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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, 24 Jan 2018 10:39:33 +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/24/t1516786796c8lvnebem2yw16i.htm/, Retrieved Mon, 06 May 2024 09:54:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=312368, Retrieved Mon, 06 May 2024 09:54:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2018-01-24 09:39:33] [6ed64e8c4e855e992fbbfd41bce49003] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
62.4
67.4
76.1
67.4
74.5
72.6
60.5
66.1
76.5
76.8
77
71
74.8
73.7
80.5
71.8
76.9
79.9
65.9
69.5
75.1
79.6
75.2
68
72.8
71.5
78.5
76.8
75.3
76.7
69.7
67.8
77.5
82.5
75.3
70.9
76
73.7
79.7
77.8
73.3
78.3
71.9
67
82
83.7
74.8
80
74.3
76.8
89
81.9
76.8
88.9
75.8
75.5
89.1
88
85.9
89.3
82.9
81.2
90.5
86.4
81.8
91.3
73.4
76.6
91
87
89.7
90.7
86.5
86.6
98.8
84.4
91.4
95.7
78.5
81.7
94.3
98.5
95.4
91.7
92.8
90.5
102.2
91.8
95
102
88.9
89.6
97.9
108.6
100.8
95.1
101
100.9
102.5
105.4
98.4
105.3
96.5
88.1
107.9
107
92.5
95.7
85.2
85.5
94.7
86.2
88.8
93.4
83.4
82.9
96.7
96.2
92.8
92.8
90
95.4
108.3
96.3
95
109
92
92.3
107
105.5
105.4
103.9
99.2
102.2
121.5
102.3
110
105.9
91.9
100
111.7
104.9
103.3
101.8
100.8
104.2
116.5
97.9
100.7
107
96.3
96
104.5
107.4
102.4
94.9
98.8
96.8
108.2
103.8
102.3
107.2
102
92.6
105.2
113
105.6
101.6
101.7
102.7
109
105.5
103.3
108.6
98.2
90
112.4
111.9
102.1
102.4
101.7
98.7
114
105.1
98.3
110
96.5
92.2
112
111.4
107.5
103.4
103.5
107.4
117.6
110.2
104.3
115.9
98.9
101.9
113.5
109.5
110
114.2
106.9
109.2
124.2
104.7
111.9
119
102.9
106.3

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312368&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=312368&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312368&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 time2 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.504455-7.11620
2-0.085947-1.21240.113393
30.3553795.01321e-06
4-0.307128-4.33261.2e-05
50.1207891.70390.044976
60.1609982.27120.012104
7-0.236584-3.33740.000505
80.0847821.1960.116559
90.0467330.65920.255249
10-0.094406-1.33180.092232
110.1689842.38380.009037
12-0.205385-2.89730.002093
13-0.004991-0.07040.471968
140.0806661.13790.128257
15-0.032775-0.46240.322167
16-0.073659-1.03910.150013
170.0585470.82590.204922
180.0402850.56830.285239
19-0.169843-2.39590.008752
200.1193961.68430.046848
210.0444980.62770.265452
22-0.262951-3.70940.000135
230.3264854.60564e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.504455 & -7.1162 & 0 \tabularnewline
2 & -0.085947 & -1.2124 & 0.113393 \tabularnewline
3 & 0.355379 & 5.0132 & 1e-06 \tabularnewline
4 & -0.307128 & -4.3326 & 1.2e-05 \tabularnewline
5 & 0.120789 & 1.7039 & 0.044976 \tabularnewline
6 & 0.160998 & 2.2712 & 0.012104 \tabularnewline
7 & -0.236584 & -3.3374 & 0.000505 \tabularnewline
8 & 0.084782 & 1.196 & 0.116559 \tabularnewline
9 & 0.046733 & 0.6592 & 0.255249 \tabularnewline
10 & -0.094406 & -1.3318 & 0.092232 \tabularnewline
11 & 0.168984 & 2.3838 & 0.009037 \tabularnewline
12 & -0.205385 & -2.8973 & 0.002093 \tabularnewline
13 & -0.004991 & -0.0704 & 0.471968 \tabularnewline
14 & 0.080666 & 1.1379 & 0.128257 \tabularnewline
15 & -0.032775 & -0.4624 & 0.322167 \tabularnewline
16 & -0.073659 & -1.0391 & 0.150013 \tabularnewline
17 & 0.058547 & 0.8259 & 0.204922 \tabularnewline
18 & 0.040285 & 0.5683 & 0.285239 \tabularnewline
19 & -0.169843 & -2.3959 & 0.008752 \tabularnewline
20 & 0.119396 & 1.6843 & 0.046848 \tabularnewline
21 & 0.044498 & 0.6277 & 0.265452 \tabularnewline
22 & -0.262951 & -3.7094 & 0.000135 \tabularnewline
23 & 0.326485 & 4.6056 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312368&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]-0.504455[/C][C]-7.1162[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.085947[/C][C]-1.2124[/C][C]0.113393[/C][/ROW]
[ROW][C]3[/C][C]0.355379[/C][C]5.0132[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.307128[/C][C]-4.3326[/C][C]1.2e-05[/C][/ROW]
[ROW][C]5[/C][C]0.120789[/C][C]1.7039[/C][C]0.044976[/C][/ROW]
[ROW][C]6[/C][C]0.160998[/C][C]2.2712[/C][C]0.012104[/C][/ROW]
[ROW][C]7[/C][C]-0.236584[/C][C]-3.3374[/C][C]0.000505[/C][/ROW]
[ROW][C]8[/C][C]0.084782[/C][C]1.196[/C][C]0.116559[/C][/ROW]
[ROW][C]9[/C][C]0.046733[/C][C]0.6592[/C][C]0.255249[/C][/ROW]
[ROW][C]10[/C][C]-0.094406[/C][C]-1.3318[/C][C]0.092232[/C][/ROW]
[ROW][C]11[/C][C]0.168984[/C][C]2.3838[/C][C]0.009037[/C][/ROW]
[ROW][C]12[/C][C]-0.205385[/C][C]-2.8973[/C][C]0.002093[/C][/ROW]
[ROW][C]13[/C][C]-0.004991[/C][C]-0.0704[/C][C]0.471968[/C][/ROW]
[ROW][C]14[/C][C]0.080666[/C][C]1.1379[/C][C]0.128257[/C][/ROW]
[ROW][C]15[/C][C]-0.032775[/C][C]-0.4624[/C][C]0.322167[/C][/ROW]
[ROW][C]16[/C][C]-0.073659[/C][C]-1.0391[/C][C]0.150013[/C][/ROW]
[ROW][C]17[/C][C]0.058547[/C][C]0.8259[/C][C]0.204922[/C][/ROW]
[ROW][C]18[/C][C]0.040285[/C][C]0.5683[/C][C]0.285239[/C][/ROW]
[ROW][C]19[/C][C]-0.169843[/C][C]-2.3959[/C][C]0.008752[/C][/ROW]
[ROW][C]20[/C][C]0.119396[/C][C]1.6843[/C][C]0.046848[/C][/ROW]
[ROW][C]21[/C][C]0.044498[/C][C]0.6277[/C][C]0.265452[/C][/ROW]
[ROW][C]22[/C][C]-0.262951[/C][C]-3.7094[/C][C]0.000135[/C][/ROW]
[ROW][C]23[/C][C]0.326485[/C][C]4.6056[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312368&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312368&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
1-0.504455-7.11620
2-0.085947-1.21240.113393
30.3553795.01321e-06
4-0.307128-4.33261.2e-05
50.1207891.70390.044976
60.1609982.27120.012104
7-0.236584-3.33740.000505
80.0847821.1960.116559
90.0467330.65920.255249
10-0.094406-1.33180.092232
110.1689842.38380.009037
12-0.205385-2.89730.002093
13-0.004991-0.07040.471968
140.0806661.13790.128257
15-0.032775-0.46240.322167
16-0.073659-1.03910.150013
170.0585470.82590.204922
180.0402850.56830.285239
19-0.169843-2.39590.008752
200.1193961.68430.046848
210.0444980.62770.265452
22-0.262951-3.70940.000135
230.3264854.60564e-06






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.504455-7.11620
2-0.45662-6.44140
30.1048691.47940.070313
4-0.073224-1.0330.15144
50.0425440.60020.274543
60.1880222.65240.004319
70.0675870.95340.170765
8-0.049025-0.69160.245005
9-0.072585-1.02390.153556
10-0.035865-0.50590.306728
110.1507312.12630.017354
12-0.12235-1.7260.042953
13-0.184076-2.59670.005057
14-0.209477-2.9550.001752
150.0100080.14120.443934
16-0.13131-1.85240.032728
17-0.081979-1.15650.12444
180.1673852.36130.00959
19-0.027634-0.38980.348539
20-0.116047-1.6370.051601
210.004930.06950.472315
22-0.205149-2.8940.002114
230.1642282.31670.010768

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.504455 & -7.1162 & 0 \tabularnewline
2 & -0.45662 & -6.4414 & 0 \tabularnewline
3 & 0.104869 & 1.4794 & 0.070313 \tabularnewline
4 & -0.073224 & -1.033 & 0.15144 \tabularnewline
5 & 0.042544 & 0.6002 & 0.274543 \tabularnewline
6 & 0.188022 & 2.6524 & 0.004319 \tabularnewline
7 & 0.067587 & 0.9534 & 0.170765 \tabularnewline
8 & -0.049025 & -0.6916 & 0.245005 \tabularnewline
9 & -0.072585 & -1.0239 & 0.153556 \tabularnewline
10 & -0.035865 & -0.5059 & 0.306728 \tabularnewline
11 & 0.150731 & 2.1263 & 0.017354 \tabularnewline
12 & -0.12235 & -1.726 & 0.042953 \tabularnewline
13 & -0.184076 & -2.5967 & 0.005057 \tabularnewline
14 & -0.209477 & -2.955 & 0.001752 \tabularnewline
15 & 0.010008 & 0.1412 & 0.443934 \tabularnewline
16 & -0.13131 & -1.8524 & 0.032728 \tabularnewline
17 & -0.081979 & -1.1565 & 0.12444 \tabularnewline
18 & 0.167385 & 2.3613 & 0.00959 \tabularnewline
19 & -0.027634 & -0.3898 & 0.348539 \tabularnewline
20 & -0.116047 & -1.637 & 0.051601 \tabularnewline
21 & 0.00493 & 0.0695 & 0.472315 \tabularnewline
22 & -0.205149 & -2.894 & 0.002114 \tabularnewline
23 & 0.164228 & 2.3167 & 0.010768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312368&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]-0.504455[/C][C]-7.1162[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.45662[/C][C]-6.4414[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.104869[/C][C]1.4794[/C][C]0.070313[/C][/ROW]
[ROW][C]4[/C][C]-0.073224[/C][C]-1.033[/C][C]0.15144[/C][/ROW]
[ROW][C]5[/C][C]0.042544[/C][C]0.6002[/C][C]0.274543[/C][/ROW]
[ROW][C]6[/C][C]0.188022[/C][C]2.6524[/C][C]0.004319[/C][/ROW]
[ROW][C]7[/C][C]0.067587[/C][C]0.9534[/C][C]0.170765[/C][/ROW]
[ROW][C]8[/C][C]-0.049025[/C][C]-0.6916[/C][C]0.245005[/C][/ROW]
[ROW][C]9[/C][C]-0.072585[/C][C]-1.0239[/C][C]0.153556[/C][/ROW]
[ROW][C]10[/C][C]-0.035865[/C][C]-0.5059[/C][C]0.306728[/C][/ROW]
[ROW][C]11[/C][C]0.150731[/C][C]2.1263[/C][C]0.017354[/C][/ROW]
[ROW][C]12[/C][C]-0.12235[/C][C]-1.726[/C][C]0.042953[/C][/ROW]
[ROW][C]13[/C][C]-0.184076[/C][C]-2.5967[/C][C]0.005057[/C][/ROW]
[ROW][C]14[/C][C]-0.209477[/C][C]-2.955[/C][C]0.001752[/C][/ROW]
[ROW][C]15[/C][C]0.010008[/C][C]0.1412[/C][C]0.443934[/C][/ROW]
[ROW][C]16[/C][C]-0.13131[/C][C]-1.8524[/C][C]0.032728[/C][/ROW]
[ROW][C]17[/C][C]-0.081979[/C][C]-1.1565[/C][C]0.12444[/C][/ROW]
[ROW][C]18[/C][C]0.167385[/C][C]2.3613[/C][C]0.00959[/C][/ROW]
[ROW][C]19[/C][C]-0.027634[/C][C]-0.3898[/C][C]0.348539[/C][/ROW]
[ROW][C]20[/C][C]-0.116047[/C][C]-1.637[/C][C]0.051601[/C][/ROW]
[ROW][C]21[/C][C]0.00493[/C][C]0.0695[/C][C]0.472315[/C][/ROW]
[ROW][C]22[/C][C]-0.205149[/C][C]-2.894[/C][C]0.002114[/C][/ROW]
[ROW][C]23[/C][C]0.164228[/C][C]2.3167[/C][C]0.010768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312368&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312368&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
1-0.504455-7.11620
2-0.45662-6.44140
30.1048691.47940.070313
4-0.073224-1.0330.15144
50.0425440.60020.274543
60.1880222.65240.004319
70.0675870.95340.170765
8-0.049025-0.69160.245005
9-0.072585-1.02390.153556
10-0.035865-0.50590.306728
110.1507312.12630.017354
12-0.12235-1.7260.042953
13-0.184076-2.59670.005057
14-0.209477-2.9550.001752
150.0100080.14120.443934
16-0.13131-1.85240.032728
17-0.081979-1.15650.12444
180.1673852.36130.00959
19-0.027634-0.38980.348539
20-0.116047-1.6370.051601
210.004930.06950.472315
22-0.205149-2.8940.002114
230.1642282.31670.010768


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; 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')