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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, 19 Dec 2012 10:26:35 -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/2012/Dec/19/t1355930818e4y4jptbalzbj6t.htm/, Retrieved Fri, 03 May 2024 22:39:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202071, Retrieved Fri, 03 May 2024 22:39:52 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [] [2012-12-10 15:16:35] [74be16979710d4c4e7c6647856088456]
-   P         [(Partial) Autocorrelation Function] [] [2012-12-19 15:26:35] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   P           [(Partial) Autocorrelation Function] [] [2012-12-19 16:17:43] [bbed103f50d9b60ea97669d7e6947a11]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
59.8
60.7
59.7
60.2
61.3
59.8
61.2
59.3
59.4
63.1
68
69.4
70.2
72.6
72.1
69.7
71.5
75.7
76
76.4
83.8
86.2
88.5
95.9
103.1
113.5
115.7
113.1
112.7
121.9
120.3
108.7
102.8
83.4
79.4
77.8
85.7
83.2
82
86.9
95.7
97.9
89.3
91.5
86.8
91
93.8
96.8
95.7
91.4
88.7
88.2
87.7
89.5
95.6
100.5
106.3
112
117.7
125
132.4
138.1
134.7
136.7
134.3
131.6
129.8
131.9
129.8
119.4
116.7
112.8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202071&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202071&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202071&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.4095673.45110.000472
20.215821.81850.0366
30.0545850.45990.323482
40.0859130.72390.235749
50.0121040.1020.459526
6-0.089832-0.75690.225795
7-0.085212-0.7180.237554
8-0.334377-2.81750.003132
9-0.197549-1.66460.050202
10-0.238668-2.01110.024059
11-0.013656-0.11510.45436
12-0.144392-1.21670.11388
13-0.174344-1.46910.073118
14-0.076874-0.64780.259616
150.0123370.1040.45875
160.1160650.9780.165703
170.0189550.15970.436777
180.0703770.5930.277531

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.409567 & 3.4511 & 0.000472 \tabularnewline
2 & 0.21582 & 1.8185 & 0.0366 \tabularnewline
3 & 0.054585 & 0.4599 & 0.323482 \tabularnewline
4 & 0.085913 & 0.7239 & 0.235749 \tabularnewline
5 & 0.012104 & 0.102 & 0.459526 \tabularnewline
6 & -0.089832 & -0.7569 & 0.225795 \tabularnewline
7 & -0.085212 & -0.718 & 0.237554 \tabularnewline
8 & -0.334377 & -2.8175 & 0.003132 \tabularnewline
9 & -0.197549 & -1.6646 & 0.050202 \tabularnewline
10 & -0.238668 & -2.0111 & 0.024059 \tabularnewline
11 & -0.013656 & -0.1151 & 0.45436 \tabularnewline
12 & -0.144392 & -1.2167 & 0.11388 \tabularnewline
13 & -0.174344 & -1.4691 & 0.073118 \tabularnewline
14 & -0.076874 & -0.6478 & 0.259616 \tabularnewline
15 & 0.012337 & 0.104 & 0.45875 \tabularnewline
16 & 0.116065 & 0.978 & 0.165703 \tabularnewline
17 & 0.018955 & 0.1597 & 0.436777 \tabularnewline
18 & 0.070377 & 0.593 & 0.277531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202071&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]0.409567[/C][C]3.4511[/C][C]0.000472[/C][/ROW]
[ROW][C]2[/C][C]0.21582[/C][C]1.8185[/C][C]0.0366[/C][/ROW]
[ROW][C]3[/C][C]0.054585[/C][C]0.4599[/C][C]0.323482[/C][/ROW]
[ROW][C]4[/C][C]0.085913[/C][C]0.7239[/C][C]0.235749[/C][/ROW]
[ROW][C]5[/C][C]0.012104[/C][C]0.102[/C][C]0.459526[/C][/ROW]
[ROW][C]6[/C][C]-0.089832[/C][C]-0.7569[/C][C]0.225795[/C][/ROW]
[ROW][C]7[/C][C]-0.085212[/C][C]-0.718[/C][C]0.237554[/C][/ROW]
[ROW][C]8[/C][C]-0.334377[/C][C]-2.8175[/C][C]0.003132[/C][/ROW]
[ROW][C]9[/C][C]-0.197549[/C][C]-1.6646[/C][C]0.050202[/C][/ROW]
[ROW][C]10[/C][C]-0.238668[/C][C]-2.0111[/C][C]0.024059[/C][/ROW]
[ROW][C]11[/C][C]-0.013656[/C][C]-0.1151[/C][C]0.45436[/C][/ROW]
[ROW][C]12[/C][C]-0.144392[/C][C]-1.2167[/C][C]0.11388[/C][/ROW]
[ROW][C]13[/C][C]-0.174344[/C][C]-1.4691[/C][C]0.073118[/C][/ROW]
[ROW][C]14[/C][C]-0.076874[/C][C]-0.6478[/C][C]0.259616[/C][/ROW]
[ROW][C]15[/C][C]0.012337[/C][C]0.104[/C][C]0.45875[/C][/ROW]
[ROW][C]16[/C][C]0.116065[/C][C]0.978[/C][C]0.165703[/C][/ROW]
[ROW][C]17[/C][C]0.018955[/C][C]0.1597[/C][C]0.436777[/C][/ROW]
[ROW][C]18[/C][C]0.070377[/C][C]0.593[/C][C]0.277531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202071&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202071&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
10.4095673.45110.000472
20.215821.81850.0366
30.0545850.45990.323482
40.0859130.72390.235749
50.0121040.1020.459526
6-0.089832-0.75690.225795
7-0.085212-0.7180.237554
8-0.334377-2.81750.003132
9-0.197549-1.66460.050202
10-0.238668-2.01110.024059
11-0.013656-0.11510.45436
12-0.144392-1.21670.11388
13-0.174344-1.46910.073118
14-0.076874-0.64780.259616
150.0123370.1040.45875
160.1160650.9780.165703
170.0189550.15970.436777
180.0703770.5930.277531






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.4095673.45110.000472
20.0577640.48670.313974
3-0.063124-0.53190.29823
40.0880910.74230.230187
5-0.049989-0.42120.337435
6-0.120299-1.01370.157095
70.001850.01560.493803
8-0.343263-2.89240.002536
90.0644180.54280.294486
10-0.121372-1.02270.154961
110.143581.20980.115178
12-0.166002-1.39880.08312
13-0.116492-0.98160.164819
140.0549520.4630.322379
150.0305260.25720.398879
16-0.005903-0.04970.480236
17-0.037864-0.3190.375314
18-0.072315-0.60930.272124

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.409567 & 3.4511 & 0.000472 \tabularnewline
2 & 0.057764 & 0.4867 & 0.313974 \tabularnewline
3 & -0.063124 & -0.5319 & 0.29823 \tabularnewline
4 & 0.088091 & 0.7423 & 0.230187 \tabularnewline
5 & -0.049989 & -0.4212 & 0.337435 \tabularnewline
6 & -0.120299 & -1.0137 & 0.157095 \tabularnewline
7 & 0.00185 & 0.0156 & 0.493803 \tabularnewline
8 & -0.343263 & -2.8924 & 0.002536 \tabularnewline
9 & 0.064418 & 0.5428 & 0.294486 \tabularnewline
10 & -0.121372 & -1.0227 & 0.154961 \tabularnewline
11 & 0.14358 & 1.2098 & 0.115178 \tabularnewline
12 & -0.166002 & -1.3988 & 0.08312 \tabularnewline
13 & -0.116492 & -0.9816 & 0.164819 \tabularnewline
14 & 0.054952 & 0.463 & 0.322379 \tabularnewline
15 & 0.030526 & 0.2572 & 0.398879 \tabularnewline
16 & -0.005903 & -0.0497 & 0.480236 \tabularnewline
17 & -0.037864 & -0.319 & 0.375314 \tabularnewline
18 & -0.072315 & -0.6093 & 0.272124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202071&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]0.409567[/C][C]3.4511[/C][C]0.000472[/C][/ROW]
[ROW][C]2[/C][C]0.057764[/C][C]0.4867[/C][C]0.313974[/C][/ROW]
[ROW][C]3[/C][C]-0.063124[/C][C]-0.5319[/C][C]0.29823[/C][/ROW]
[ROW][C]4[/C][C]0.088091[/C][C]0.7423[/C][C]0.230187[/C][/ROW]
[ROW][C]5[/C][C]-0.049989[/C][C]-0.4212[/C][C]0.337435[/C][/ROW]
[ROW][C]6[/C][C]-0.120299[/C][C]-1.0137[/C][C]0.157095[/C][/ROW]
[ROW][C]7[/C][C]0.00185[/C][C]0.0156[/C][C]0.493803[/C][/ROW]
[ROW][C]8[/C][C]-0.343263[/C][C]-2.8924[/C][C]0.002536[/C][/ROW]
[ROW][C]9[/C][C]0.064418[/C][C]0.5428[/C][C]0.294486[/C][/ROW]
[ROW][C]10[/C][C]-0.121372[/C][C]-1.0227[/C][C]0.154961[/C][/ROW]
[ROW][C]11[/C][C]0.14358[/C][C]1.2098[/C][C]0.115178[/C][/ROW]
[ROW][C]12[/C][C]-0.166002[/C][C]-1.3988[/C][C]0.08312[/C][/ROW]
[ROW][C]13[/C][C]-0.116492[/C][C]-0.9816[/C][C]0.164819[/C][/ROW]
[ROW][C]14[/C][C]0.054952[/C][C]0.463[/C][C]0.322379[/C][/ROW]
[ROW][C]15[/C][C]0.030526[/C][C]0.2572[/C][C]0.398879[/C][/ROW]
[ROW][C]16[/C][C]-0.005903[/C][C]-0.0497[/C][C]0.480236[/C][/ROW]
[ROW][C]17[/C][C]-0.037864[/C][C]-0.319[/C][C]0.375314[/C][/ROW]
[ROW][C]18[/C][C]-0.072315[/C][C]-0.6093[/C][C]0.272124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202071&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202071&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
10.4095673.45110.000472
20.0577640.48670.313974
3-0.063124-0.53190.29823
40.0880910.74230.230187
5-0.049989-0.42120.337435
6-0.120299-1.01370.157095
70.001850.01560.493803
8-0.343263-2.89240.002536
90.0644180.54280.294486
10-0.121372-1.02270.154961
110.143581.20980.115178
12-0.166002-1.39880.08312
13-0.116492-0.98160.164819
140.0549520.4630.322379
150.0305260.25720.398879
16-0.005903-0.04970.480236
17-0.037864-0.3190.375314
18-0.072315-0.60930.272124


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')