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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 13:15:11 -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/02/t1228248939899y1kixzhxxctq.htm/, Retrieved Sun, 19 May 2024 11:29:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28347, Retrieved Sun, 19 May 2024 11:29:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

150

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

F     [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:08:00] [c94d7012e41b73cfa20d93e879679ede]
-   PD  [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:10:31] [c94d7012e41b73cfa20d93e879679ede]
-   PD    [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:13:09] [c94d7012e41b73cfa20d93e879679ede]
-   PD        [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 20:15:11] [72e979bcc364082694890d2eccc1a66f] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28347&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28347&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28347&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.153726	-1.0539	0.148659
2	0.271548	1.8616	0.034457
3	-0.054016	-0.3703	0.356406
4	0.155472	1.0659	0.145965
5	-0.032552	-0.2232	0.412188
6	-0.187606	-1.2862	0.102343
7	0.027903	0.1913	0.42456
8	-0.260763	-1.7877	0.040137
9	0.086456	0.5927	0.278106
10	-0.194842	-1.3358	0.094028
11	0.059843	0.4103	0.341738
12	-0.301725	-2.0685	0.022058
13	0.016284	0.1116	0.455793
14	-0.002338	-0.016	0.493639
15	-0.047055	-0.3226	0.374217
16	0.0589	0.4038	0.344097
17	-0.033816	-0.2318	0.408839

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.153726 & -1.0539 & 0.148659 \tabularnewline
2 & 0.271548 & 1.8616 & 0.034457 \tabularnewline
3 & -0.054016 & -0.3703 & 0.356406 \tabularnewline
4 & 0.155472 & 1.0659 & 0.145965 \tabularnewline
5 & -0.032552 & -0.2232 & 0.412188 \tabularnewline
6 & -0.187606 & -1.2862 & 0.102343 \tabularnewline
7 & 0.027903 & 0.1913 & 0.42456 \tabularnewline
8 & -0.260763 & -1.7877 & 0.040137 \tabularnewline
9 & 0.086456 & 0.5927 & 0.278106 \tabularnewline
10 & -0.194842 & -1.3358 & 0.094028 \tabularnewline
11 & 0.059843 & 0.4103 & 0.341738 \tabularnewline
12 & -0.301725 & -2.0685 & 0.022058 \tabularnewline
13 & 0.016284 & 0.1116 & 0.455793 \tabularnewline
14 & -0.002338 & -0.016 & 0.493639 \tabularnewline
15 & -0.047055 & -0.3226 & 0.374217 \tabularnewline
16 & 0.0589 & 0.4038 & 0.344097 \tabularnewline
17 & -0.033816 & -0.2318 & 0.408839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28347&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]-0.153726[/C][C]-1.0539[/C][C]0.148659[/C][/ROW]
[ROW][C]2[/C][C]0.271548[/C][C]1.8616[/C][C]0.034457[/C][/ROW]
[ROW][C]3[/C][C]-0.054016[/C][C]-0.3703[/C][C]0.356406[/C][/ROW]
[ROW][C]4[/C][C]0.155472[/C][C]1.0659[/C][C]0.145965[/C][/ROW]
[ROW][C]5[/C][C]-0.032552[/C][C]-0.2232[/C][C]0.412188[/C][/ROW]
[ROW][C]6[/C][C]-0.187606[/C][C]-1.2862[/C][C]0.102343[/C][/ROW]
[ROW][C]7[/C][C]0.027903[/C][C]0.1913[/C][C]0.42456[/C][/ROW]
[ROW][C]8[/C][C]-0.260763[/C][C]-1.7877[/C][C]0.040137[/C][/ROW]
[ROW][C]9[/C][C]0.086456[/C][C]0.5927[/C][C]0.278106[/C][/ROW]
[ROW][C]10[/C][C]-0.194842[/C][C]-1.3358[/C][C]0.094028[/C][/ROW]
[ROW][C]11[/C][C]0.059843[/C][C]0.4103[/C][C]0.341738[/C][/ROW]
[ROW][C]12[/C][C]-0.301725[/C][C]-2.0685[/C][C]0.022058[/C][/ROW]
[ROW][C]13[/C][C]0.016284[/C][C]0.1116[/C][C]0.455793[/C][/ROW]
[ROW][C]14[/C][C]-0.002338[/C][C]-0.016[/C][C]0.493639[/C][/ROW]
[ROW][C]15[/C][C]-0.047055[/C][C]-0.3226[/C][C]0.374217[/C][/ROW]
[ROW][C]16[/C][C]0.0589[/C][C]0.4038[/C][C]0.344097[/C][/ROW]
[ROW][C]17[/C][C]-0.033816[/C][C]-0.2318[/C][C]0.408839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28347&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28347&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	-0.153726	-1.0539	0.148659
2	0.271548	1.8616	0.034457
3	-0.054016	-0.3703	0.356406
4	0.155472	1.0659	0.145965
5	-0.032552	-0.2232	0.412188
6	-0.187606	-1.2862	0.102343
7	0.027903	0.1913	0.42456
8	-0.260763	-1.7877	0.040137
9	0.086456	0.5927	0.278106
10	-0.194842	-1.3358	0.094028
11	0.059843	0.4103	0.341738
12	-0.301725	-2.0685	0.022058
13	0.016284	0.1116	0.455793
14	-0.002338	-0.016	0.493639
15	-0.047055	-0.3226	0.374217
16	0.0589	0.4038	0.344097
17	-0.033816	-0.2318	0.408839

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.153726	-1.0539	0.148659
2	0.253917	1.7408	0.044134
3	0.017695	0.1213	0.451982
4	0.090078	0.6175	0.269929
5	0.005447	0.0373	0.485186
6	-0.276111	-1.8929	0.032268
7	-0.021542	-0.1477	0.441611
8	-0.192321	-1.3185	0.096866
9	0.039865	0.2733	0.39291
10	-0.00971	-0.0666	0.473605
11	-0.001261	-0.0086	0.49657
12	-0.274959	-1.885	0.032809
13	-0.120102	-0.8234	0.207226
14	0.054723	0.3752	0.354613
15	-0.011007	-0.0755	0.470084
16	0.062524	0.4286	0.33507
17	0.013052	0.0895	0.464541

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.153726 & -1.0539 & 0.148659 \tabularnewline
2 & 0.253917 & 1.7408 & 0.044134 \tabularnewline
3 & 0.017695 & 0.1213 & 0.451982 \tabularnewline
4 & 0.090078 & 0.6175 & 0.269929 \tabularnewline
5 & 0.005447 & 0.0373 & 0.485186 \tabularnewline
6 & -0.276111 & -1.8929 & 0.032268 \tabularnewline
7 & -0.021542 & -0.1477 & 0.441611 \tabularnewline
8 & -0.192321 & -1.3185 & 0.096866 \tabularnewline
9 & 0.039865 & 0.2733 & 0.39291 \tabularnewline
10 & -0.00971 & -0.0666 & 0.473605 \tabularnewline
11 & -0.001261 & -0.0086 & 0.49657 \tabularnewline
12 & -0.274959 & -1.885 & 0.032809 \tabularnewline
13 & -0.120102 & -0.8234 & 0.207226 \tabularnewline
14 & 0.054723 & 0.3752 & 0.354613 \tabularnewline
15 & -0.011007 & -0.0755 & 0.470084 \tabularnewline
16 & 0.062524 & 0.4286 & 0.33507 \tabularnewline
17 & 0.013052 & 0.0895 & 0.464541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28347&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]-0.153726[/C][C]-1.0539[/C][C]0.148659[/C][/ROW]
[ROW][C]2[/C][C]0.253917[/C][C]1.7408[/C][C]0.044134[/C][/ROW]
[ROW][C]3[/C][C]0.017695[/C][C]0.1213[/C][C]0.451982[/C][/ROW]
[ROW][C]4[/C][C]0.090078[/C][C]0.6175[/C][C]0.269929[/C][/ROW]
[ROW][C]5[/C][C]0.005447[/C][C]0.0373[/C][C]0.485186[/C][/ROW]
[ROW][C]6[/C][C]-0.276111[/C][C]-1.8929[/C][C]0.032268[/C][/ROW]
[ROW][C]7[/C][C]-0.021542[/C][C]-0.1477[/C][C]0.441611[/C][/ROW]
[ROW][C]8[/C][C]-0.192321[/C][C]-1.3185[/C][C]0.096866[/C][/ROW]
[ROW][C]9[/C][C]0.039865[/C][C]0.2733[/C][C]0.39291[/C][/ROW]
[ROW][C]10[/C][C]-0.00971[/C][C]-0.0666[/C][C]0.473605[/C][/ROW]
[ROW][C]11[/C][C]-0.001261[/C][C]-0.0086[/C][C]0.49657[/C][/ROW]
[ROW][C]12[/C][C]-0.274959[/C][C]-1.885[/C][C]0.032809[/C][/ROW]
[ROW][C]13[/C][C]-0.120102[/C][C]-0.8234[/C][C]0.207226[/C][/ROW]
[ROW][C]14[/C][C]0.054723[/C][C]0.3752[/C][C]0.354613[/C][/ROW]
[ROW][C]15[/C][C]-0.011007[/C][C]-0.0755[/C][C]0.470084[/C][/ROW]
[ROW][C]16[/C][C]0.062524[/C][C]0.4286[/C][C]0.33507[/C][/ROW]
[ROW][C]17[/C][C]0.013052[/C][C]0.0895[/C][C]0.464541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28347&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28347&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	-0.153726	-1.0539	0.148659
2	0.253917	1.7408	0.044134
3	0.017695	0.1213	0.451982
4	0.090078	0.6175	0.269929
5	0.005447	0.0373	0.485186
6	-0.276111	-1.8929	0.032268
7	-0.021542	-0.1477	0.441611
8	-0.192321	-1.3185	0.096866
9	0.039865	0.2733	0.39291
10	-0.00971	-0.0666	0.473605
11	-0.001261	-0.0086	0.49657
12	-0.274959	-1.885	0.032809
13	-0.120102	-0.8234	0.207226
14	0.054723	0.3752	0.354613
15	-0.011007	-0.0755	0.470084
16	0.062524	0.4286	0.33507
17	0.013052	0.0895	0.464541

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 = 1 ; par5 = 12 ;

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 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')

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Figures (Output of Computation)

Input Parameters & R Code