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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationWed, 21 Dec 2011 17:08:52 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/21/t1324505346tzv3jbln4f3wbfw.htm/, Retrieved Fri, 26 Apr 2024 22:35:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159086, Retrieved Fri, 26 Apr 2024 22:35:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Univariate Data Series] [] [2011-11-25 14:57:13] [493236dcc414c5f9e1823f06b33a5ad6]
- RMPD    [(Partial) Autocorrelation Function] [] [2011-12-05 14:06:22] [493236dcc414c5f9e1823f06b33a5ad6]
- R           [(Partial) Autocorrelation Function] [] [2011-12-21 22:08:52] [75a32e1bc492240bc1028714aca23077] [Current]
-               [(Partial) Autocorrelation Function] [] [2011-12-21 22:28:13] [493236dcc414c5f9e1823f06b33a5ad6]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.249
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.202
1.2271
1.277
1.265
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227
1.4684
1.457

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159086&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159086&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159086&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.2156951.65680.051436
2-0.183046-1.4060.082485
3-0.139892-1.07450.14348
40.100880.77490.220754
50.0246260.18920.425311
6-0.218674-1.67970.049155
70.0110410.08480.466351
80.0342720.26320.396639
90.0381210.29280.385346
10-0.00107-0.00820.496735
110.0057140.04390.48257
12-0.045982-0.35320.362601
13-0.021234-0.16310.435498
140.1450891.11440.134803
15-0.022598-0.17360.431394
16-0.13703-1.05260.148419
17-0.021361-0.16410.435117

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.215695 & 1.6568 & 0.051436 \tabularnewline
2 & -0.183046 & -1.406 & 0.082485 \tabularnewline
3 & -0.139892 & -1.0745 & 0.14348 \tabularnewline
4 & 0.10088 & 0.7749 & 0.220754 \tabularnewline
5 & 0.024626 & 0.1892 & 0.425311 \tabularnewline
6 & -0.218674 & -1.6797 & 0.049155 \tabularnewline
7 & 0.011041 & 0.0848 & 0.466351 \tabularnewline
8 & 0.034272 & 0.2632 & 0.396639 \tabularnewline
9 & 0.038121 & 0.2928 & 0.385346 \tabularnewline
10 & -0.00107 & -0.0082 & 0.496735 \tabularnewline
11 & 0.005714 & 0.0439 & 0.48257 \tabularnewline
12 & -0.045982 & -0.3532 & 0.362601 \tabularnewline
13 & -0.021234 & -0.1631 & 0.435498 \tabularnewline
14 & 0.145089 & 1.1144 & 0.134803 \tabularnewline
15 & -0.022598 & -0.1736 & 0.431394 \tabularnewline
16 & -0.13703 & -1.0526 & 0.148419 \tabularnewline
17 & -0.021361 & -0.1641 & 0.435117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159086&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]0.215695[/C][C]1.6568[/C][C]0.051436[/C][/ROW]
[ROW][C]2[/C][C]-0.183046[/C][C]-1.406[/C][C]0.082485[/C][/ROW]
[ROW][C]3[/C][C]-0.139892[/C][C]-1.0745[/C][C]0.14348[/C][/ROW]
[ROW][C]4[/C][C]0.10088[/C][C]0.7749[/C][C]0.220754[/C][/ROW]
[ROW][C]5[/C][C]0.024626[/C][C]0.1892[/C][C]0.425311[/C][/ROW]
[ROW][C]6[/C][C]-0.218674[/C][C]-1.6797[/C][C]0.049155[/C][/ROW]
[ROW][C]7[/C][C]0.011041[/C][C]0.0848[/C][C]0.466351[/C][/ROW]
[ROW][C]8[/C][C]0.034272[/C][C]0.2632[/C][C]0.396639[/C][/ROW]
[ROW][C]9[/C][C]0.038121[/C][C]0.2928[/C][C]0.385346[/C][/ROW]
[ROW][C]10[/C][C]-0.00107[/C][C]-0.0082[/C][C]0.496735[/C][/ROW]
[ROW][C]11[/C][C]0.005714[/C][C]0.0439[/C][C]0.48257[/C][/ROW]
[ROW][C]12[/C][C]-0.045982[/C][C]-0.3532[/C][C]0.362601[/C][/ROW]
[ROW][C]13[/C][C]-0.021234[/C][C]-0.1631[/C][C]0.435498[/C][/ROW]
[ROW][C]14[/C][C]0.145089[/C][C]1.1144[/C][C]0.134803[/C][/ROW]
[ROW][C]15[/C][C]-0.022598[/C][C]-0.1736[/C][C]0.431394[/C][/ROW]
[ROW][C]16[/C][C]-0.13703[/C][C]-1.0526[/C][C]0.148419[/C][/ROW]
[ROW][C]17[/C][C]-0.021361[/C][C]-0.1641[/C][C]0.435117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159086&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159086&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.2156951.65680.051436
2-0.183046-1.4060.082485
3-0.139892-1.07450.14348
40.100880.77490.220754
50.0246260.18920.425311
6-0.218674-1.67970.049155
70.0110410.08480.466351
80.0342720.26320.396639
90.0381210.29280.385346
10-0.00107-0.00820.496735
110.0057140.04390.48257
12-0.045982-0.35320.362601
13-0.021234-0.16310.435498
140.1450891.11440.134803
15-0.022598-0.17360.431394
16-0.13703-1.05260.148419
17-0.021361-0.16410.435117






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.2156951.65680.051436
2-0.240772-1.84940.034706
3-0.043387-0.33330.370058
40.1163060.89340.187647
5-0.077637-0.59630.276615
6-0.199126-1.52950.06574
70.1589061.22060.113551
8-0.113525-0.8720.19337
90.0300110.23050.409244
100.0589750.4530.326107
11-0.032343-0.24840.402331
12-0.097651-0.75010.228097
130.0847610.65110.258766
140.1069580.82160.207316
15-0.138859-1.06660.14525
16-0.032549-0.250.401724
170.0813030.62450.267354

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.215695 & 1.6568 & 0.051436 \tabularnewline
2 & -0.240772 & -1.8494 & 0.034706 \tabularnewline
3 & -0.043387 & -0.3333 & 0.370058 \tabularnewline
4 & 0.116306 & 0.8934 & 0.187647 \tabularnewline
5 & -0.077637 & -0.5963 & 0.276615 \tabularnewline
6 & -0.199126 & -1.5295 & 0.06574 \tabularnewline
7 & 0.158906 & 1.2206 & 0.113551 \tabularnewline
8 & -0.113525 & -0.872 & 0.19337 \tabularnewline
9 & 0.030011 & 0.2305 & 0.409244 \tabularnewline
10 & 0.058975 & 0.453 & 0.326107 \tabularnewline
11 & -0.032343 & -0.2484 & 0.402331 \tabularnewline
12 & -0.097651 & -0.7501 & 0.228097 \tabularnewline
13 & 0.084761 & 0.6511 & 0.258766 \tabularnewline
14 & 0.106958 & 0.8216 & 0.207316 \tabularnewline
15 & -0.138859 & -1.0666 & 0.14525 \tabularnewline
16 & -0.032549 & -0.25 & 0.401724 \tabularnewline
17 & 0.081303 & 0.6245 & 0.267354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159086&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]0.215695[/C][C]1.6568[/C][C]0.051436[/C][/ROW]
[ROW][C]2[/C][C]-0.240772[/C][C]-1.8494[/C][C]0.034706[/C][/ROW]
[ROW][C]3[/C][C]-0.043387[/C][C]-0.3333[/C][C]0.370058[/C][/ROW]
[ROW][C]4[/C][C]0.116306[/C][C]0.8934[/C][C]0.187647[/C][/ROW]
[ROW][C]5[/C][C]-0.077637[/C][C]-0.5963[/C][C]0.276615[/C][/ROW]
[ROW][C]6[/C][C]-0.199126[/C][C]-1.5295[/C][C]0.06574[/C][/ROW]
[ROW][C]7[/C][C]0.158906[/C][C]1.2206[/C][C]0.113551[/C][/ROW]
[ROW][C]8[/C][C]-0.113525[/C][C]-0.872[/C][C]0.19337[/C][/ROW]
[ROW][C]9[/C][C]0.030011[/C][C]0.2305[/C][C]0.409244[/C][/ROW]
[ROW][C]10[/C][C]0.058975[/C][C]0.453[/C][C]0.326107[/C][/ROW]
[ROW][C]11[/C][C]-0.032343[/C][C]-0.2484[/C][C]0.402331[/C][/ROW]
[ROW][C]12[/C][C]-0.097651[/C][C]-0.7501[/C][C]0.228097[/C][/ROW]
[ROW][C]13[/C][C]0.084761[/C][C]0.6511[/C][C]0.258766[/C][/ROW]
[ROW][C]14[/C][C]0.106958[/C][C]0.8216[/C][C]0.207316[/C][/ROW]
[ROW][C]15[/C][C]-0.138859[/C][C]-1.0666[/C][C]0.14525[/C][/ROW]
[ROW][C]16[/C][C]-0.032549[/C][C]-0.25[/C][C]0.401724[/C][/ROW]
[ROW][C]17[/C][C]0.081303[/C][C]0.6245[/C][C]0.267354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159086&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159086&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.2156951.65680.051436
2-0.240772-1.84940.034706
3-0.043387-0.33330.370058
40.1163060.89340.187647
5-0.077637-0.59630.276615
6-0.199126-1.52950.06574
70.1589061.22060.113551
8-0.113525-0.8720.19337
90.0300110.23050.409244
100.0589750.4530.326107
11-0.032343-0.24840.402331
12-0.097651-0.75010.228097
130.0847610.65110.258766
140.1069580.82160.207316
15-0.138859-1.06660.14525
16-0.032549-0.250.401724
170.0813030.62450.267354


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')