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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 computationSat, 29 Nov 2008 13:35:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/29/t1227990998wamwkuddwxs2ygf.htm/, Retrieved Thu, 20 Feb 2025 19:06:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26370, Retrieved Thu, 20 Feb 2025 19:06:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact281

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] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:10:39] [57fa5e3679c393aa19449b2f1be9928b]
-   P     [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:18:39] [57fa5e3679c393aa19449b2f1be9928b]
- RM        [Variance Reduction Matrix] [Q6 Variance] [2008-11-29 20:25:29] [57fa5e3679c393aa19449b2f1be9928b]
- RM            [(Partial) Autocorrelation Function] [Q6 ACF] [2008-11-29 20:35:57] [270782e2502ae87124d0ebdcd1862d6a] [Current]
- RM              [Spectral Analysis] [Q6 Spectrum] [2008-11-29 20:38:15] [57fa5e3679c393aa19449b2f1be9928b]
-                   [Spectral Analysis] [Aangepast spectrum] [2008-11-29 20:47:16] [57fa5e3679c393aa19449b2f1be9928b]
-   P                 [Spectral Analysis] [] [2008-11-30 11:16:46] [a4ee3bef49b119f4bd2e925060c84f5e]
-                       [Spectral Analysis] [] [2008-12-01 19:22:10] [d134696a922d84037f02d49ded84b0bd]
-   P               [Spectral Analysis] [] [2008-11-30 11:11:32] [a4ee3bef49b119f4bd2e925060c84f5e]
-                     [Spectral Analysis] [] [2008-11-30 18:09:44] [4300be8b33fd3dcdacd2aa9800ceba23]
F                       [Spectral Analysis] [] [2008-12-01 17:25:59] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P                   [Spectral Analysis] [] [2008-12-01 17:26:12] [29747f79f5beb5b2516e1271770ecb47]
F   P                   [Spectral Analysis] [] [2008-12-01 17:28:41] [29747f79f5beb5b2516e1271770ecb47]
-   P                   [Spectral Analysis] [3 q6 taak 7] [2008-12-01 17:32:31] [7506b5e9e41ec66c6657f4234f97306e]
-   P                   [Spectral Analysis] [q6 deel 3] [2008-12-01 17:43:59] [491a70d26f8c977398d8a0c1c87d3dd4]
F                       [Spectral Analysis] [q6] [2008-12-01 18:37:38] [4ad596f10399a71ad29b7d76e6ab90ac]
-                       [Spectral Analysis] [Non Stationary Ti...] [2008-12-01 18:52:49] [79c17183721a40a589db5f9f561947d8]
-                       [Spectral Analysis] [] [2008-12-01 18:59:52] [c5e27150943bc3d623392efb0d98f8d3]
-                       [Spectral Analysis] [Q6] [2008-12-01 19:05:39] [b47fceb71c9525e79a89b5fc6d023d0e]
F                       [Spectral Analysis] [Non Stationary Ti...] [2008-12-01 19:49:41] [db72903d7941c8279d5ce0e4e873d517]
F                       [Spectral Analysis] [] [2008-12-01 23:54:06] [fad8a251ac01c156a8ae23a83577546f]
F                     [Spectral Analysis] [] [2008-12-01 19:17:44] [d134696a922d84037f02d49ded84b0bd]
-                 [(Partial) Autocorrelation Function] [Q6 aangepaste ACF] [2008-11-29 20:44:03] [57fa5e3679c393aa19449b2f1be9928b]
- RM D              [Cross Correlation Function] [Q7] [2008-11-29 20:55:14] [57fa5e3679c393aa19449b2f1be9928b]
F RM D                [Standard Deviation-Mean Plot] [Q8 Mean plot insc...] [2008-11-29 21:03:17] [57fa5e3679c393aa19449b2f1be9928b]
F RM                    [Variance Reduction Matrix] [Q8 VRM Inschrijvi...] [2008-11-29 21:06:11] [57fa5e3679c393aa19449b2f1be9928b]
-                         [Variance Reduction Matrix] [] [2008-11-30 11:19:07] [ffbe22449df335faef31f462015daa42]
-   P                     [Variance Reduction Matrix] [] [2008-11-30 11:22:31] [a4ee3bef49b119f4bd2e925060c84f5e]
- RM                      [(Partial) Autocorrelation Function] [Q2 inschrijvingen...] [2008-12-07 14:47:46] [57fa5e3679c393aa19449b2f1be9928b]
- RM                        [Spectral Analysis] [Q2 inschrijvingen...] [2008-12-07 14:51:43] [57fa5e3679c393aa19449b2f1be9928b]
-                             [Spectral Analysis] [Q3 Spec analyse] [2008-12-07 14:56:15] [57fa5e3679c393aa19449b2f1be9928b]
-   P                           [Spectral Analysis] [Q3 Spec analyse] [2008-12-08 19:19:32] [57fa5e3679c393aa19449b2f1be9928b]
-   P                         [Spectral Analysis] [Q2 inschrijvingen...] [2008-12-08 19:15:44] [57fa5e3679c393aa19449b2f1be9928b]
-                           [(Partial) Autocorrelation Function] [Q3] [2008-12-07 14:59:20] [57fa5e3679c393aa19449b2f1be9928b]
- RM                          [ARIMA Backward Selection] [Q5 inschrijvingen] [2008-12-07 15:06:11] [57fa5e3679c393aa19449b2f1be9928b]
F   P                           [ARIMA Backward Selection] [Q5 inschrijvingen] [2008-12-08 19:21:54] [57fa5e3679c393aa19449b2f1be9928b]
-   P                             [ARIMA Backward Selection] [] [2008-12-11 16:10:37] [d134696a922d84037f02d49ded84b0bd]
-   P                         [(Partial) Autocorrelation Function] [Q3] [2008-12-08 19:17:56] [57fa5e3679c393aa19449b2f1be9928b]
-   P                       [(Partial) Autocorrelation Function] [Q2 inschrijvingen...] [2008-12-08 19:13:41] [57fa5e3679c393aa19449b2f1be9928b]
-    D                  [Standard Deviation-Mean Plot] [Q8 Mean plot bouw...] [2008-11-29 21:08:55] [57fa5e3679c393aa19449b2f1be9928b]
- RM                      [Variance Reduction Matrix] [Q8 VRM Bouwvergun...] [2008-11-29 21:11:38] [57fa5e3679c393aa19449b2f1be9928b]
-                           [Variance Reduction Matrix] [] [2008-11-30 11:21:50] [ffbe22449df335faef31f462015daa42]
-                             [Variance Reduction Matrix] [] [2008-11-30 11:22:57] [ffbe22449df335faef31f462015daa42]
-   P                       [Variance Reduction Matrix] [] [2008-11-30 11:25:19] [a4ee3bef49b119f4bd2e925060c84f5e]
-                         [Standard Deviation-Mean Plot] [] [2008-11-30 11:20:10] [ffbe22449df335faef31f462015daa42]
-   P                     [Standard Deviation-Mean Plot] [] [2008-11-30 11:23:30] [a4ee3bef49b119f4bd2e925060c84f5e]
-                       [Standard Deviation-Mean Plot] [] [2008-11-30 11:16:46] [ffbe22449df335faef31f462015daa42]
-   P                   [Standard Deviation-Mean Plot] [] [2008-11-30 11:21:31] [a4ee3bef49b119f4bd2e925060c84f5e]
F    D                    [Standard Deviation-Mean Plot] [] [2008-12-01 19:27:47] [d134696a922d84037f02d49ded84b0bd]
F                         [Standard Deviation-Mean Plot] [] [2008-12-01 19:29:03] [d134696a922d84037f02d49ded84b0bd]
-                     [Cross Correlation Function] [Q9] [2008-11-29 21:16:34] [57fa5e3679c393aa19449b2f1be9928b]
-   P                   [Cross Correlation Function] [] [2008-11-30 11:26:05] [a4ee3bef49b119f4bd2e925060c84f5e]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26370&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26370&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'Gwilym Jenkins' @ 72.249.127.135






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.94804711.37660
20.87557510.50690
30.8066819.68020
40.7526259.03150
50.713778.56520
60.6817348.18080
70.6629047.95490
80.655617.86730
90.6709488.05140
100.702728.43260
110.743248.91890
120.7603959.12470

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948047 & 11.3766 & 0 \tabularnewline
2 & 0.875575 & 10.5069 & 0 \tabularnewline
3 & 0.806681 & 9.6802 & 0 \tabularnewline
4 & 0.752625 & 9.0315 & 0 \tabularnewline
5 & 0.71377 & 8.5652 & 0 \tabularnewline
6 & 0.681734 & 8.1808 & 0 \tabularnewline
7 & 0.662904 & 7.9549 & 0 \tabularnewline
8 & 0.65561 & 7.8673 & 0 \tabularnewline
9 & 0.670948 & 8.0514 & 0 \tabularnewline
10 & 0.70272 & 8.4326 & 0 \tabularnewline
11 & 0.74324 & 8.9189 & 0 \tabularnewline
12 & 0.760395 & 9.1247 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26370&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]0.948047[/C][C]11.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.875575[/C][C]10.5069[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.806681[/C][C]9.6802[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.752625[/C][C]9.0315[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.71377[/C][C]8.5652[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.681734[/C][C]8.1808[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.662904[/C][C]7.9549[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.65561[/C][C]7.8673[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.670948[/C][C]8.0514[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.70272[/C][C]8.4326[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.74324[/C][C]8.9189[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.760395[/C][C]9.1247[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26370&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
10.94804711.37660
20.87557510.50690
30.8066819.68020
40.7526259.03150
50.713778.56520
60.6817348.18080
70.6629047.95490
80.655617.86730
90.6709488.05140
100.702728.43260
110.743248.91890
120.7603959.12470






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.94804711.37660
2-0.229422-2.75310.003332
30.0381480.45780.323903
40.0937851.12540.131141
50.0736070.88330.189279
60.0077280.09270.463123
70.1255971.50720.066979
80.0899511.07940.141103
90.2324892.78990.002994
100.1660511.99260.024097
110.1712742.05530.020829
12-0.135431-1.62520.053156

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948047 & 11.3766 & 0 \tabularnewline
2 & -0.229422 & -2.7531 & 0.003332 \tabularnewline
3 & 0.038148 & 0.4578 & 0.323903 \tabularnewline
4 & 0.093785 & 1.1254 & 0.131141 \tabularnewline
5 & 0.073607 & 0.8833 & 0.189279 \tabularnewline
6 & 0.007728 & 0.0927 & 0.463123 \tabularnewline
7 & 0.125597 & 1.5072 & 0.066979 \tabularnewline
8 & 0.089951 & 1.0794 & 0.141103 \tabularnewline
9 & 0.232489 & 2.7899 & 0.002994 \tabularnewline
10 & 0.166051 & 1.9926 & 0.024097 \tabularnewline
11 & 0.171274 & 2.0553 & 0.020829 \tabularnewline
12 & -0.135431 & -1.6252 & 0.053156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26370&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]0.948047[/C][C]11.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.229422[/C][C]-2.7531[/C][C]0.003332[/C][/ROW]
[ROW][C]3[/C][C]0.038148[/C][C]0.4578[/C][C]0.323903[/C][/ROW]
[ROW][C]4[/C][C]0.093785[/C][C]1.1254[/C][C]0.131141[/C][/ROW]
[ROW][C]5[/C][C]0.073607[/C][C]0.8833[/C][C]0.189279[/C][/ROW]
[ROW][C]6[/C][C]0.007728[/C][C]0.0927[/C][C]0.463123[/C][/ROW]
[ROW][C]7[/C][C]0.125597[/C][C]1.5072[/C][C]0.066979[/C][/ROW]
[ROW][C]8[/C][C]0.089951[/C][C]1.0794[/C][C]0.141103[/C][/ROW]
[ROW][C]9[/C][C]0.232489[/C][C]2.7899[/C][C]0.002994[/C][/ROW]
[ROW][C]10[/C][C]0.166051[/C][C]1.9926[/C][C]0.024097[/C][/ROW]
[ROW][C]11[/C][C]0.171274[/C][C]2.0553[/C][C]0.020829[/C][/ROW]
[ROW][C]12[/C][C]-0.135431[/C][C]-1.6252[/C][C]0.053156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26370&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26370&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
10.94804711.37660
2-0.229422-2.75310.003332
30.0381480.45780.323903
40.0937851.12540.131141
50.0736070.88330.189279
60.0077280.09270.463123
70.1255971.50720.066979
80.0899511.07940.141103
90.2324892.78990.002994
100.1660511.99260.024097
110.1712742.05530.020829
12-0.135431-1.62520.053156


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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')