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*The author of this computation has been verified*

R Software Module: rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 14 Dec 2008 00:53:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/14/t122924127550xavkph4wzg4t3.htm/, Retrieved Sun, 14 Dec 2008 08:54:37 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/14/t122924127550xavkph4wzg4t3.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

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

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.147575	2.7962	0.002725
2	0.271382	5.142	0
3	0.181838	3.4453	0.000319
4	0.114064	2.1612	0.01567
5	0.14792	2.8027	0.002671
6	0.052571	0.9961	0.159942
7	-0.038673	-0.7328	0.232094
8	0.001933	0.0366	0.485399
9	-0.080036	-1.5165	0.065141
10	-0.166146	-3.148	0.000891
11	-0.025738	-0.4877	0.313045
12	-0.46171	-8.7482	0
13	-0.159456	-3.0213	0.001349
14	-0.159783	-3.0274	0.001322
15	-0.146797	-2.7814	0.002849
16	-0.152304	-2.8857	0.00207
17	-0.12947	-2.4531	0.007319
18	-0.103993	-1.9704	0.024781
19	0.015172	0.2875	0.386962
20	0.014983	0.2839	0.388328
21	-0.02523	-0.478	0.316458
22	0.006065	0.1149	0.454291
23	-0.023971	-0.4542	0.324985
24	0.00024	0.0045	0.498187
25	0.116549	2.2083	0.013928
26	0.035493	0.6725	0.250852
27	0.063929	1.2113	0.113292
28	0.10714	2.03	0.021546
29	0.030853	0.5846	0.279599
30	0.058345	1.1055	0.134846
31	0.029931	0.5671	0.285495
32	-0.076832	-1.4558	0.073168
33	0.010447	0.1979	0.421598
34	-0.01339	-0.2537	0.399935
35	-0.084746	-1.6057	0.054609
36	-0.045278	-0.8579	0.195762
37	-0.099926	-1.8933	0.029559
38	-0.024743	-0.4688	0.319741
39	-0.064258	-1.2175	0.112103
40	-0.108143	-2.049	0.020594
41	-0.102158	-1.9356	0.02685
42	-0.027392	-0.519	0.30204
43	-0.16464	-3.1195	0.000979
44	0.032915	0.6237	0.266625
45	-0.026475	-0.5016	0.308119
46	0.022113	0.419	0.337737
47	0.072432	1.3724	0.0854
48	0.073781	1.398	0.081495
49	0.096567	1.8297	0.034063
50	0.073709	1.3966	0.081699
51	0.070766	1.3408	0.090414
52	0.153524	2.9089	0.001927
53	0.197438	3.7409	0.000107
54	0.016085	0.3048	0.380362
55	0.168562	3.1938	0.000764
56	0.018348	0.3477	0.364153
57	0.05682	1.0766	0.141196
58	0.054532	1.0332	0.151097
59	0.012445	0.2358	0.406863
60	-0.015257	-0.2891	0.386342

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.147575	2.7962	0.002725
2	0.255161	4.8346	1e-06
3	0.125039	2.3692	0.009179
4	0.017672	0.3348	0.368974
5	0.066652	1.2629	0.103726
6	-0.019477	-0.369	0.356157
7	-0.120383	-2.2809	0.011569
8	-0.02782	-0.5271	0.299221
9	-0.06351	-1.2033	0.114819
10	-0.158782	-3.0085	0.001405
11	0.047672	0.9033	0.183499
12	-0.409489	-7.7587	0
13	-0.065752	-1.2458	0.106819
14	0.075203	1.4249	0.077528
15	0.035626	0.675	0.250052
16	-0.072596	-1.3755	0.084916
17	0.012967	0.2457	0.403034
18	0.001892	0.0359	0.485708
19	0.041563	0.7875	0.215751
20	0.08105	1.5357	0.06275
21	-0.057615	-1.0917	0.137858
22	-0.146492	-2.7756	0.002899
23	-0.001559	-0.0295	0.488228
24	-0.234984	-4.4523	6e-06
25	0.055992	1.0609	0.144727
26	0.040967	0.7762	0.219066
27	0.020747	0.3931	0.347242
28	0.019193	0.3637	0.358162
29	-0.015692	-0.2973	0.3832
30	-0.039368	-0.7459	0.228101
31	0.040245	0.7625	0.223122
32	-0.066385	-1.2578	0.104637
33	-0.063626	-1.2055	0.114393
34	-0.079254	-1.5017	0.067033
35	-0.096831	-1.8347	0.03369
36	-0.201347	-3.815	8e-05
37	0.032718	0.6199	0.267854
38	0.062613	1.1863	0.118137
39	-0.048182	-0.9129	0.180947
40	-0.042507	-0.8054	0.210564
41	-0.086829	-1.6452	0.050404
42	0.015646	0.2964	0.38353
43	-0.100618	-1.9064	0.028695
44	0.012392	0.2348	0.407249
45	-0.04872	-0.9231	0.178284
46	-0.013241	-0.2509	0.401025
47	-0.024437	-0.463	0.321818
48	-0.053708	-1.0176	0.154774
49	0.051367	0.9733	0.165537
50	0.034695	0.6574	0.255678
51	-0.02972	-0.5631	0.286853
52	0.075886	1.4378	0.075675
53	0.037617	0.7127	0.238233
54	-0.083309	-1.5785	0.057667
55	-0.032649	-0.6186	0.268281
56	-0.061898	-1.1728	0.120825
57	-0.076165	-1.4431	0.074928
58	0.021895	0.4148	0.339252
59	0.004833	0.0916	0.463544
60	-0.031161	-0.5904	0.277643

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t122924127550xavkph4wzg4t3/1uuek1229241207.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t122924127550xavkph4wzg4t3/1uuek1229241207.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t122924127550xavkph4wzg4t3/2l6f01229241207.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t122924127550xavkph4wzg4t3/2l6f01229241207.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = -0.1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = -0.1 ; 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('http://www.xycoon.com/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('http://www.xycoon.com/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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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