.16656	-1.7939	0.962283
7	-0.112112	-1.2075	0.885149
8	0.019757	0.2128	0.415932
9	0.027831	0.2997	0.382452
10	0.104187	1.1221	0.132063
11	0.195712	2.1079	0.018597
12	-0.052089	-0.561	0.712064
13	0.170177	1.8329	0.034694
14	-0.088163	-0.9495	0.827841
15	0.028512	0.3071	0.379663
16	-0.001508	-0.0162	0.506466
17	-0.038515	-0.4148	0.66048
18	-0.052792	-0.5686	0.714634
19	-0.067488	-0.7269	0.765615

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.026225 & 0.2825 & 0.389049 \tabularnewline
1 & 0.011592 & 0.1249 & 0.450428 \tabularnewline
2 & -0.110574 & -1.1909 & 0.881942 \tabularnewline
3 & -0.201185 & -2.1668 & 0.983854 \tabularnewline
4 & 0.034426 & 0.3708 & 0.35574 \tabularnewline
5 & -0.053102 & -0.5719 & 0.715761 \tabularnewline
6 & -0.16656 & -1.7939 & 0.962283 \tabularnewline
7 & -0.112112 & -1.2075 & 0.885149 \tabularnewline
8 & 0.019757 & 0.2128 & 0.415932 \tabularnewline
9 & 0.027831 & 0.2997 & 0.382452 \tabularnewline
10 & 0.104187 & 1.1221 & 0.132063 \tabularnewline
11 & 0.195712 & 2.1079 & 0.018597 \tabularnewline
12 & -0.052089 & -0.561 & 0.712064 \tabularnewline
13 & 0.170177 & 1.8329 & 0.034694 \tabularnewline
14 & -0.088163 & -0.9495 & 0.827841 \tabularnewline
15 & 0.028512 & 0.3071 & 0.379663 \tabularnewline
16 & -0.001508 & -0.0162 & 0.506466 \tabularnewline
17 & -0.038515 & -0.4148 & 0.66048 \tabularnewline
18 & -0.052792 & -0.5686 & 0.714634 \tabularnewline
19 & -0.067488 & -0.7269 & 0.765615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7602&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]0.026225[/C][C]0.2825[/C][C]0.389049[/C][/ROW]
[ROW][C]1[/C][C]0.011592[/C][C]0.1249[/C][C]0.450428[/C][/ROW]
[ROW][C]2[/C][C]-0.110574[/C][C]-1.1909[/C][C]0.881942[/C][/ROW]
[ROW][C]3[/C][C]-0.201185[/C][C]-2.1668[/C][C]0.983854[/C][/ROW]
[ROW][C]4[/C][C]0.034426[/C][C]0.3708[/C][C]0.35574[/C][/ROW]
[ROW][C]5[/C][C]-0.053102[/C][C]-0.5719[/C][C]0.715761[/C][/ROW]
[ROW][C]6[/C][C]-0.16656[/C][C]-1.7939[/C][C]0.962283[/C][/ROW]
[ROW][C]7[/C][C]-0.112112[/C][C]-1.2075[/C][C]0.885149[/C][/ROW]
[ROW][C]8[/C][C]0.019757[/C][C]0.2128[/C][C]0.415932[/C][/ROW]
[ROW][C]9[/C][C]0.027831[/C][C]0.2997[/C][C]0.382452[/C][/ROW]
[ROW][C]10[/C][C]0.104187[/C][C]1.1221[/C][C]0.132063[/C][/ROW]
[ROW][C]11[/C][C]0.195712[/C][C]2.1079[/C][C]0.018597[/C][/ROW]
[ROW][C]12[/C][C]-0.052089[/C][C]-0.561[/C][C]0.712064[/C][/ROW]
[ROW][C]13[/C][C]0.170177[/C][C]1.8329[/C][C]0.034694[/C][/ROW]
[ROW][C]14[/C][C]-0.088163[/C][C]-0.9495[/C][C]0.827841[/C][/ROW]
[ROW][C]15[/C][C]0.028512[/C][C]0.3071[/C][C]0.379663[/C][/ROW]
[ROW][C]16[/C][C]-0.001508[/C][C]-0.0162[/C][C]0.506466[/C][/ROW]
[ROW][C]17[/C][C]-0.038515[/C][C]-0.4148[/C][C]0.66048[/C][/ROW]
[ROW][C]18[/C][C]-0.052792[/C][C]-0.5686[/C][C]0.714634[/C][/ROW]
[ROW][C]19[/C][C]-0.067488[/C][C]-0.7269[/C][C]0.765615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7602&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7602&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	0.026225	0.2825	0.389049
1	0.011592	0.1249	0.450428
2	-0.110574	-1.1909	0.881942
3	-0.201185	-2.1668	0.983854
4	0.034426	0.3708	0.35574
5	-0.053102	-0.5719	0.715761
6	-0.16656	-1.7939	0.962283
7	-0.112112	-1.2075	0.885149
8	0.019757	0.2128	0.415932
9	0.027831	0.2997	0.382452
10	0.104187	1.1221	0.132063
11	0.195712	2.1079	0.018597
12	-0.052089	-0.561	0.712064
13	0.170177	1.8329	0.034694
14	-0.088163	-0.9495	0.827841
15	0.028512	0.3071	0.379663
16	-0.001508	-0.0162	0.506466
17	-0.038515	-0.4148	0.66048
18	-0.052792	-0.5686	0.714634
19	-0.067488	-0.7269	0.765615

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code