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rwasp_autocorrelation.wasp

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(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 12:32:37 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t1228764791u4svj5giy96cd2h.htm/, Retrieved Thu, 16 May 2024 11:26:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30827, Retrieved Thu, 16 May 2024 11:26:37 +0000

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User-defined keywords

ARMA proces WS5 Q3: ACF

Estimated Impact

224

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]
F RMP   [Standard Deviation-Mean Plot] [ARMA proces WS5 Q...] [2008-12-08 18:26:08] [47f64d63202c1921bd27f3073f07a153]
F RM      [Variance Reduction Matrix] [ARMA proces WS5 Q...] [2008-12-08 18:38:24] [47f64d63202c1921bd27f3073f07a153]
- RMP       [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:44:52] [47f64d63202c1921bd27f3073f07a153]
-   P         [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:50:21] [47f64d63202c1921bd27f3073f07a153]
F   P           [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:53:02] [47f64d63202c1921bd27f3073f07a153]
-   P             [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:57:23] [47f64d63202c1921bd27f3073f07a153]
F RMP               [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:01:20] [47f64d63202c1921bd27f3073f07a153]
F   P                 [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:03:44] [47f64d63202c1921bd27f3073f07a153]
F   P                   [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:04:59] [47f64d63202c1921bd27f3073f07a153]
-                         [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:28:19] [47f64d63202c1921bd27f3073f07a153]
F RM                          [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 19:32:37] [74c7506a1ea162af3aa8be25bcd05d28] [Current]
F RM                            [ARIMA Backward Selection] [ARMA proces WS5 Q...] [2008-12-08 20:01:06] [47f64d63202c1921bd27f3073f07a153] 

Feedback Forum

2008-12-11 10:50:15 [72e979bcc364082694890d2eccc1a66f] [reply] 
In de ACF mag je de eerste staaf vergeten want die staat op lag 0. We hebben hier dus te maken met een AR-proces. Dit zie je aan de positieve staafjes die snel naar 0 gaan. We moeten hier kijken naar de eerste 4 à 5 staafjes. Aan het staafje op lag 1 mag je wat trekken zodat het patroon duidelijker wordt. Er is geen sprake van seizoenaliteit. 
Om te zien van welke orde dit AR- proces is moeten we kijken naar de PACF, de student heeft niet vermeld waar zij haar gegevens hiervoor haalde. Ik vermoed dat ze gebruik gemaakt heeft van ACF. 
In de PACF zijn de eerste 2 correlaties significant, de 3e net niet. Je kan hier ook wat aan trekken. Voorlopig gaan we er dus van uit dat het om een derde orde gaat.
  2008-12-11 10:52:44 [72e979bcc364082694890d2eccc1a66f] [reply] 
In de PACF zie je geen duidelijk MA-proces, er is wel seizoenaliteit merkbaar. 
Om de orde te bepalen kijken we nu naar de autocorrelatie functie. Er is 1 significante uitschieter van de seizoenale correlatiecoëfficiënten. 
Ook hier maakt de student niet duidelijk waar zij P bepaalt.
    2008-12-11 10:56:49 [72e979bcc364082694890d2eccc1a66f] [reply] 
De student heeft geen gebruik gemaakt van de spectrale analyse om het resultaat te controleren.
2008-12-15 19:16:20 [Bénédicte Soens] [reply] 
De modelvergelijking die werd uitgeschreven is correct. 
Wel is de uitleg te kort bij het bekomen van de p, P, q en Q. Er moet duidelijker vermeld worden wat er gebruikt wordt: ACF of PACF. Bij de p wordt er vermeld welke orde dat het is maar is het niet duidelijk van waar het komt. Deze komt uit de PACF aangezien de eerste 2 à 3 staafjes significant verschillend zijn. Uit step 5 zal dan wel blijken of het een AR(2) of AR(3) proces is. 
De bespreken van q en Q vindt ik wel juist. 
 
De spectraal analyse ontbreekt hier wel bij.
2008-12-16 19:55:44 [Stef Vermeiren] [reply] 
Eerst moet er gecontroleerd worden of er in de ACF een AR proces herkend kan worden. Als ik naar de eerste 4 streepjes kijk (het eerste bij 0 niet meegerekend), en ik rek het eerstvolgende streepje een beetje uit, dan zie ik een dalende trend. Streepjes die convergeren naar 0. Dit is typisch voor een AR proces. Om te weten welke orde het AR proces is, kijken we naar de PACF. 
De twee eerste streepjes zijn significant, want ze komen buiten het 95% betrouwbaarheidsinterval. Het derde streepje is een twijfelgeval. Maar we gaan voor de eerste 2, daar zijn we zeker van. Er is dus een AR(2) proces aanwezig in de tijdreeks. 
p=2 
In de ACF heb ik niet echt seizoenaliteit gemerkt. P=0. 
 
Vervolgens gaan we kijken of er ook een MA proces aanwezig is. Hiervoor kijken we opnieuw naar de PACF. Het gaat hier om de negatieve correlatiecoëfficiënten, onder 0. Wat mij opvalt zijn de significante negatieve pieken om de twaalf maanden. Dit wijst op seizoenaliteit. Die pieken convergeren naar 0. Dit is typisch voor een MA proces. In het algemeen is er niet echt een trend merkbaar aan de onderkant. q=0  
Er is wel een seizoenale trend. Hiervoor moeten we kijken naar de ACF. Het eerste seizoenale streepje, op lag 12, komt significant buiten het betrouwbaarheidsinterval. Het streepje bij lag 24 al niet meer. Q=1. Er is dus een SMA(1) proces aanwezig. 

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30827&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30827&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.317794	6.0213	0
3	0.179563	3.4022	0.000372
4	0.155303	2.9426	0.001733
5	0.127596	2.4176	0.008061
6	0.06371	1.2071	0.114087
7	-0.054701	-1.0364	0.150347
8	-0.011735	-0.2224	0.412083
9	-0.080833	-1.5316	0.063255
10	-0.174708	-3.3102	0.000513
11	-0.055263	-1.0471	0.147883
12	-0.480698	-9.1079	0
13	-0.168514	-3.1929	0.000767
14	-0.172913	-3.2762	0.000577
15	-0.128287	-2.4307	0.007779
16	-0.163167	-3.0916	0.001073
17	-0.121097	-2.2945	0.01117
18	-0.103099	-1.9534	0.025772
19	0.020128	0.3814	0.351578
20	-0.002775	-0.0526	0.479049
21	-0.006426	-0.1217	0.451583
22	-0.006358	-0.1205	0.45209
23	-0.004364	-0.0827	0.467075
24	-0.006343	-0.1202	0.452205
25	0.094911	1.7983	0.036484
26	-0.008505	-0.1611	0.436036
27	0.017661	0.3346	0.369052
28	0.077035	1.4596	0.072638
29	0.068023	1.2888	0.09914
30	0.041632	0.7888	0.215369
31	0.032895	0.6233	0.266752
32	-0.068171	-1.2917	0.098653
33	0.011323	0.2145	0.415122
34	0.002674	0.0507	0.479811
35	-0.0721	-1.3661	0.08638
36	-0.031172	-0.5906	0.277571
37	-0.113841	-2.157	0.015835
38	-0.00152	-0.0288	0.488517
39	-0.046567	-0.8823	0.189098
40	-0.067976	-1.288	0.099295
41	-0.105451	-1.998	0.023234
42	-0.033256	-0.6301	0.264511
43	-0.158298	-2.9993	0.001447
44	0.01837	0.3481	0.364001
45	-0.043872	-0.8313	0.203191
46	0.021162	0.401	0.34434
47	0.042179	0.7992	0.21236
48	0.097675	1.8507	0.032519
49	0.125528	2.3784	0.008955
50	0.090564	1.7159	0.043518
51	0.082527	1.5637	0.059388
52	0.128164	2.4284	0.007829
53	0.160308	3.0374	0.00128
54	0.042213	0.7998	0.212173
55	0.160649	3.0439	0.001254
56	0.042494	0.8052	0.210633
57	0.055698	1.0553	0.145992
58	0.043943	0.8326	0.202814
59	0.043887	0.8315	0.203111
60	-0.02979	-0.5644	0.286401

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.187552 & 3.5536 & 0.000215 \tabularnewline
2 & 0.317794 & 6.0213 & 0 \tabularnewline
3 & 0.179563 & 3.4022 & 0.000372 \tabularnewline
4 & 0.155303 & 2.9426 & 0.001733 \tabularnewline
5 & 0.127596 & 2.4176 & 0.008061 \tabularnewline
6 & 0.06371 & 1.2071 & 0.114087 \tabularnewline
7 & -0.054701 & -1.0364 & 0.150347 \tabularnewline
8 & -0.011735 & -0.2224 & 0.412083 \tabularnewline
9 & -0.080833 & -1.5316 & 0.063255 \tabularnewline
10 & -0.174708 & -3.3102 & 0.000513 \tabularnewline
11 & -0.055263 & -1.0471 & 0.147883 \tabularnewline
12 & -0.480698 & -9.1079 & 0 \tabularnewline
13 & -0.168514 & -3.1929 & 0.000767 \tabularnewline
14 & -0.172913 & -3.2762 & 0.000577 \tabularnewline
15 & -0.128287 & -2.4307 & 0.007779 \tabularnewline
16 & -0.163167 & -3.0916 & 0.001073 \tabularnewline
17 & -0.121097 & -2.2945 & 0.01117 \tabularnewline
18 & -0.103099 & -1.9534 & 0.025772 \tabularnewline
19 & 0.020128 & 0.3814 & 0.351578 \tabularnewline
20 & -0.002775 & -0.0526 & 0.479049 \tabularnewline
21 & -0.006426 & -0.1217 & 0.451583 \tabularnewline
22 & -0.006358 & -0.1205 & 0.45209 \tabularnewline
23 & -0.004364 & -0.0827 & 0.467075 \tabularnewline
24 & -0.006343 & -0.1202 & 0.452205 \tabularnewline
25 & 0.094911 & 1.7983 & 0.036484 \tabularnewline
26 & -0.008505 & -0.1611 & 0.436036 \tabularnewline
27 & 0.017661 & 0.3346 & 0.369052 \tabularnewline
28 & 0.077035 & 1.4596 & 0.072638 \tabularnewline
29 & 0.068023 & 1.2888 & 0.09914 \tabularnewline
30 & 0.041632 & 0.7888 & 0.215369 \tabularnewline
31 & 0.032895 & 0.6233 & 0.266752 \tabularnewline
32 & -0.068171 & -1.2917 & 0.098653 \tabularnewline
33 & 0.011323 & 0.2145 & 0.415122 \tabularnewline
34 & 0.002674 & 0.0507 & 0.479811 \tabularnewline
35 & -0.0721 & -1.3661 & 0.08638 \tabularnewline
36 & -0.031172 & -0.5906 & 0.277571 \tabularnewline
37 & -0.113841 & -2.157 & 0.015835 \tabularnewline
38 & -0.00152 & -0.0288 & 0.488517 \tabularnewline
39 & -0.046567 & -0.8823 & 0.189098 \tabularnewline
40 & -0.067976 & -1.288 & 0.099295 \tabularnewline
41 & -0.105451 & -1.998 & 0.023234 \tabularnewline
42 & -0.033256 & -0.6301 & 0.264511 \tabularnewline
43 & -0.158298 & -2.9993 & 0.001447 \tabularnewline
44 & 0.01837 & 0.3481 & 0.364001 \tabularnewline
45 & -0.043872 & -0.8313 & 0.203191 \tabularnewline
46 & 0.021162 & 0.401 & 0.34434 \tabularnewline
47 & 0.042179 & 0.7992 & 0.21236 \tabularnewline
48 & 0.097675 & 1.8507 & 0.032519 \tabularnewline
49 & 0.125528 & 2.3784 & 0.008955 \tabularnewline
50 & 0.090564 & 1.7159 & 0.043518 \tabularnewline
51 & 0.082527 & 1.5637 & 0.059388 \tabularnewline
52 & 0.128164 & 2.4284 & 0.007829 \tabularnewline
53 & 0.160308 & 3.0374 & 0.00128 \tabularnewline
54 & 0.042213 & 0.7998 & 0.212173 \tabularnewline
55 & 0.160649 & 3.0439 & 0.001254 \tabularnewline
56 & 0.042494 & 0.8052 & 0.210633 \tabularnewline
57 & 0.055698 & 1.0553 & 0.145992 \tabularnewline
58 & 0.043943 & 0.8326 & 0.202814 \tabularnewline
59 & 0.043887 & 0.8315 & 0.203111 \tabularnewline
60 & -0.02979 & -0.5644 & 0.286401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30827&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]0.187552[/C][C]3.5536[/C][C]0.000215[/C][/ROW]
[ROW][C]2[/C][C]0.317794[/C][C]6.0213[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.179563[/C][C]3.4022[/C][C]0.000372[/C][/ROW]
[ROW][C]4[/C][C]0.155303[/C][C]2.9426[/C][C]0.001733[/C][/ROW]
[ROW][C]5[/C][C]0.127596[/C][C]2.4176[/C][C]0.008061[/C][/ROW]
[ROW][C]6[/C][C]0.06371[/C][C]1.2071[/C][C]0.114087[/C][/ROW]
[ROW][C]7[/C][C]-0.054701[/C][C]-1.0364[/C][C]0.150347[/C][/ROW]
[ROW][C]8[/C][C]-0.011735[/C][C]-0.2224[/C][C]0.412083[/C][/ROW]
[ROW][C]9[/C][C]-0.080833[/C][C]-1.5316[/C][C]0.063255[/C][/ROW]
[ROW][C]10[/C][C]-0.174708[/C][C]-3.3102[/C][C]0.000513[/C][/ROW]
[ROW][C]11[/C][C]-0.055263[/C][C]-1.0471[/C][C]0.147883[/C][/ROW]
[ROW][C]12[/C][C]-0.480698[/C][C]-9.1079[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.168514[/C][C]-3.1929[/C][C]0.000767[/C][/ROW]
[ROW][C]14[/C][C]-0.172913[/C][C]-3.2762[/C][C]0.000577[/C][/ROW]
[ROW][C]15[/C][C]-0.128287[/C][C]-2.4307[/C][C]0.007779[/C][/ROW]
[ROW][C]16[/C][C]-0.163167[/C][C]-3.0916[/C][C]0.001073[/C][/ROW]
[ROW][C]17[/C][C]-0.121097[/C][C]-2.2945[/C][C]0.01117[/C][/ROW]
[ROW][C]18[/C][C]-0.103099[/C][C]-1.9534[/C][C]0.025772[/C][/ROW]
[ROW][C]19[/C][C]0.020128[/C][C]0.3814[/C][C]0.351578[/C][/ROW]
[ROW][C]20[/C][C]-0.002775[/C][C]-0.0526[/C][C]0.479049[/C][/ROW]
[ROW][C]21[/C][C]-0.006426[/C][C]-0.1217[/C][C]0.451583[/C][/ROW]
[ROW][C]22[/C][C]-0.006358[/C][C]-0.1205[/C][C]0.45209[/C][/ROW]
[ROW][C]23[/C][C]-0.004364[/C][C]-0.0827[/C][C]0.467075[/C][/ROW]
[ROW][C]24[/C][C]-0.006343[/C][C]-0.1202[/C][C]0.452205[/C][/ROW]
[ROW][C]25[/C][C]0.094911[/C][C]1.7983[/C][C]0.036484[/C][/ROW]
[ROW][C]26[/C][C]-0.008505[/C][C]-0.1611[/C][C]0.436036[/C][/ROW]
[ROW][C]27[/C][C]0.017661[/C][C]0.3346[/C][C]0.369052[/C][/ROW]
[ROW][C]28[/C][C]0.077035[/C][C]1.4596[/C][C]0.072638[/C][/ROW]
[ROW][C]29[/C][C]0.068023[/C][C]1.2888[/C][C]0.09914[/C][/ROW]
[ROW][C]30[/C][C]0.041632[/C][C]0.7888[/C][C]0.215369[/C][/ROW]
[ROW][C]31[/C][C]0.032895[/C][C]0.6233[/C][C]0.266752[/C][/ROW]
[ROW][C]32[/C][C]-0.068171[/C][C]-1.2917[/C][C]0.098653[/C][/ROW]
[ROW][C]33[/C][C]0.011323[/C][C]0.2145[/C][C]0.415122[/C][/ROW]
[ROW][C]34[/C][C]0.002674[/C][C]0.0507[/C][C]0.479811[/C][/ROW]
[ROW][C]35[/C][C]-0.0721[/C][C]-1.3661[/C][C]0.08638[/C][/ROW]
[ROW][C]36[/C][C]-0.031172[/C][C]-0.5906[/C][C]0.277571[/C][/ROW]
[ROW][C]37[/C][C]-0.113841[/C][C]-2.157[/C][C]0.015835[/C][/ROW]
[ROW][C]38[/C][C]-0.00152[/C][C]-0.0288[/C][C]0.488517[/C][/ROW]
[ROW][C]39[/C][C]-0.046567[/C][C]-0.8823[/C][C]0.189098[/C][/ROW]
[ROW][C]40[/C][C]-0.067976[/C][C]-1.288[/C][C]0.099295[/C][/ROW]
[ROW][C]41[/C][C]-0.105451[/C][C]-1.998[/C][C]0.023234[/C][/ROW]
[ROW][C]42[/C][C]-0.033256[/C][C]-0.6301[/C][C]0.264511[/C][/ROW]
[ROW][C]43[/C][C]-0.158298[/C][C]-2.9993[/C][C]0.001447[/C][/ROW]
[ROW][C]44[/C][C]0.01837[/C][C]0.3481[/C][C]0.364001[/C][/ROW]
[ROW][C]45[/C][C]-0.043872[/C][C]-0.8313[/C][C]0.203191[/C][/ROW]
[ROW][C]46[/C][C]0.021162[/C][C]0.401[/C][C]0.34434[/C][/ROW]
[ROW][C]47[/C][C]0.042179[/C][C]0.7992[/C][C]0.21236[/C][/ROW]
[ROW][C]48[/C][C]0.097675[/C][C]1.8507[/C][C]0.032519[/C][/ROW]
[ROW][C]49[/C][C]0.125528[/C][C]2.3784[/C][C]0.008955[/C][/ROW]
[ROW][C]50[/C][C]0.090564[/C][C]1.7159[/C][C]0.043518[/C][/ROW]
[ROW][C]51[/C][C]0.082527[/C][C]1.5637[/C][C]0.059388[/C][/ROW]
[ROW][C]52[/C][C]0.128164[/C][C]2.4284[/C][C]0.007829[/C][/ROW]
[ROW][C]53[/C][C]0.160308[/C][C]3.0374[/C][C]0.00128[/C][/ROW]
[ROW][C]54[/C][C]0.042213[/C][C]0.7998[/C][C]0.212173[/C][/ROW]
[ROW][C]55[/C][C]0.160649[/C][C]3.0439[/C][C]0.001254[/C][/ROW]
[ROW][C]56[/C][C]0.042494[/C][C]0.8052[/C][C]0.210633[/C][/ROW]
[ROW][C]57[/C][C]0.055698[/C][C]1.0553[/C][C]0.145992[/C][/ROW]
[ROW][C]58[/C][C]0.043943[/C][C]0.8326[/C][C]0.202814[/C][/ROW]
[ROW][C]59[/C][C]0.043887[/C][C]0.8315[/C][C]0.203111[/C][/ROW]
[ROW][C]60[/C][C]-0.02979[/C][C]-0.5644[/C][C]0.286401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30827&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 k	ACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.317794	6.0213	0
3	0.179563	3.4022	0.000372
4	0.155303	2.9426	0.001733
5	0.127596	2.4176	0.008061
6	0.06371	1.2071	0.114087
7	-0.054701	-1.0364	0.150347
8	-0.011735	-0.2224	0.412083
9	-0.080833	-1.5316	0.063255
10	-0.174708	-3.3102	0.000513
11	-0.055263	-1.0471	0.147883
12	-0.480698	-9.1079	0
13	-0.168514	-3.1929	0.000767
14	-0.172913	-3.2762	0.000577
15	-0.128287	-2.4307	0.007779
16	-0.163167	-3.0916	0.001073
17	-0.121097	-2.2945	0.01117
18	-0.103099	-1.9534	0.025772
19	0.020128	0.3814	0.351578
20	-0.002775	-0.0526	0.479049
21	-0.006426	-0.1217	0.451583
22	-0.006358	-0.1205	0.45209
23	-0.004364	-0.0827	0.467075
24	-0.006343	-0.1202	0.452205
25	0.094911	1.7983	0.036484
26	-0.008505	-0.1611	0.436036
27	0.017661	0.3346	0.369052
28	0.077035	1.4596	0.072638
29	0.068023	1.2888	0.09914
30	0.041632	0.7888	0.215369
31	0.032895	0.6233	0.266752
32	-0.068171	-1.2917	0.098653
33	0.011323	0.2145	0.415122
34	0.002674	0.0507	0.479811
35	-0.0721	-1.3661	0.08638
36	-0.031172	-0.5906	0.277571
37	-0.113841	-2.157	0.015835
38	-0.00152	-0.0288	0.488517
39	-0.046567	-0.8823	0.189098
40	-0.067976	-1.288	0.099295
41	-0.105451	-1.998	0.023234
42	-0.033256	-0.6301	0.264511
43	-0.158298	-2.9993	0.001447
44	0.01837	0.3481	0.364001
45	-0.043872	-0.8313	0.203191
46	0.021162	0.401	0.34434
47	0.042179	0.7992	0.21236
48	0.097675	1.8507	0.032519
49	0.125528	2.3784	0.008955
50	0.090564	1.7159	0.043518
51	0.082527	1.5637	0.059388
52	0.128164	2.4284	0.007829
53	0.160308	3.0374	0.00128
54	0.042213	0.7998	0.212173
55	0.160649	3.0439	0.001254
56	0.042494	0.8052	0.210633
57	0.055698	1.0553	0.145992
58	0.043943	0.8326	0.202814
59	0.043887	0.8315	0.203111
60	-0.02979	-0.5644	0.286401

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.292922	5.5501	0
3	0.093512	1.7718	0.038638
4	0.033995	0.6441	0.259959
5	0.032214	0.6104	0.271005
6	-0.024285	-0.4601	0.322846
7	-0.139405	-2.6414	0.004309
8	-0.030697	-0.5816	0.280592
9	-0.045877	-0.8693	0.192645
10	-0.156693	-2.9689	0.001595
11	0.037591	0.7122	0.238389
12	-0.427945	-8.1084	0
13	-0.036401	-0.6897	0.245414
14	0.123319	2.3366	0.010006
15	0.047112	0.8926	0.186322
16	-0.060609	-1.1484	0.125789
17	-0.017722	-0.3358	0.368615
18	0.007818	0.1481	0.44116
19	0.023368	0.4428	0.329106
20	0.047983	0.9091	0.181941
21	-0.03962	-0.7507	0.226664
22	-0.157258	-2.9796	0.001541
23	0.010195	0.1932	0.42347
24	-0.263321	-4.9892	0
25	0.056986	1.0797	0.140495
26	0.017452	0.3307	0.370544
27	-0.01152	-0.2183	0.413674
28	0.033761	0.6397	0.261394
29	0.035746	0.6773	0.249331
30	-0.027638	-0.5237	0.300414
31	0.037568	0.7118	0.238523
32	-0.076586	-1.4511	0.073812
33	-0.04242	-0.8037	0.211038
34	-0.086262	-1.6344	0.051522
35	-0.078156	-1.4808	0.069763
36	-0.219062	-4.1506	2.1e-05
37	-0.029885	-0.5662	0.285794
38	0.062408	1.1825	0.118901
39	-0.055153	-1.045	0.148363
40	-0.019687	-0.373	0.354676
41	-0.030763	-0.5829	0.280174
42	-0.01269	-0.2404	0.405061
43	-0.11499	-2.1787	0.015
44	-0.017441	-0.3305	0.37062
45	-0.006089	-0.1154	0.454112
46	0.002743	0.052	0.479293
47	-0.026375	-0.4997	0.308785
48	-0.056646	-1.0733	0.141932
49	0.037272	0.7062	0.240259
50	0.038077	0.7214	0.235552
51	-0.031982	-0.606	0.272461
52	0.055379	1.0493	0.147378
53	0.0148	0.2804	0.389656
54	-0.095807	-1.8153	0.035157
55	-0.024197	-0.4585	0.323449
56	-0.032014	-0.6066	0.272256
57	-0.058488	-1.1082	0.134259
58	0.043184	0.8182	0.206889
59	0.009712	0.184	0.427053
60	-0.049846	-0.9444	0.172791

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.187552 & 3.5536 & 0.000215 \tabularnewline
2 & 0.292922 & 5.5501 & 0 \tabularnewline
3 & 0.093512 & 1.7718 & 0.038638 \tabularnewline
4 & 0.033995 & 0.6441 & 0.259959 \tabularnewline
5 & 0.032214 & 0.6104 & 0.271005 \tabularnewline
6 & -0.024285 & -0.4601 & 0.322846 \tabularnewline
7 & -0.139405 & -2.6414 & 0.004309 \tabularnewline
8 & -0.030697 & -0.5816 & 0.280592 \tabularnewline
9 & -0.045877 & -0.8693 & 0.192645 \tabularnewline
10 & -0.156693 & -2.9689 & 0.001595 \tabularnewline
11 & 0.037591 & 0.7122 & 0.238389 \tabularnewline
12 & -0.427945 & -8.1084 & 0 \tabularnewline
13 & -0.036401 & -0.6897 & 0.245414 \tabularnewline
14 & 0.123319 & 2.3366 & 0.010006 \tabularnewline
15 & 0.047112 & 0.8926 & 0.186322 \tabularnewline
16 & -0.060609 & -1.1484 & 0.125789 \tabularnewline
17 & -0.017722 & -0.3358 & 0.368615 \tabularnewline
18 & 0.007818 & 0.1481 & 0.44116 \tabularnewline
19 & 0.023368 & 0.4428 & 0.329106 \tabularnewline
20 & 0.047983 & 0.9091 & 0.181941 \tabularnewline
21 & -0.03962 & -0.7507 & 0.226664 \tabularnewline
22 & -0.157258 & -2.9796 & 0.001541 \tabularnewline
23 & 0.010195 & 0.1932 & 0.42347 \tabularnewline
24 & -0.263321 & -4.9892 & 0 \tabularnewline
25 & 0.056986 & 1.0797 & 0.140495 \tabularnewline
26 & 0.017452 & 0.3307 & 0.370544 \tabularnewline
27 & -0.01152 & -0.2183 & 0.413674 \tabularnewline
28 & 0.033761 & 0.6397 & 0.261394 \tabularnewline
29 & 0.035746 & 0.6773 & 0.249331 \tabularnewline
30 & -0.027638 & -0.5237 & 0.300414 \tabularnewline
31 & 0.037568 & 0.7118 & 0.238523 \tabularnewline
32 & -0.076586 & -1.4511 & 0.073812 \tabularnewline
33 & -0.04242 & -0.8037 & 0.211038 \tabularnewline
34 & -0.086262 & -1.6344 & 0.051522 \tabularnewline
35 & -0.078156 & -1.4808 & 0.069763 \tabularnewline
36 & -0.219062 & -4.1506 & 2.1e-05 \tabularnewline
37 & -0.029885 & -0.5662 & 0.285794 \tabularnewline
38 & 0.062408 & 1.1825 & 0.118901 \tabularnewline
39 & -0.055153 & -1.045 & 0.148363 \tabularnewline
40 & -0.019687 & -0.373 & 0.354676 \tabularnewline
41 & -0.030763 & -0.5829 & 0.280174 \tabularnewline
42 & -0.01269 & -0.2404 & 0.405061 \tabularnewline
43 & -0.11499 & -2.1787 & 0.015 \tabularnewline
44 & -0.017441 & -0.3305 & 0.37062 \tabularnewline
45 & -0.006089 & -0.1154 & 0.454112 \tabularnewline
46 & 0.002743 & 0.052 & 0.479293 \tabularnewline
47 & -0.026375 & -0.4997 & 0.308785 \tabularnewline
48 & -0.056646 & -1.0733 & 0.141932 \tabularnewline
49 & 0.037272 & 0.7062 & 0.240259 \tabularnewline
50 & 0.038077 & 0.7214 & 0.235552 \tabularnewline
51 & -0.031982 & -0.606 & 0.272461 \tabularnewline
52 & 0.055379 & 1.0493 & 0.147378 \tabularnewline
53 & 0.0148 & 0.2804 & 0.389656 \tabularnewline
54 & -0.095807 & -1.8153 & 0.035157 \tabularnewline
55 & -0.024197 & -0.4585 & 0.323449 \tabularnewline
56 & -0.032014 & -0.6066 & 0.272256 \tabularnewline
57 & -0.058488 & -1.1082 & 0.134259 \tabularnewline
58 & 0.043184 & 0.8182 & 0.206889 \tabularnewline
59 & 0.009712 & 0.184 & 0.427053 \tabularnewline
60 & -0.049846 & -0.9444 & 0.172791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30827&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]0.187552[/C][C]3.5536[/C][C]0.000215[/C][/ROW]
[ROW][C]2[/C][C]0.292922[/C][C]5.5501[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.093512[/C][C]1.7718[/C][C]0.038638[/C][/ROW]
[ROW][C]4[/C][C]0.033995[/C][C]0.6441[/C][C]0.259959[/C][/ROW]
[ROW][C]5[/C][C]0.032214[/C][C]0.6104[/C][C]0.271005[/C][/ROW]
[ROW][C]6[/C][C]-0.024285[/C][C]-0.4601[/C][C]0.322846[/C][/ROW]
[ROW][C]7[/C][C]-0.139405[/C][C]-2.6414[/C][C]0.004309[/C][/ROW]
[ROW][C]8[/C][C]-0.030697[/C][C]-0.5816[/C][C]0.280592[/C][/ROW]
[ROW][C]9[/C][C]-0.045877[/C][C]-0.8693[/C][C]0.192645[/C][/ROW]
[ROW][C]10[/C][C]-0.156693[/C][C]-2.9689[/C][C]0.001595[/C][/ROW]
[ROW][C]11[/C][C]0.037591[/C][C]0.7122[/C][C]0.238389[/C][/ROW]
[ROW][C]12[/C][C]-0.427945[/C][C]-8.1084[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.036401[/C][C]-0.6897[/C][C]0.245414[/C][/ROW]
[ROW][C]14[/C][C]0.123319[/C][C]2.3366[/C][C]0.010006[/C][/ROW]
[ROW][C]15[/C][C]0.047112[/C][C]0.8926[/C][C]0.186322[/C][/ROW]
[ROW][C]16[/C][C]-0.060609[/C][C]-1.1484[/C][C]0.125789[/C][/ROW]
[ROW][C]17[/C][C]-0.017722[/C][C]-0.3358[/C][C]0.368615[/C][/ROW]
[ROW][C]18[/C][C]0.007818[/C][C]0.1481[/C][C]0.44116[/C][/ROW]
[ROW][C]19[/C][C]0.023368[/C][C]0.4428[/C][C]0.329106[/C][/ROW]
[ROW][C]20[/C][C]0.047983[/C][C]0.9091[/C][C]0.181941[/C][/ROW]
[ROW][C]21[/C][C]-0.03962[/C][C]-0.7507[/C][C]0.226664[/C][/ROW]
[ROW][C]22[/C][C]-0.157258[/C][C]-2.9796[/C][C]0.001541[/C][/ROW]
[ROW][C]23[/C][C]0.010195[/C][C]0.1932[/C][C]0.42347[/C][/ROW]
[ROW][C]24[/C][C]-0.263321[/C][C]-4.9892[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.056986[/C][C]1.0797[/C][C]0.140495[/C][/ROW]
[ROW][C]26[/C][C]0.017452[/C][C]0.3307[/C][C]0.370544[/C][/ROW]
[ROW][C]27[/C][C]-0.01152[/C][C]-0.2183[/C][C]0.413674[/C][/ROW]
[ROW][C]28[/C][C]0.033761[/C][C]0.6397[/C][C]0.261394[/C][/ROW]
[ROW][C]29[/C][C]0.035746[/C][C]0.6773[/C][C]0.249331[/C][/ROW]
[ROW][C]30[/C][C]-0.027638[/C][C]-0.5237[/C][C]0.300414[/C][/ROW]
[ROW][C]31[/C][C]0.037568[/C][C]0.7118[/C][C]0.238523[/C][/ROW]
[ROW][C]32[/C][C]-0.076586[/C][C]-1.4511[/C][C]0.073812[/C][/ROW]
[ROW][C]33[/C][C]-0.04242[/C][C]-0.8037[/C][C]0.211038[/C][/ROW]
[ROW][C]34[/C][C]-0.086262[/C][C]-1.6344[/C][C]0.051522[/C][/ROW]
[ROW][C]35[/C][C]-0.078156[/C][C]-1.4808[/C][C]0.069763[/C][/ROW]
[ROW][C]36[/C][C]-0.219062[/C][C]-4.1506[/C][C]2.1e-05[/C][/ROW]
[ROW][C]37[/C][C]-0.029885[/C][C]-0.5662[/C][C]0.285794[/C][/ROW]
[ROW][C]38[/C][C]0.062408[/C][C]1.1825[/C][C]0.118901[/C][/ROW]
[ROW][C]39[/C][C]-0.055153[/C][C]-1.045[/C][C]0.148363[/C][/ROW]
[ROW][C]40[/C][C]-0.019687[/C][C]-0.373[/C][C]0.354676[/C][/ROW]
[ROW][C]41[/C][C]-0.030763[/C][C]-0.5829[/C][C]0.280174[/C][/ROW]
[ROW][C]42[/C][C]-0.01269[/C][C]-0.2404[/C][C]0.405061[/C][/ROW]
[ROW][C]43[/C][C]-0.11499[/C][C]-2.1787[/C][C]0.015[/C][/ROW]
[ROW][C]44[/C][C]-0.017441[/C][C]-0.3305[/C][C]0.37062[/C][/ROW]
[ROW][C]45[/C][C]-0.006089[/C][C]-0.1154[/C][C]0.454112[/C][/ROW]
[ROW][C]46[/C][C]0.002743[/C][C]0.052[/C][C]0.479293[/C][/ROW]
[ROW][C]47[/C][C]-0.026375[/C][C]-0.4997[/C][C]0.308785[/C][/ROW]
[ROW][C]48[/C][C]-0.056646[/C][C]-1.0733[/C][C]0.141932[/C][/ROW]
[ROW][C]49[/C][C]0.037272[/C][C]0.7062[/C][C]0.240259[/C][/ROW]
[ROW][C]50[/C][C]0.038077[/C][C]0.7214[/C][C]0.235552[/C][/ROW]
[ROW][C]51[/C][C]-0.031982[/C][C]-0.606[/C][C]0.272461[/C][/ROW]
[ROW][C]52[/C][C]0.055379[/C][C]1.0493[/C][C]0.147378[/C][/ROW]
[ROW][C]53[/C][C]0.0148[/C][C]0.2804[/C][C]0.389656[/C][/ROW]
[ROW][C]54[/C][C]-0.095807[/C][C]-1.8153[/C][C]0.035157[/C][/ROW]
[ROW][C]55[/C][C]-0.024197[/C][C]-0.4585[/C][C]0.323449[/C][/ROW]
[ROW][C]56[/C][C]-0.032014[/C][C]-0.6066[/C][C]0.272256[/C][/ROW]
[ROW][C]57[/C][C]-0.058488[/C][C]-1.1082[/C][C]0.134259[/C][/ROW]
[ROW][C]58[/C][C]0.043184[/C][C]0.8182[/C][C]0.206889[/C][/ROW]
[ROW][C]59[/C][C]0.009712[/C][C]0.184[/C][C]0.427053[/C][/ROW]
[ROW][C]60[/C][C]-0.049846[/C][C]-0.9444[/C][C]0.172791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30827&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30827&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 k	PACF(k)	T-STAT	P-value
1	0.187552	3.5536	0.000215
2	0.292922	5.5501	0
3	0.093512	1.7718	0.038638
4	0.033995	0.6441	0.259959
5	0.032214	0.6104	0.271005
6	-0.024285	-0.4601	0.322846
7	-0.139405	-2.6414	0.004309
8	-0.030697	-0.5816	0.280592
9	-0.045877	-0.8693	0.192645
10	-0.156693	-2.9689	0.001595
11	0.037591	0.7122	0.238389
12	-0.427945	-8.1084	0
13	-0.036401	-0.6897	0.245414
14	0.123319	2.3366	0.010006
15	0.047112	0.8926	0.186322
16	-0.060609	-1.1484	0.125789
17	-0.017722	-0.3358	0.368615
18	0.007818	0.1481	0.44116
19	0.023368	0.4428	0.329106
20	0.047983	0.9091	0.181941
21	-0.03962	-0.7507	0.226664
22	-0.157258	-2.9796	0.001541
23	0.010195	0.1932	0.42347
24	-0.263321	-4.9892	0
25	0.056986	1.0797	0.140495
26	0.017452	0.3307	0.370544
27	-0.01152	-0.2183	0.413674
28	0.033761	0.6397	0.261394
29	0.035746	0.6773	0.249331
30	-0.027638	-0.5237	0.300414
31	0.037568	0.7118	0.238523
32	-0.076586	-1.4511	0.073812
33	-0.04242	-0.8037	0.211038
34	-0.086262	-1.6344	0.051522
35	-0.078156	-1.4808	0.069763
36	-0.219062	-4.1506	2.1e-05
37	-0.029885	-0.5662	0.285794
38	0.062408	1.1825	0.118901
39	-0.055153	-1.045	0.148363
40	-0.019687	-0.373	0.354676
41	-0.030763	-0.5829	0.280174
42	-0.01269	-0.2404	0.405061
43	-0.11499	-2.1787	0.015
44	-0.017441	-0.3305	0.37062
45	-0.006089	-0.1154	0.454112
46	0.002743	0.052	0.479293
47	-0.026375	-0.4997	0.308785
48	-0.056646	-1.0733	0.141932
49	0.037272	0.7062	0.240259
50	0.038077	0.7214	0.235552
51	-0.031982	-0.606	0.272461
52	0.055379	1.0493	0.147378
53	0.0148	0.2804	0.389656
54	-0.095807	-1.8153	0.035157
55	-0.024197	-0.4585	0.323449
56	-0.032014	-0.6066	0.272256
57	-0.058488	-1.1082	0.134259
58	0.043184	0.8182	0.206889
59	0.009712	0.184	0.427053
60	-0.049846	-0.9444	0.172791

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code