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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

Thu, 27 Nov 2008 15:42:39 -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/Nov/27/t1227825815yvgagazi3j7zrru.htm/, Retrieved Mon, 20 May 2024 12:25:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25938, Retrieved Mon, 20 May 2024 12:25:52 +0000

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Original text written by user:

d=1 D=1

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

156

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

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [Random Walk Simul...] [2008-11-27 19:45:04] [58bf45a666dc5198906262e8815a9722]
F RMPD    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-11-27 22:08:29] [58bf45a666dc5198906262e8815a9722]
- RMPD        [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-27 22:42:39] [63db34dadd44fb018112addcdefe949f] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25938&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25938&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.533999	-3.6609	0.000318
2	-0.125472	-0.8602	0.197026
3	0.317641	2.1776	0.017243
4	-0.109517	-0.7508	0.228254
5	-0.164195	-1.1257	0.133012
6	0.244927	1.6791	0.049881
7	-0.195505	-1.3403	0.093293
8	0.013598	0.0932	0.463061
9	0.175424	1.2026	0.117569
10	-0.146056	-1.0013	0.160902
11	-0.016349	-0.1121	0.455618
12	0.141818	0.9723	0.167951
13	-0.175819	-1.2054	0.11705
14	0.006014	0.0412	0.483645
15	0.192267	1.3181	0.096927
16	-0.210562	-1.4435	0.07775
17	0.023083	0.1583	0.437468

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.533999 & -3.6609 & 0.000318 \tabularnewline
2 & -0.125472 & -0.8602 & 0.197026 \tabularnewline
3 & 0.317641 & 2.1776 & 0.017243 \tabularnewline
4 & -0.109517 & -0.7508 & 0.228254 \tabularnewline
5 & -0.164195 & -1.1257 & 0.133012 \tabularnewline
6 & 0.244927 & 1.6791 & 0.049881 \tabularnewline
7 & -0.195505 & -1.3403 & 0.093293 \tabularnewline
8 & 0.013598 & 0.0932 & 0.463061 \tabularnewline
9 & 0.175424 & 1.2026 & 0.117569 \tabularnewline
10 & -0.146056 & -1.0013 & 0.160902 \tabularnewline
11 & -0.016349 & -0.1121 & 0.455618 \tabularnewline
12 & 0.141818 & 0.9723 & 0.167951 \tabularnewline
13 & -0.175819 & -1.2054 & 0.11705 \tabularnewline
14 & 0.006014 & 0.0412 & 0.483645 \tabularnewline
15 & 0.192267 & 1.3181 & 0.096927 \tabularnewline
16 & -0.210562 & -1.4435 & 0.07775 \tabularnewline
17 & 0.023083 & 0.1583 & 0.437468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25938&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]-0.533999[/C][C]-3.6609[/C][C]0.000318[/C][/ROW]
[ROW][C]2[/C][C]-0.125472[/C][C]-0.8602[/C][C]0.197026[/C][/ROW]
[ROW][C]3[/C][C]0.317641[/C][C]2.1776[/C][C]0.017243[/C][/ROW]
[ROW][C]4[/C][C]-0.109517[/C][C]-0.7508[/C][C]0.228254[/C][/ROW]
[ROW][C]5[/C][C]-0.164195[/C][C]-1.1257[/C][C]0.133012[/C][/ROW]
[ROW][C]6[/C][C]0.244927[/C][C]1.6791[/C][C]0.049881[/C][/ROW]
[ROW][C]7[/C][C]-0.195505[/C][C]-1.3403[/C][C]0.093293[/C][/ROW]
[ROW][C]8[/C][C]0.013598[/C][C]0.0932[/C][C]0.463061[/C][/ROW]
[ROW][C]9[/C][C]0.175424[/C][C]1.2026[/C][C]0.117569[/C][/ROW]
[ROW][C]10[/C][C]-0.146056[/C][C]-1.0013[/C][C]0.160902[/C][/ROW]
[ROW][C]11[/C][C]-0.016349[/C][C]-0.1121[/C][C]0.455618[/C][/ROW]
[ROW][C]12[/C][C]0.141818[/C][C]0.9723[/C][C]0.167951[/C][/ROW]
[ROW][C]13[/C][C]-0.175819[/C][C]-1.2054[/C][C]0.11705[/C][/ROW]
[ROW][C]14[/C][C]0.006014[/C][C]0.0412[/C][C]0.483645[/C][/ROW]
[ROW][C]15[/C][C]0.192267[/C][C]1.3181[/C][C]0.096927[/C][/ROW]
[ROW][C]16[/C][C]-0.210562[/C][C]-1.4435[/C][C]0.07775[/C][/ROW]
[ROW][C]17[/C][C]0.023083[/C][C]0.1583[/C][C]0.437468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25938&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	-0.533999	-3.6609	0.000318
2	-0.125472	-0.8602	0.197026
3	0.317641	2.1776	0.017243
4	-0.109517	-0.7508	0.228254
5	-0.164195	-1.1257	0.133012
6	0.244927	1.6791	0.049881
7	-0.195505	-1.3403	0.093293
8	0.013598	0.0932	0.463061
9	0.175424	1.2026	0.117569
10	-0.146056	-1.0013	0.160902
11	-0.016349	-0.1121	0.455618
12	0.141818	0.9723	0.167951
13	-0.175819	-1.2054	0.11705
14	0.006014	0.0412	0.483645
15	0.192267	1.3181	0.096927
16	-0.210562	-1.4435	0.07775
17	0.023083	0.1583	0.437468

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.533999	-3.6609	0.000318
2	-0.574428	-3.9381	0.000135
3	-0.197491	-1.3539	0.091117
4	-0.010419	-0.0714	0.471679
5	-0.136577	-0.9363	0.176947
6	0.022944	0.1573	0.437842
7	-0.187864	-1.2879	0.102037
8	-0.202276	-1.3867	0.086033
9	-0.01497	-0.1026	0.459347
10	0.044397	0.3044	0.381094
11	0.04035	0.2766	0.391639
12	0.046366	0.3179	0.375996
13	-0.132025	-0.9051	0.18501
14	-0.270894	-1.8572	0.034781
15	-0.064379	-0.4414	0.330487
16	-0.042483	-0.2912	0.386072
17	-0.077464	-0.5311	0.298938

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.533999 & -3.6609 & 0.000318 \tabularnewline
2 & -0.574428 & -3.9381 & 0.000135 \tabularnewline
3 & -0.197491 & -1.3539 & 0.091117 \tabularnewline
4 & -0.010419 & -0.0714 & 0.471679 \tabularnewline
5 & -0.136577 & -0.9363 & 0.176947 \tabularnewline
6 & 0.022944 & 0.1573 & 0.437842 \tabularnewline
7 & -0.187864 & -1.2879 & 0.102037 \tabularnewline
8 & -0.202276 & -1.3867 & 0.086033 \tabularnewline
9 & -0.01497 & -0.1026 & 0.459347 \tabularnewline
10 & 0.044397 & 0.3044 & 0.381094 \tabularnewline
11 & 0.04035 & 0.2766 & 0.391639 \tabularnewline
12 & 0.046366 & 0.3179 & 0.375996 \tabularnewline
13 & -0.132025 & -0.9051 & 0.18501 \tabularnewline
14 & -0.270894 & -1.8572 & 0.034781 \tabularnewline
15 & -0.064379 & -0.4414 & 0.330487 \tabularnewline
16 & -0.042483 & -0.2912 & 0.386072 \tabularnewline
17 & -0.077464 & -0.5311 & 0.298938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25938&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]-0.533999[/C][C]-3.6609[/C][C]0.000318[/C][/ROW]
[ROW][C]2[/C][C]-0.574428[/C][C]-3.9381[/C][C]0.000135[/C][/ROW]
[ROW][C]3[/C][C]-0.197491[/C][C]-1.3539[/C][C]0.091117[/C][/ROW]
[ROW][C]4[/C][C]-0.010419[/C][C]-0.0714[/C][C]0.471679[/C][/ROW]
[ROW][C]5[/C][C]-0.136577[/C][C]-0.9363[/C][C]0.176947[/C][/ROW]
[ROW][C]6[/C][C]0.022944[/C][C]0.1573[/C][C]0.437842[/C][/ROW]
[ROW][C]7[/C][C]-0.187864[/C][C]-1.2879[/C][C]0.102037[/C][/ROW]
[ROW][C]8[/C][C]-0.202276[/C][C]-1.3867[/C][C]0.086033[/C][/ROW]
[ROW][C]9[/C][C]-0.01497[/C][C]-0.1026[/C][C]0.459347[/C][/ROW]
[ROW][C]10[/C][C]0.044397[/C][C]0.3044[/C][C]0.381094[/C][/ROW]
[ROW][C]11[/C][C]0.04035[/C][C]0.2766[/C][C]0.391639[/C][/ROW]
[ROW][C]12[/C][C]0.046366[/C][C]0.3179[/C][C]0.375996[/C][/ROW]
[ROW][C]13[/C][C]-0.132025[/C][C]-0.9051[/C][C]0.18501[/C][/ROW]
[ROW][C]14[/C][C]-0.270894[/C][C]-1.8572[/C][C]0.034781[/C][/ROW]
[ROW][C]15[/C][C]-0.064379[/C][C]-0.4414[/C][C]0.330487[/C][/ROW]
[ROW][C]16[/C][C]-0.042483[/C][C]-0.2912[/C][C]0.386072[/C][/ROW]
[ROW][C]17[/C][C]-0.077464[/C][C]-0.5311[/C][C]0.298938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25938&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	-0.533999	-3.6609	0.000318
2	-0.574428	-3.9381	0.000135
3	-0.197491	-1.3539	0.091117
4	-0.010419	-0.0714	0.471679
5	-0.136577	-0.9363	0.176947
6	0.022944	0.1573	0.437842
7	-0.187864	-1.2879	0.102037
8	-0.202276	-1.3867	0.086033
9	-0.01497	-0.1026	0.459347
10	0.044397	0.3044	0.381094
11	0.04035	0.2766	0.391639
12	0.046366	0.3179	0.375996
13	-0.132025	-0.9051	0.18501
14	-0.270894	-1.8572	0.034781
15	-0.064379	-0.4414	0.330487
16	-0.042483	-0.2912	0.386072
17	-0.077464	-0.5311	0.298938

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code