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Author's title

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, 13 Dec 2008 05:13:54 -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/t122917048934or5k3vy1l1bik.htm/, Retrieved Sun, 19 May 2024 05:58:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32999, Retrieved Sun, 19 May 2024 05:58:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

jenske_cole@hotmail.com

Estimated Impact

182

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

F     [Bivariate Kernel Density Estimation] [Various EDA Topic...] [2008-11-12 13:37:39] [8094ad203a218aaca2d1cea2c78c2d6e]
F    D  [Bivariate Kernel Density Estimation] [opdracht3 blok8 q...] [2008-11-12 17:51:49] [975daa21de49eaf4d491226310243f5a]
- RMPD      [(Partial) Autocorrelation Function] [paper autocorrela...] [2008-12-13 12:13:54] [120dfa2440e51a0cfc0f5296bc5d7460] [Current]

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Dataseries X:

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Histogram

Boxplots

7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
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
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
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9
6.8
6.7

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=32999&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=32999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32999&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	0.888902	8.0494	0
2	0.713347	6.4596	0
3	0.570289	5.1642	1e-06
4	0.510466	4.6225	7e-06
5	0.502053	4.5463	9e-06
6	0.494933	4.4818	1.2e-05
7	0.447134	4.049	5.8e-05
8	0.374798	3.3939	0.000532
9	0.33202	3.0066	0.001753
10	0.345788	3.1312	0.001206
11	0.384496	3.4818	0.000401
12	0.387717	3.5109	0.000364
13	0.291396	2.6387	0.004979
14	0.165383	1.4976	0.069038
15	0.066291	0.6003	0.274983
16	0.023596	0.2137	0.415668
17	0.005539	0.0502	0.48006
18	0.001925	0.0174	0.493069
19	-0.023155	-0.2097	0.417219

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.888902 & 8.0494 & 0 \tabularnewline
2 & 0.713347 & 6.4596 & 0 \tabularnewline
3 & 0.570289 & 5.1642 & 1e-06 \tabularnewline
4 & 0.510466 & 4.6225 & 7e-06 \tabularnewline
5 & 0.502053 & 4.5463 & 9e-06 \tabularnewline
6 & 0.494933 & 4.4818 & 1.2e-05 \tabularnewline
7 & 0.447134 & 4.049 & 5.8e-05 \tabularnewline
8 & 0.374798 & 3.3939 & 0.000532 \tabularnewline
9 & 0.33202 & 3.0066 & 0.001753 \tabularnewline
10 & 0.345788 & 3.1312 & 0.001206 \tabularnewline
11 & 0.384496 & 3.4818 & 0.000401 \tabularnewline
12 & 0.387717 & 3.5109 & 0.000364 \tabularnewline
13 & 0.291396 & 2.6387 & 0.004979 \tabularnewline
14 & 0.165383 & 1.4976 & 0.069038 \tabularnewline
15 & 0.066291 & 0.6003 & 0.274983 \tabularnewline
16 & 0.023596 & 0.2137 & 0.415668 \tabularnewline
17 & 0.005539 & 0.0502 & 0.48006 \tabularnewline
18 & 0.001925 & 0.0174 & 0.493069 \tabularnewline
19 & -0.023155 & -0.2097 & 0.417219 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32999&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]0.888902[/C][C]8.0494[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.713347[/C][C]6.4596[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.570289[/C][C]5.1642[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.510466[/C][C]4.6225[/C][C]7e-06[/C][/ROW]
[ROW][C]5[/C][C]0.502053[/C][C]4.5463[/C][C]9e-06[/C][/ROW]
[ROW][C]6[/C][C]0.494933[/C][C]4.4818[/C][C]1.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.447134[/C][C]4.049[/C][C]5.8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.374798[/C][C]3.3939[/C][C]0.000532[/C][/ROW]
[ROW][C]9[/C][C]0.33202[/C][C]3.0066[/C][C]0.001753[/C][/ROW]
[ROW][C]10[/C][C]0.345788[/C][C]3.1312[/C][C]0.001206[/C][/ROW]
[ROW][C]11[/C][C]0.384496[/C][C]3.4818[/C][C]0.000401[/C][/ROW]
[ROW][C]12[/C][C]0.387717[/C][C]3.5109[/C][C]0.000364[/C][/ROW]
[ROW][C]13[/C][C]0.291396[/C][C]2.6387[/C][C]0.004979[/C][/ROW]
[ROW][C]14[/C][C]0.165383[/C][C]1.4976[/C][C]0.069038[/C][/ROW]
[ROW][C]15[/C][C]0.066291[/C][C]0.6003[/C][C]0.274983[/C][/ROW]
[ROW][C]16[/C][C]0.023596[/C][C]0.2137[/C][C]0.415668[/C][/ROW]
[ROW][C]17[/C][C]0.005539[/C][C]0.0502[/C][C]0.48006[/C][/ROW]
[ROW][C]18[/C][C]0.001925[/C][C]0.0174[/C][C]0.493069[/C][/ROW]
[ROW][C]19[/C][C]-0.023155[/C][C]-0.2097[/C][C]0.417219[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32999&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	0.888902	8.0494	0
2	0.713347	6.4596	0
3	0.570289	5.1642	1e-06
4	0.510466	4.6225	7e-06
5	0.502053	4.5463	9e-06
6	0.494933	4.4818	1.2e-05
7	0.447134	4.049	5.8e-05
8	0.374798	3.3939	0.000532
9	0.33202	3.0066	0.001753
10	0.345788	3.1312	0.001206
11	0.384496	3.4818	0.000401
12	0.387717	3.5109	0.000364
13	0.291396	2.6387	0.004979
14	0.165383	1.4976	0.069038
15	0.066291	0.6003	0.274983
16	0.023596	0.2137	0.415668
17	0.005539	0.0502	0.48006
18	0.001925	0.0174	0.493069
19	-0.023155	-0.2097	0.417219

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.888902	8.0494	0
2	-0.365972	-3.314	0.000685
3	0.162015	1.4671	0.073086
4	0.234936	2.1274	0.018194
5	0.035451	0.321	0.374504
6	-0.013208	-0.1196	0.452543
7	-0.095028	-0.8605	0.196007
8	0.012388	0.1122	0.455478
9	0.151014	1.3675	0.087604
10	0.120403	1.0903	0.139389
11	-0.001679	-0.0152	0.493955
12	-0.112397	-1.0178	0.155884
13	-0.338294	-3.0634	0.00148
14	0.090335	0.818	0.207857
15	-0.043241	-0.3916	0.348198
16	-0.070173	-0.6354	0.263453
17	-0.10762	-0.9745	0.166328
18	0.112174	1.0158	0.15636
19	-0.023474	-0.2126	0.416095

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.888902 & 8.0494 & 0 \tabularnewline
2 & -0.365972 & -3.314 & 0.000685 \tabularnewline
3 & 0.162015 & 1.4671 & 0.073086 \tabularnewline
4 & 0.234936 & 2.1274 & 0.018194 \tabularnewline
5 & 0.035451 & 0.321 & 0.374504 \tabularnewline
6 & -0.013208 & -0.1196 & 0.452543 \tabularnewline
7 & -0.095028 & -0.8605 & 0.196007 \tabularnewline
8 & 0.012388 & 0.1122 & 0.455478 \tabularnewline
9 & 0.151014 & 1.3675 & 0.087604 \tabularnewline
10 & 0.120403 & 1.0903 & 0.139389 \tabularnewline
11 & -0.001679 & -0.0152 & 0.493955 \tabularnewline
12 & -0.112397 & -1.0178 & 0.155884 \tabularnewline
13 & -0.338294 & -3.0634 & 0.00148 \tabularnewline
14 & 0.090335 & 0.818 & 0.207857 \tabularnewline
15 & -0.043241 & -0.3916 & 0.348198 \tabularnewline
16 & -0.070173 & -0.6354 & 0.263453 \tabularnewline
17 & -0.10762 & -0.9745 & 0.166328 \tabularnewline
18 & 0.112174 & 1.0158 & 0.15636 \tabularnewline
19 & -0.023474 & -0.2126 & 0.416095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32999&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]0.888902[/C][C]8.0494[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.365972[/C][C]-3.314[/C][C]0.000685[/C][/ROW]
[ROW][C]3[/C][C]0.162015[/C][C]1.4671[/C][C]0.073086[/C][/ROW]
[ROW][C]4[/C][C]0.234936[/C][C]2.1274[/C][C]0.018194[/C][/ROW]
[ROW][C]5[/C][C]0.035451[/C][C]0.321[/C][C]0.374504[/C][/ROW]
[ROW][C]6[/C][C]-0.013208[/C][C]-0.1196[/C][C]0.452543[/C][/ROW]
[ROW][C]7[/C][C]-0.095028[/C][C]-0.8605[/C][C]0.196007[/C][/ROW]
[ROW][C]8[/C][C]0.012388[/C][C]0.1122[/C][C]0.455478[/C][/ROW]
[ROW][C]9[/C][C]0.151014[/C][C]1.3675[/C][C]0.087604[/C][/ROW]
[ROW][C]10[/C][C]0.120403[/C][C]1.0903[/C][C]0.139389[/C][/ROW]
[ROW][C]11[/C][C]-0.001679[/C][C]-0.0152[/C][C]0.493955[/C][/ROW]
[ROW][C]12[/C][C]-0.112397[/C][C]-1.0178[/C][C]0.155884[/C][/ROW]
[ROW][C]13[/C][C]-0.338294[/C][C]-3.0634[/C][C]0.00148[/C][/ROW]
[ROW][C]14[/C][C]0.090335[/C][C]0.818[/C][C]0.207857[/C][/ROW]
[ROW][C]15[/C][C]-0.043241[/C][C]-0.3916[/C][C]0.348198[/C][/ROW]
[ROW][C]16[/C][C]-0.070173[/C][C]-0.6354[/C][C]0.263453[/C][/ROW]
[ROW][C]17[/C][C]-0.10762[/C][C]-0.9745[/C][C]0.166328[/C][/ROW]
[ROW][C]18[/C][C]0.112174[/C][C]1.0158[/C][C]0.15636[/C][/ROW]
[ROW][C]19[/C][C]-0.023474[/C][C]-0.2126[/C][C]0.416095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32999&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32999&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	0.888902	8.0494	0
2	-0.365972	-3.314	0.000685
3	0.162015	1.4671	0.073086
4	0.234936	2.1274	0.018194
5	0.035451	0.321	0.374504
6	-0.013208	-0.1196	0.452543
7	-0.095028	-0.8605	0.196007
8	0.012388	0.1122	0.455478
9	0.151014	1.3675	0.087604
10	0.120403	1.0903	0.139389
11	-0.001679	-0.0152	0.493955
12	-0.112397	-1.0178	0.155884
13	-0.338294	-3.0634	0.00148
14	0.090335	0.818	0.207857
15	-0.043241	-0.3916	0.348198
16	-0.070173	-0.6354	0.263453
17	-0.10762	-0.9745	0.166328
18	0.112174	1.0158	0.15636
19	-0.023474	-0.2126	0.416095

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

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