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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 computationTue, 20 Dec 2011 11:21:00 -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/2011/Dec/20/t1324398070tqj4v14ylfjc8px.htm/, Retrieved Fri, 01 Nov 2024 00:36:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158027, Retrieved Fri, 01 Nov 2024 00:36:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2011-12-20 16:21:00] [f50da5813474ccf433aab0e23f7d15ed] [Current]
- R       [(Partial) Autocorrelation Function] [tt] [2012-12-11 18:01:14] [b6dc7003e7767578f97246d87c77862e]
- R P     [(Partial) Autocorrelation Function] [yh] [2012-12-11 18:04:35] [b6dc7003e7767578f97246d87c77862e]
- R P     [(Partial) Autocorrelation Function] [dd] [2012-12-11 18:06:26] [b6dc7003e7767578f97246d87c77862e]
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Dataseries X:
235.1
280.7
264.6
240.7
201.4
240.8
241.1
223.8
206.1
174.7
203.3
220.5
299.5
347.4
338.3
327.7
351.6
396.6
438.8
395.6
363.5
378.8
357
369
464.8
479.1
431.3
366.5
326.3
355.1
331.6
261.3
249
205.5
235.6
240.9
264.9
253.8
232.3
193.8
177
213.2
207.2
180.6
188.6
175.4
199
179.6
225.8
234
200.2
183.6
178.2
203.2
208.5
191.8
172.8
148
159.4
154.5
213.2
196.4
182.8
176.4
153.6
173.2
171
151.2
161.9
157.2
201.7
236.4
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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158027&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158027&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.95302918.38140
20.90590517.47250
30.86694116.7210
40.84824316.36030
50.83616316.12730
60.80342815.4960
70.78038415.05150
80.73907414.25470
90.70755713.64690
100.69730913.44920
110.70143813.52880
120.70586813.61430
130.65014312.53950
140.59770811.52820
150.55911710.78390
160.5444710.50140
170.54201310.4540
180.52401410.10680
190.51852310.00090
200.4949439.54610
210.4814829.28650
220.4903659.45780
230.509549.82760
240.530910.23960
250.4926199.50130

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953029 & 18.3814 & 0 \tabularnewline
2 & 0.905905 & 17.4725 & 0 \tabularnewline
3 & 0.866941 & 16.721 & 0 \tabularnewline
4 & 0.848243 & 16.3603 & 0 \tabularnewline
5 & 0.836163 & 16.1273 & 0 \tabularnewline
6 & 0.803428 & 15.496 & 0 \tabularnewline
7 & 0.780384 & 15.0515 & 0 \tabularnewline
8 & 0.739074 & 14.2547 & 0 \tabularnewline
9 & 0.707557 & 13.6469 & 0 \tabularnewline
10 & 0.697309 & 13.4492 & 0 \tabularnewline
11 & 0.701438 & 13.5288 & 0 \tabularnewline
12 & 0.705868 & 13.6143 & 0 \tabularnewline
13 & 0.650143 & 12.5395 & 0 \tabularnewline
14 & 0.597708 & 11.5282 & 0 \tabularnewline
15 & 0.559117 & 10.7839 & 0 \tabularnewline
16 & 0.54447 & 10.5014 & 0 \tabularnewline
17 & 0.542013 & 10.454 & 0 \tabularnewline
18 & 0.524014 & 10.1068 & 0 \tabularnewline
19 & 0.518523 & 10.0009 & 0 \tabularnewline
20 & 0.494943 & 9.5461 & 0 \tabularnewline
21 & 0.481482 & 9.2865 & 0 \tabularnewline
22 & 0.490365 & 9.4578 & 0 \tabularnewline
23 & 0.50954 & 9.8276 & 0 \tabularnewline
24 & 0.5309 & 10.2396 & 0 \tabularnewline
25 & 0.492619 & 9.5013 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158027&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]0.953029[/C][C]18.3814[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.905905[/C][C]17.4725[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.866941[/C][C]16.721[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.848243[/C][C]16.3603[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.836163[/C][C]16.1273[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.803428[/C][C]15.496[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.780384[/C][C]15.0515[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.739074[/C][C]14.2547[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.707557[/C][C]13.6469[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.697309[/C][C]13.4492[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.701438[/C][C]13.5288[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.705868[/C][C]13.6143[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.650143[/C][C]12.5395[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.597708[/C][C]11.5282[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.559117[/C][C]10.7839[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.54447[/C][C]10.5014[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.542013[/C][C]10.454[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.524014[/C][C]10.1068[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.518523[/C][C]10.0009[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.494943[/C][C]9.5461[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.481482[/C][C]9.2865[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.490365[/C][C]9.4578[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.50954[/C][C]9.8276[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.5309[/C][C]10.2396[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.492619[/C][C]9.5013[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158027&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
10.95302918.38140
20.90590517.47250
30.86694116.7210
40.84824316.36030
50.83616316.12730
60.80342815.4960
70.78038415.05150
80.73907414.25470
90.70755713.64690
100.69730913.44920
110.70143813.52880
120.70586813.61430
130.65014312.53950
140.59770811.52820
150.55911710.78390
160.5444710.50140
170.54201310.4540
180.52401410.10680
190.51852310.00090
200.4949439.54610
210.4814829.28650
220.4903659.45780
230.509549.82760
240.530910.23960
250.4926199.50130







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.95302918.38140
2-0.025716-0.4960.310095
30.0642851.23990.107901
40.2004623.86646.5e-05
50.0733211.41420.079076
6-0.203911-3.93295e-05
70.1545272.98040.001534
8-0.232935-4.49275e-06
90.0432520.83420.202348
100.2448234.7222e-06
110.1412312.7240.003377
12-0.026246-0.50620.306502
13-0.55096-10.62650
140.0418690.80750.209937
150.1317432.5410.00573
160.0941421.81580.035107
170.1473842.84260.00236
180.0490.94510.172619
190.1150292.21860.013559
20-0.048429-0.93410.175436
21-0.001037-0.020.492025
220.097841.88710.029964
23-0.048905-0.94320.173084
240.0705171.36010.087315
25-0.284097-5.47950

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953029 & 18.3814 & 0 \tabularnewline
2 & -0.025716 & -0.496 & 0.310095 \tabularnewline
3 & 0.064285 & 1.2399 & 0.107901 \tabularnewline
4 & 0.200462 & 3.8664 & 6.5e-05 \tabularnewline
5 & 0.073321 & 1.4142 & 0.079076 \tabularnewline
6 & -0.203911 & -3.9329 & 5e-05 \tabularnewline
7 & 0.154527 & 2.9804 & 0.001534 \tabularnewline
8 & -0.232935 & -4.4927 & 5e-06 \tabularnewline
9 & 0.043252 & 0.8342 & 0.202348 \tabularnewline
10 & 0.244823 & 4.722 & 2e-06 \tabularnewline
11 & 0.141231 & 2.724 & 0.003377 \tabularnewline
12 & -0.026246 & -0.5062 & 0.306502 \tabularnewline
13 & -0.55096 & -10.6265 & 0 \tabularnewline
14 & 0.041869 & 0.8075 & 0.209937 \tabularnewline
15 & 0.131743 & 2.541 & 0.00573 \tabularnewline
16 & 0.094142 & 1.8158 & 0.035107 \tabularnewline
17 & 0.147384 & 2.8426 & 0.00236 \tabularnewline
18 & 0.049 & 0.9451 & 0.172619 \tabularnewline
19 & 0.115029 & 2.2186 & 0.013559 \tabularnewline
20 & -0.048429 & -0.9341 & 0.175436 \tabularnewline
21 & -0.001037 & -0.02 & 0.492025 \tabularnewline
22 & 0.09784 & 1.8871 & 0.029964 \tabularnewline
23 & -0.048905 & -0.9432 & 0.173084 \tabularnewline
24 & 0.070517 & 1.3601 & 0.087315 \tabularnewline
25 & -0.284097 & -5.4795 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158027&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]0.953029[/C][C]18.3814[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.025716[/C][C]-0.496[/C][C]0.310095[/C][/ROW]
[ROW][C]3[/C][C]0.064285[/C][C]1.2399[/C][C]0.107901[/C][/ROW]
[ROW][C]4[/C][C]0.200462[/C][C]3.8664[/C][C]6.5e-05[/C][/ROW]
[ROW][C]5[/C][C]0.073321[/C][C]1.4142[/C][C]0.079076[/C][/ROW]
[ROW][C]6[/C][C]-0.203911[/C][C]-3.9329[/C][C]5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.154527[/C][C]2.9804[/C][C]0.001534[/C][/ROW]
[ROW][C]8[/C][C]-0.232935[/C][C]-4.4927[/C][C]5e-06[/C][/ROW]
[ROW][C]9[/C][C]0.043252[/C][C]0.8342[/C][C]0.202348[/C][/ROW]
[ROW][C]10[/C][C]0.244823[/C][C]4.722[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.141231[/C][C]2.724[/C][C]0.003377[/C][/ROW]
[ROW][C]12[/C][C]-0.026246[/C][C]-0.5062[/C][C]0.306502[/C][/ROW]
[ROW][C]13[/C][C]-0.55096[/C][C]-10.6265[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.041869[/C][C]0.8075[/C][C]0.209937[/C][/ROW]
[ROW][C]15[/C][C]0.131743[/C][C]2.541[/C][C]0.00573[/C][/ROW]
[ROW][C]16[/C][C]0.094142[/C][C]1.8158[/C][C]0.035107[/C][/ROW]
[ROW][C]17[/C][C]0.147384[/C][C]2.8426[/C][C]0.00236[/C][/ROW]
[ROW][C]18[/C][C]0.049[/C][C]0.9451[/C][C]0.172619[/C][/ROW]
[ROW][C]19[/C][C]0.115029[/C][C]2.2186[/C][C]0.013559[/C][/ROW]
[ROW][C]20[/C][C]-0.048429[/C][C]-0.9341[/C][C]0.175436[/C][/ROW]
[ROW][C]21[/C][C]-0.001037[/C][C]-0.02[/C][C]0.492025[/C][/ROW]
[ROW][C]22[/C][C]0.09784[/C][C]1.8871[/C][C]0.029964[/C][/ROW]
[ROW][C]23[/C][C]-0.048905[/C][C]-0.9432[/C][C]0.173084[/C][/ROW]
[ROW][C]24[/C][C]0.070517[/C][C]1.3601[/C][C]0.087315[/C][/ROW]
[ROW][C]25[/C][C]-0.284097[/C][C]-5.4795[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158027&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158027&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
10.95302918.38140
2-0.025716-0.4960.310095
30.0642851.23990.107901
40.2004623.86646.5e-05
50.0733211.41420.079076
6-0.203911-3.93295e-05
70.1545272.98040.001534
8-0.232935-4.49275e-06
90.0432520.83420.202348
100.2448234.7222e-06
110.1412312.7240.003377
12-0.026246-0.50620.306502
13-0.55096-10.62650
140.0418690.80750.209937
150.1317432.5410.00573
160.0941421.81580.035107
170.1473842.84260.00236
180.0490.94510.172619
190.1150292.21860.013559
20-0.048429-0.93410.175436
21-0.001037-0.020.492025
220.097841.88710.029964
23-0.048905-0.94320.173084
240.0705171.36010.087315
25-0.284097-5.47950



Parameters (Session):
par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 0.0 ; 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')