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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 2014 15:19:51 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/29/t14172744005dvdfkmsh6qhej3.htm/, Retrieved Fri, 17 May 2024 06:40:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261174, Retrieved Fri, 17 May 2024 06:40:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [WS9] [2014-11-29 15:19:51] [c15d474939d69eac0efd26ce7542850f] [Current]
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Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626
356.1
398.3
403.7
384.6
365.8
368.1
367.9
347
343.3
292.9
311.5
300.9
366.9
356.9
329.7
316.2
269
289.3
266.2
253.6
233.8
228.4
253.6
260.1
306.6
309.2
309.5
271
279.9
317.9
298.4
246.7
227.3
209.1
259.9
266
320.6
308.5
282.2
262.7
263.5
313.1
284.3
252.6
250.3
246.5
312.7
333.2
446.4
511.6
515.5
506.4
483.2
522.3
509.8
460.7
405.8
375
378.5
406.8
467.8
469.8
429.8
355.8
332.7
378
360.5
334.7
319.5
323.1
363.6
352.1
411.9
388.6
416.4
360.7
338
417.2
388.4
371.1
331.5
353.7
396.7
447
533.5
565.4
542.3
488.7
467.1
531.3
496.1
444
403.4
386.3
394.1
404.1
462.1
448.1
432.3
386.3
395.2
421.9
382.9
384.2
345.5
323.4
372.6
376
462.7
487
444.2
399.3
394.9
455.4
414
375.5
347
339.4
385.8
378.8
451.8
446.1
422.5
383.1
352.8
445.3
367.5
355.1
326.2
319.8
331.8
340.9
394.1
417.2
369.9
349.2
321.4
405.7
342.9
316.5
284.2
270.9
288.8
278.8
324.4
310.9
299
273
279.3
359.2
305
282.1
250.3
246.5
257.9
266.5
315.9
318.4
295.4
266.4
245.8
362.8
324.9
294.2
289.5
295.2
290.3
272
307.4
328.7
292.9
249.1
230.4
361.5
321.7
277.2
260.7
251
257.6
241.8
287.5
292.3
274.7
254.2
230
339
318.2
287
295.8
284
271
262.7
340.6
379.4
373.3
355.2
338.4
466.9
451
422
429.2
425.9
460.7
463.6
541.4
544.2
517.5
469.4
439.4
549
533
506.1
484
457
481.5
469.5
544.7
541.2
521.5
469.7
434.4
542.6
517.3
485.7
465.8
447
426.6
411.6
467.5
484.5
451.2
417.4
379.9
484.7
455
420.8
416.5
376.3
405.6
405.8
500.8
514
475.5
430.1
414.4
538
526
488.5
520.2
504.4
568.5
610.6
818
830.9
835.9
782
762.3
856.9
820.9
769.6
752.2
724.4
723.1
719.5
817.4
803.3
752.5
689
630.4
765.5
757.7
732.2
702.6
683.3
709.5
702.2
784.8
810.9
755.6
656.8
615.1
745.3
694.1
675.7
643.7
622.1
634.6
588
689.7
673.9
647.9
568.8
545.7
632.6
643.8
593.1
579.7
546
562.9
572.5




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=261174&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=261174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261174&T=0

As an alternative you can also use a 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
10.91110517.57280
20.82160315.84650
30.77291714.90750
40.69510913.40680
50.62240712.00450
60.57725211.13360
70.58104211.20670
80.6147711.85730
90.66215512.77120
100.69081813.3240
110.76030914.66430
120.82789215.96780
130.75762714.61260
140.68240513.16170
150.64056812.35480
160.57322511.0560
170.5094229.82540
180.4668469.00420
190.4640058.94940
200.4878119.40860
210.52211310.07020
220.5439610.49150
230.5963511.5020
240.65261212.58710
250.6013811.5990

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.911105 & 17.5728 & 0 \tabularnewline
2 & 0.821603 & 15.8465 & 0 \tabularnewline
3 & 0.772917 & 14.9075 & 0 \tabularnewline
4 & 0.695109 & 13.4068 & 0 \tabularnewline
5 & 0.622407 & 12.0045 & 0 \tabularnewline
6 & 0.577252 & 11.1336 & 0 \tabularnewline
7 & 0.581042 & 11.2067 & 0 \tabularnewline
8 & 0.61477 & 11.8573 & 0 \tabularnewline
9 & 0.662155 & 12.7712 & 0 \tabularnewline
10 & 0.690818 & 13.324 & 0 \tabularnewline
11 & 0.760309 & 14.6643 & 0 \tabularnewline
12 & 0.827892 & 15.9678 & 0 \tabularnewline
13 & 0.757627 & 14.6126 & 0 \tabularnewline
14 & 0.682405 & 13.1617 & 0 \tabularnewline
15 & 0.640568 & 12.3548 & 0 \tabularnewline
16 & 0.573225 & 11.056 & 0 \tabularnewline
17 & 0.509422 & 9.8254 & 0 \tabularnewline
18 & 0.466846 & 9.0042 & 0 \tabularnewline
19 & 0.464005 & 8.9494 & 0 \tabularnewline
20 & 0.487811 & 9.4086 & 0 \tabularnewline
21 & 0.522113 & 10.0702 & 0 \tabularnewline
22 & 0.54396 & 10.4915 & 0 \tabularnewline
23 & 0.59635 & 11.502 & 0 \tabularnewline
24 & 0.652612 & 12.5871 & 0 \tabularnewline
25 & 0.60138 & 11.599 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261174&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]0.911105[/C][C]17.5728[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.821603[/C][C]15.8465[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.772917[/C][C]14.9075[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.695109[/C][C]13.4068[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.622407[/C][C]12.0045[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.577252[/C][C]11.1336[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.581042[/C][C]11.2067[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.61477[/C][C]11.8573[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.662155[/C][C]12.7712[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.690818[/C][C]13.324[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.760309[/C][C]14.6643[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.827892[/C][C]15.9678[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.757627[/C][C]14.6126[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.682405[/C][C]13.1617[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.640568[/C][C]12.3548[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.573225[/C][C]11.056[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.509422[/C][C]9.8254[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.466846[/C][C]9.0042[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.464005[/C][C]8.9494[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.487811[/C][C]9.4086[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.522113[/C][C]10.0702[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.54396[/C][C]10.4915[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.59635[/C][C]11.502[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.652612[/C][C]12.5871[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.60138[/C][C]11.599[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261174&T=1

As an alternative you can also use a QR Code:  

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

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.91110517.57280
20.82160315.84650
30.77291714.90750
40.69510913.40680
50.62240712.00450
60.57725211.13360
70.58104211.20670
80.6147711.85730
90.66215512.77120
100.69081813.3240
110.76030914.66430
120.82789215.96780
130.75762714.61260
140.68240513.16170
150.64056812.35480
160.57322511.0560
170.5094229.82540
180.4668469.00420
190.4640058.94940
200.4878119.40860
210.52211310.07020
220.5439610.49150
230.5963511.5020
240.65261212.58710
250.6013811.5990







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.91110517.57280
2-0.050084-0.9660.16734
30.191733.6980.000125
4-0.212075-4.09042.6e-05
50.0546571.05420.146241
60.0399310.77020.220846
70.3317636.39880
80.214494.13692.2e-05
90.2596085.00710
10-0.092992-1.79360.036848
110.4401928.49010
120.0516330.99590.159983
13-0.608221-11.73090
14-0.07735-1.49190.06829
15-0.000961-0.01850.492615
160.1271842.4530.007312
170.1722683.32260.00049
180.0200420.38650.349656
19-0.025484-0.49150.311678
20-0.093546-1.80420.036001
21-0.090538-1.74620.040798
22-0.019741-0.38080.351801
23-0.065771-1.26850.102698
240.1358672.62050.00457
250.0489040.94320.173087

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.911105 & 17.5728 & 0 \tabularnewline
2 & -0.050084 & -0.966 & 0.16734 \tabularnewline
3 & 0.19173 & 3.698 & 0.000125 \tabularnewline
4 & -0.212075 & -4.0904 & 2.6e-05 \tabularnewline
5 & 0.054657 & 1.0542 & 0.146241 \tabularnewline
6 & 0.039931 & 0.7702 & 0.220846 \tabularnewline
7 & 0.331763 & 6.3988 & 0 \tabularnewline
8 & 0.21449 & 4.1369 & 2.2e-05 \tabularnewline
9 & 0.259608 & 5.0071 & 0 \tabularnewline
10 & -0.092992 & -1.7936 & 0.036848 \tabularnewline
11 & 0.440192 & 8.4901 & 0 \tabularnewline
12 & 0.051633 & 0.9959 & 0.159983 \tabularnewline
13 & -0.608221 & -11.7309 & 0 \tabularnewline
14 & -0.07735 & -1.4919 & 0.06829 \tabularnewline
15 & -0.000961 & -0.0185 & 0.492615 \tabularnewline
16 & 0.127184 & 2.453 & 0.007312 \tabularnewline
17 & 0.172268 & 3.3226 & 0.00049 \tabularnewline
18 & 0.020042 & 0.3865 & 0.349656 \tabularnewline
19 & -0.025484 & -0.4915 & 0.311678 \tabularnewline
20 & -0.093546 & -1.8042 & 0.036001 \tabularnewline
21 & -0.090538 & -1.7462 & 0.040798 \tabularnewline
22 & -0.019741 & -0.3808 & 0.351801 \tabularnewline
23 & -0.065771 & -1.2685 & 0.102698 \tabularnewline
24 & 0.135867 & 2.6205 & 0.00457 \tabularnewline
25 & 0.048904 & 0.9432 & 0.173087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261174&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]0.911105[/C][C]17.5728[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.050084[/C][C]-0.966[/C][C]0.16734[/C][/ROW]
[ROW][C]3[/C][C]0.19173[/C][C]3.698[/C][C]0.000125[/C][/ROW]
[ROW][C]4[/C][C]-0.212075[/C][C]-4.0904[/C][C]2.6e-05[/C][/ROW]
[ROW][C]5[/C][C]0.054657[/C][C]1.0542[/C][C]0.146241[/C][/ROW]
[ROW][C]6[/C][C]0.039931[/C][C]0.7702[/C][C]0.220846[/C][/ROW]
[ROW][C]7[/C][C]0.331763[/C][C]6.3988[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.21449[/C][C]4.1369[/C][C]2.2e-05[/C][/ROW]
[ROW][C]9[/C][C]0.259608[/C][C]5.0071[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]-0.092992[/C][C]-1.7936[/C][C]0.036848[/C][/ROW]
[ROW][C]11[/C][C]0.440192[/C][C]8.4901[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.051633[/C][C]0.9959[/C][C]0.159983[/C][/ROW]
[ROW][C]13[/C][C]-0.608221[/C][C]-11.7309[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.07735[/C][C]-1.4919[/C][C]0.06829[/C][/ROW]
[ROW][C]15[/C][C]-0.000961[/C][C]-0.0185[/C][C]0.492615[/C][/ROW]
[ROW][C]16[/C][C]0.127184[/C][C]2.453[/C][C]0.007312[/C][/ROW]
[ROW][C]17[/C][C]0.172268[/C][C]3.3226[/C][C]0.00049[/C][/ROW]
[ROW][C]18[/C][C]0.020042[/C][C]0.3865[/C][C]0.349656[/C][/ROW]
[ROW][C]19[/C][C]-0.025484[/C][C]-0.4915[/C][C]0.311678[/C][/ROW]
[ROW][C]20[/C][C]-0.093546[/C][C]-1.8042[/C][C]0.036001[/C][/ROW]
[ROW][C]21[/C][C]-0.090538[/C][C]-1.7462[/C][C]0.040798[/C][/ROW]
[ROW][C]22[/C][C]-0.019741[/C][C]-0.3808[/C][C]0.351801[/C][/ROW]
[ROW][C]23[/C][C]-0.065771[/C][C]-1.2685[/C][C]0.102698[/C][/ROW]
[ROW][C]24[/C][C]0.135867[/C][C]2.6205[/C][C]0.00457[/C][/ROW]
[ROW][C]25[/C][C]0.048904[/C][C]0.9432[/C][C]0.173087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261174&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261174&T=2

As an alternative you can also use a QR Code:  

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

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.91110517.57280
2-0.050084-0.9660.16734
30.191733.6980.000125
4-0.212075-4.09042.6e-05
50.0546571.05420.146241
60.0399310.77020.220846
70.3317636.39880
80.214494.13692.2e-05
90.2596085.00710
10-0.092992-1.79360.036848
110.4401928.49010
120.0516330.99590.159983
13-0.608221-11.73090
14-0.07735-1.49190.06829
15-0.000961-0.01850.492615
160.1271842.4530.007312
170.1722683.32260.00049
180.0200420.38650.349656
19-0.025484-0.49150.311678
20-0.093546-1.80420.036001
21-0.090538-1.74620.040798
22-0.019741-0.38080.351801
23-0.065771-1.26850.102698
240.1358672.62050.00457
250.0489040.94320.173087



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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)
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')