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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 computationTue, 23 Jan 2018 15:21:12 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Jan/23/t1516717364o7rrjd19rdfi6t7.htm/, Retrieved Wed, 08 May 2024 08:00:28 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 08 May 2024 08:00:28 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
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Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.025227-0.42060.33718
2-0.014174-0.23630.406677
30.1045311.74290.04123
40.0655721.09330.137603
5-0.160796-2.6810.003889
6-0.028392-0.47340.318154
7-0.055588-0.92680.177409
8-0.046395-0.77360.219922
9-0.075562-1.25990.104385
10-0.021612-0.36030.359432
11-0.002052-0.03420.486369
12-0.019628-0.32730.371854
130.0483240.80570.210545
140.059640.99440.160447
15-0.030137-0.50250.307863
160.11411.90240.029074
170.0387710.64640.259265
18-0.065908-1.09890.136379
19-0.117961-1.96680.0251
200.0526080.87720.19058
21-0.05536-0.9230.178393
220.0496820.82840.204089
23-0.037781-0.62990.264629
240.0212270.35390.36183

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.025227 & -0.4206 & 0.33718 \tabularnewline
2 & -0.014174 & -0.2363 & 0.406677 \tabularnewline
3 & 0.104531 & 1.7429 & 0.04123 \tabularnewline
4 & 0.065572 & 1.0933 & 0.137603 \tabularnewline
5 & -0.160796 & -2.681 & 0.003889 \tabularnewline
6 & -0.028392 & -0.4734 & 0.318154 \tabularnewline
7 & -0.055588 & -0.9268 & 0.177409 \tabularnewline
8 & -0.046395 & -0.7736 & 0.219922 \tabularnewline
9 & -0.075562 & -1.2599 & 0.104385 \tabularnewline
10 & -0.021612 & -0.3603 & 0.359432 \tabularnewline
11 & -0.002052 & -0.0342 & 0.486369 \tabularnewline
12 & -0.019628 & -0.3273 & 0.371854 \tabularnewline
13 & 0.048324 & 0.8057 & 0.210545 \tabularnewline
14 & 0.05964 & 0.9944 & 0.160447 \tabularnewline
15 & -0.030137 & -0.5025 & 0.307863 \tabularnewline
16 & 0.1141 & 1.9024 & 0.029074 \tabularnewline
17 & 0.038771 & 0.6464 & 0.259265 \tabularnewline
18 & -0.065908 & -1.0989 & 0.136379 \tabularnewline
19 & -0.117961 & -1.9668 & 0.0251 \tabularnewline
20 & 0.052608 & 0.8772 & 0.19058 \tabularnewline
21 & -0.05536 & -0.923 & 0.178393 \tabularnewline
22 & 0.049682 & 0.8284 & 0.204089 \tabularnewline
23 & -0.037781 & -0.6299 & 0.264629 \tabularnewline
24 & 0.021227 & 0.3539 & 0.36183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.025227[/C][C]-0.4206[/C][C]0.33718[/C][/ROW]
[ROW][C]2[/C][C]-0.014174[/C][C]-0.2363[/C][C]0.406677[/C][/ROW]
[ROW][C]3[/C][C]0.104531[/C][C]1.7429[/C][C]0.04123[/C][/ROW]
[ROW][C]4[/C][C]0.065572[/C][C]1.0933[/C][C]0.137603[/C][/ROW]
[ROW][C]5[/C][C]-0.160796[/C][C]-2.681[/C][C]0.003889[/C][/ROW]
[ROW][C]6[/C][C]-0.028392[/C][C]-0.4734[/C][C]0.318154[/C][/ROW]
[ROW][C]7[/C][C]-0.055588[/C][C]-0.9268[/C][C]0.177409[/C][/ROW]
[ROW][C]8[/C][C]-0.046395[/C][C]-0.7736[/C][C]0.219922[/C][/ROW]
[ROW][C]9[/C][C]-0.075562[/C][C]-1.2599[/C][C]0.104385[/C][/ROW]
[ROW][C]10[/C][C]-0.021612[/C][C]-0.3603[/C][C]0.359432[/C][/ROW]
[ROW][C]11[/C][C]-0.002052[/C][C]-0.0342[/C][C]0.486369[/C][/ROW]
[ROW][C]12[/C][C]-0.019628[/C][C]-0.3273[/C][C]0.371854[/C][/ROW]
[ROW][C]13[/C][C]0.048324[/C][C]0.8057[/C][C]0.210545[/C][/ROW]
[ROW][C]14[/C][C]0.05964[/C][C]0.9944[/C][C]0.160447[/C][/ROW]
[ROW][C]15[/C][C]-0.030137[/C][C]-0.5025[/C][C]0.307863[/C][/ROW]
[ROW][C]16[/C][C]0.1141[/C][C]1.9024[/C][C]0.029074[/C][/ROW]
[ROW][C]17[/C][C]0.038771[/C][C]0.6464[/C][C]0.259265[/C][/ROW]
[ROW][C]18[/C][C]-0.065908[/C][C]-1.0989[/C][C]0.136379[/C][/ROW]
[ROW][C]19[/C][C]-0.117961[/C][C]-1.9668[/C][C]0.0251[/C][/ROW]
[ROW][C]20[/C][C]0.052608[/C][C]0.8772[/C][C]0.19058[/C][/ROW]
[ROW][C]21[/C][C]-0.05536[/C][C]-0.923[/C][C]0.178393[/C][/ROW]
[ROW][C]22[/C][C]0.049682[/C][C]0.8284[/C][C]0.204089[/C][/ROW]
[ROW][C]23[/C][C]-0.037781[/C][C]-0.6299[/C][C]0.264629[/C][/ROW]
[ROW][C]24[/C][C]0.021227[/C][C]0.3539[/C][C]0.36183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1-0.025227-0.42060.33718
2-0.014174-0.23630.406677
30.1045311.74290.04123
40.0655721.09330.137603
5-0.160796-2.6810.003889
6-0.028392-0.47340.318154
7-0.055588-0.92680.177409
8-0.046395-0.77360.219922
9-0.075562-1.25990.104385
10-0.021612-0.36030.359432
11-0.002052-0.03420.486369
12-0.019628-0.32730.371854
130.0483240.80570.210545
140.059640.99440.160447
15-0.030137-0.50250.307863
160.11411.90240.029074
170.0387710.64640.259265
18-0.065908-1.09890.136379
19-0.117961-1.96680.0251
200.0526080.87720.19058
21-0.05536-0.9230.178393
220.0496820.82840.204089
23-0.037781-0.62990.264629
240.0212270.35390.36183






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.025227-0.42060.33718
2-0.01482-0.24710.402509
30.1038831.73210.042185
40.0713661.18990.117548
5-0.15687-2.61550.004697
6-0.047822-0.79740.212963
7-0.075831-1.26440.103581
8-0.02211-0.36870.356334
9-0.050662-0.84470.199501
10-0.033285-0.5550.28968
11-0.000383-0.00640.497455
12-0.025268-0.42130.336928
130.0480040.80040.212086
140.0419610.69960.242374
15-0.041431-0.69080.245134
160.0994641.65840.049183
170.014910.24860.401926
18-0.058046-0.96780.166989
19-0.135588-2.26070.012275
200.0213340.35570.361162
21-0.008285-0.13810.445113
220.1087421.81310.035448
23-0.023766-0.39630.346111
24-0.013077-0.2180.413781

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.025227 & -0.4206 & 0.33718 \tabularnewline
2 & -0.01482 & -0.2471 & 0.402509 \tabularnewline
3 & 0.103883 & 1.7321 & 0.042185 \tabularnewline
4 & 0.071366 & 1.1899 & 0.117548 \tabularnewline
5 & -0.15687 & -2.6155 & 0.004697 \tabularnewline
6 & -0.047822 & -0.7974 & 0.212963 \tabularnewline
7 & -0.075831 & -1.2644 & 0.103581 \tabularnewline
8 & -0.02211 & -0.3687 & 0.356334 \tabularnewline
9 & -0.050662 & -0.8447 & 0.199501 \tabularnewline
10 & -0.033285 & -0.555 & 0.28968 \tabularnewline
11 & -0.000383 & -0.0064 & 0.497455 \tabularnewline
12 & -0.025268 & -0.4213 & 0.336928 \tabularnewline
13 & 0.048004 & 0.8004 & 0.212086 \tabularnewline
14 & 0.041961 & 0.6996 & 0.242374 \tabularnewline
15 & -0.041431 & -0.6908 & 0.245134 \tabularnewline
16 & 0.099464 & 1.6584 & 0.049183 \tabularnewline
17 & 0.01491 & 0.2486 & 0.401926 \tabularnewline
18 & -0.058046 & -0.9678 & 0.166989 \tabularnewline
19 & -0.135588 & -2.2607 & 0.012275 \tabularnewline
20 & 0.021334 & 0.3557 & 0.361162 \tabularnewline
21 & -0.008285 & -0.1381 & 0.445113 \tabularnewline
22 & 0.108742 & 1.8131 & 0.035448 \tabularnewline
23 & -0.023766 & -0.3963 & 0.346111 \tabularnewline
24 & -0.013077 & -0.218 & 0.413781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.025227[/C][C]-0.4206[/C][C]0.33718[/C][/ROW]
[ROW][C]2[/C][C]-0.01482[/C][C]-0.2471[/C][C]0.402509[/C][/ROW]
[ROW][C]3[/C][C]0.103883[/C][C]1.7321[/C][C]0.042185[/C][/ROW]
[ROW][C]4[/C][C]0.071366[/C][C]1.1899[/C][C]0.117548[/C][/ROW]
[ROW][C]5[/C][C]-0.15687[/C][C]-2.6155[/C][C]0.004697[/C][/ROW]
[ROW][C]6[/C][C]-0.047822[/C][C]-0.7974[/C][C]0.212963[/C][/ROW]
[ROW][C]7[/C][C]-0.075831[/C][C]-1.2644[/C][C]0.103581[/C][/ROW]
[ROW][C]8[/C][C]-0.02211[/C][C]-0.3687[/C][C]0.356334[/C][/ROW]
[ROW][C]9[/C][C]-0.050662[/C][C]-0.8447[/C][C]0.199501[/C][/ROW]
[ROW][C]10[/C][C]-0.033285[/C][C]-0.555[/C][C]0.28968[/C][/ROW]
[ROW][C]11[/C][C]-0.000383[/C][C]-0.0064[/C][C]0.497455[/C][/ROW]
[ROW][C]12[/C][C]-0.025268[/C][C]-0.4213[/C][C]0.336928[/C][/ROW]
[ROW][C]13[/C][C]0.048004[/C][C]0.8004[/C][C]0.212086[/C][/ROW]
[ROW][C]14[/C][C]0.041961[/C][C]0.6996[/C][C]0.242374[/C][/ROW]
[ROW][C]15[/C][C]-0.041431[/C][C]-0.6908[/C][C]0.245134[/C][/ROW]
[ROW][C]16[/C][C]0.099464[/C][C]1.6584[/C][C]0.049183[/C][/ROW]
[ROW][C]17[/C][C]0.01491[/C][C]0.2486[/C][C]0.401926[/C][/ROW]
[ROW][C]18[/C][C]-0.058046[/C][C]-0.9678[/C][C]0.166989[/C][/ROW]
[ROW][C]19[/C][C]-0.135588[/C][C]-2.2607[/C][C]0.012275[/C][/ROW]
[ROW][C]20[/C][C]0.021334[/C][C]0.3557[/C][C]0.361162[/C][/ROW]
[ROW][C]21[/C][C]-0.008285[/C][C]-0.1381[/C][C]0.445113[/C][/ROW]
[ROW][C]22[/C][C]0.108742[/C][C]1.8131[/C][C]0.035448[/C][/ROW]
[ROW][C]23[/C][C]-0.023766[/C][C]-0.3963[/C][C]0.346111[/C][/ROW]
[ROW][C]24[/C][C]-0.013077[/C][C]-0.218[/C][C]0.413781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1-0.025227-0.42060.33718
2-0.01482-0.24710.402509
30.1038831.73210.042185
40.0713661.18990.117548
5-0.15687-2.61550.004697
6-0.047822-0.79740.212963
7-0.075831-1.26440.103581
8-0.02211-0.36870.356334
9-0.050662-0.84470.199501
10-0.033285-0.5550.28968
11-0.000383-0.00640.497455
12-0.025268-0.42130.336928
130.0480040.80040.212086
140.0419610.69960.242374
15-0.041431-0.69080.245134
160.0994641.65840.049183
170.014910.24860.401926
18-0.058046-0.96780.166989
19-0.135588-2.26070.012275
200.0213340.35570.361162
21-0.008285-0.13810.445113
220.1087421.81310.035448
23-0.023766-0.39630.346111
24-0.013077-0.2180.413781


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 011Default1redtwo.sidedtwo.sided1111FALSE1211811Default ; par2 = noDo not include Seasonal DummiesDo not include Seasonal Dummies1Do not include Seasonal Dummiesno0,990.99Do not include Seasonal Dummies222-0.3-0.3Do not include Seasonal DummiesDo not include Seasonal Dummies0Do not include Seasonal DummiesDo not include Seasonal Dummies1 ; par3 = 512No Linear TrendNo Linear Trend0No Linear Trend1515No Linear Trend3No Linear TrendExact Pearson Chi-Squared by Simulation00No Linear TrendNo Linear TrendNo Linear TrendNo Linear Trend0 ; par4 = 0000TRUETRUE1100 ; par5 = 001201212012 ; par6 = 1212White Noise123312121212White Noise ; par7 = 0.95100.95 ; par8 = 22 ; par9 = 10 ; par10 = FALSE ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; 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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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')