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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

Tue, 04 Dec 2007 13:19:52 -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/Dec/04/t1196798859h883khtwcysk4ib.htm/, Retrieved Thu, 02 May 2024 09:23:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2443, Retrieved Thu, 02 May 2024 09:23:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

WS8 Q4 autocorrelatie assumption1 marleen

Estimated Impact

200

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

-       [(Partial) Autocorrelation Function] [WS8 Q4 autocorrel...] [2007-12-04 20:19:52] [87b6915e48e03972eaa4a0940182012f] [Current]

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Dataseries X:

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Histogram

Boxplots

-0.0157849668494866
-0.0271243010459872
-0.00792489154600524
0.0459148837142854
-0.107916181571559
-0.0438458600342877
-0.0271360801903513
0.00521599837540238
0.00344739379213696
0.0462884673027588
-0.00976918475560182
0.0050866877592345
-0.0268378742497628
-0.0460202969387869
0.00457411682055295
0.0202703370108024
0.0138780874221882
-0.0368570893621345
-0.0373042102182677
-0.0141720137855576
0.0279211612252405
-0.0237502531453190
-0.087199473568876
-0.0268651976802244
0.0225803058445590
-0.0294893683948694
0.0123811767063646
-0.0285515432644254
-0.0382291635675997
0.00431996960950776
0.06468414985189
-0.0335672378538977
0.0472156054558626
0.0146421371606427
-0.0178345540240388
-0.00226478772904236
-0.0249815068169007
0.00796397473835646
0.0239811700103298
-0.00474979278015027
-0.0102587630332712
-0.0409266443312390
-0.0134088339827680
-0.0362048327139919
0.0235300662773532
-0.0139176221956711
-0.0042540794454387
-0.0107326457092543

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2443&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]2 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=2443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2443&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	6.9282	0
1	-0.021504	-0.149	0.558904
2	-0.150293	-1.0413	0.848514
3	-0.119995	-0.8313	0.795053
4	-0.03429	-0.2376	0.593387
5	0.004728	0.0328	0.487001
6	0.210808	1.4605	0.075331
7	-0.123616	-0.8564	0.801994
8	-0.067175	-0.4654	0.678126
9	0.091031	0.6307	0.265621
10	-0.143717	-0.9957	0.837806
11	-0.181582	-1.258	0.892768
12	0.032869	0.2277	0.410414
13	-0.053665	-0.3718	0.644162
14	0.067431	0.4672	0.321243
15	-0.044364	-0.3074	0.620052

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & -0.021504 & -0.149 & 0.558904 \tabularnewline
2 & -0.150293 & -1.0413 & 0.848514 \tabularnewline
3 & -0.119995 & -0.8313 & 0.795053 \tabularnewline
4 & -0.03429 & -0.2376 & 0.593387 \tabularnewline
5 & 0.004728 & 0.0328 & 0.487001 \tabularnewline
6 & 0.210808 & 1.4605 & 0.075331 \tabularnewline
7 & -0.123616 & -0.8564 & 0.801994 \tabularnewline
8 & -0.067175 & -0.4654 & 0.678126 \tabularnewline
9 & 0.091031 & 0.6307 & 0.265621 \tabularnewline
10 & -0.143717 & -0.9957 & 0.837806 \tabularnewline
11 & -0.181582 & -1.258 & 0.892768 \tabularnewline
12 & 0.032869 & 0.2277 & 0.410414 \tabularnewline
13 & -0.053665 & -0.3718 & 0.644162 \tabularnewline
14 & 0.067431 & 0.4672 & 0.321243 \tabularnewline
15 & -0.044364 & -0.3074 & 0.620052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2443&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.021504[/C][C]-0.149[/C][C]0.558904[/C][/ROW]
[ROW][C]2[/C][C]-0.150293[/C][C]-1.0413[/C][C]0.848514[/C][/ROW]
[ROW][C]3[/C][C]-0.119995[/C][C]-0.8313[/C][C]0.795053[/C][/ROW]
[ROW][C]4[/C][C]-0.03429[/C][C]-0.2376[/C][C]0.593387[/C][/ROW]
[ROW][C]5[/C][C]0.004728[/C][C]0.0328[/C][C]0.487001[/C][/ROW]
[ROW][C]6[/C][C]0.210808[/C][C]1.4605[/C][C]0.075331[/C][/ROW]
[ROW][C]7[/C][C]-0.123616[/C][C]-0.8564[/C][C]0.801994[/C][/ROW]
[ROW][C]8[/C][C]-0.067175[/C][C]-0.4654[/C][C]0.678126[/C][/ROW]
[ROW][C]9[/C][C]0.091031[/C][C]0.6307[/C][C]0.265621[/C][/ROW]
[ROW][C]10[/C][C]-0.143717[/C][C]-0.9957[/C][C]0.837806[/C][/ROW]
[ROW][C]11[/C][C]-0.181582[/C][C]-1.258[/C][C]0.892768[/C][/ROW]
[ROW][C]12[/C][C]0.032869[/C][C]0.2277[/C][C]0.410414[/C][/ROW]
[ROW][C]13[/C][C]-0.053665[/C][C]-0.3718[/C][C]0.644162[/C][/ROW]
[ROW][C]14[/C][C]0.067431[/C][C]0.4672[/C][C]0.321243[/C][/ROW]
[ROW][C]15[/C][C]-0.044364[/C][C]-0.3074[/C][C]0.620052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2443&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	6.9282	0
1	-0.021504	-0.149	0.558904
2	-0.150293	-1.0413	0.848514
3	-0.119995	-0.8313	0.795053
4	-0.03429	-0.2376	0.593387
5	0.004728	0.0328	0.487001
6	0.210808	1.4605	0.075331
7	-0.123616	-0.8564	0.801994
8	-0.067175	-0.4654	0.678126
9	0.091031	0.6307	0.265621
10	-0.143717	-0.9957	0.837806
11	-0.181582	-1.258	0.892768
12	0.032869	0.2277	0.410414
13	-0.053665	-0.3718	0.644162
14	0.067431	0.4672	0.321243
15	-0.044364	-0.3074	0.620052

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.021504	-0.149	0.558904
1	-0.150825	-1.0449	0.849359
2	-0.129973	-0.9005	0.813819
3	-0.068269	-0.473	0.680814
4	-0.04007	-0.2776	0.608749
5	0.185535	1.2854	0.102406
6	-0.132056	-0.9149	0.817594
7	-0.021549	-0.1493	0.559028
8	0.104145	0.7215	0.237039
9	-0.184977	-1.2816	0.896923
10	-0.19654	-1.3617	0.91017
11	-0.053043	-0.3675	0.642567
12	-0.11728	-0.8125	0.789754
13	0.001433	0.0099	0.49606
14	-0.160821	-1.1142	0.864629
15	-0.062794	-0.4351	0.667263

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.021504 & -0.149 & 0.558904 \tabularnewline
1 & -0.150825 & -1.0449 & 0.849359 \tabularnewline
2 & -0.129973 & -0.9005 & 0.813819 \tabularnewline
3 & -0.068269 & -0.473 & 0.680814 \tabularnewline
4 & -0.04007 & -0.2776 & 0.608749 \tabularnewline
5 & 0.185535 & 1.2854 & 0.102406 \tabularnewline
6 & -0.132056 & -0.9149 & 0.817594 \tabularnewline
7 & -0.021549 & -0.1493 & 0.559028 \tabularnewline
8 & 0.104145 & 0.7215 & 0.237039 \tabularnewline
9 & -0.184977 & -1.2816 & 0.896923 \tabularnewline
10 & -0.19654 & -1.3617 & 0.91017 \tabularnewline
11 & -0.053043 & -0.3675 & 0.642567 \tabularnewline
12 & -0.11728 & -0.8125 & 0.789754 \tabularnewline
13 & 0.001433 & 0.0099 & 0.49606 \tabularnewline
14 & -0.160821 & -1.1142 & 0.864629 \tabularnewline
15 & -0.062794 & -0.4351 & 0.667263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2443&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]-0.021504[/C][C]-0.149[/C][C]0.558904[/C][/ROW]
[ROW][C]1[/C][C]-0.150825[/C][C]-1.0449[/C][C]0.849359[/C][/ROW]
[ROW][C]2[/C][C]-0.129973[/C][C]-0.9005[/C][C]0.813819[/C][/ROW]
[ROW][C]3[/C][C]-0.068269[/C][C]-0.473[/C][C]0.680814[/C][/ROW]
[ROW][C]4[/C][C]-0.04007[/C][C]-0.2776[/C][C]0.608749[/C][/ROW]
[ROW][C]5[/C][C]0.185535[/C][C]1.2854[/C][C]0.102406[/C][/ROW]
[ROW][C]6[/C][C]-0.132056[/C][C]-0.9149[/C][C]0.817594[/C][/ROW]
[ROW][C]7[/C][C]-0.021549[/C][C]-0.1493[/C][C]0.559028[/C][/ROW]
[ROW][C]8[/C][C]0.104145[/C][C]0.7215[/C][C]0.237039[/C][/ROW]
[ROW][C]9[/C][C]-0.184977[/C][C]-1.2816[/C][C]0.896923[/C][/ROW]
[ROW][C]10[/C][C]-0.19654[/C][C]-1.3617[/C][C]0.91017[/C][/ROW]
[ROW][C]11[/C][C]-0.053043[/C][C]-0.3675[/C][C]0.642567[/C][/ROW]
[ROW][C]12[/C][C]-0.11728[/C][C]-0.8125[/C][C]0.789754[/C][/ROW]
[ROW][C]13[/C][C]0.001433[/C][C]0.0099[/C][C]0.49606[/C][/ROW]
[ROW][C]14[/C][C]-0.160821[/C][C]-1.1142[/C][C]0.864629[/C][/ROW]
[ROW][C]15[/C][C]-0.062794[/C][C]-0.4351[/C][C]0.667263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2443&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2443&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	-0.021504	-0.149	0.558904
1	-0.150825	-1.0449	0.849359
2	-0.129973	-0.9005	0.813819
3	-0.068269	-0.473	0.680814
4	-0.04007	-0.2776	0.608749
5	0.185535	1.2854	0.102406
6	-0.132056	-0.9149	0.817594
7	-0.021549	-0.1493	0.559028
8	0.104145	0.7215	0.237039
9	-0.184977	-1.2816	0.896923
10	-0.19654	-1.3617	0.91017
11	-0.053043	-0.3675	0.642567
12	-0.11728	-0.8125	0.789754
13	0.001433	0.0099	0.49606
14	-0.160821	-1.1142	0.864629
15	-0.062794	-0.4351	0.667263

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code