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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: Tue, 12 Jan 2010 05:09:59 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/12/t126329840660u4p0llv4s9owu.htm/, Retrieved Tue, 12 Jan 2010 13:13:28 +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/2010/Jan/12/t126329840660u4p0llv4s9owu.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

277 260.6 291.6 275.4 275.3 231.7 238.8 274.2 277.8 299.1 286.6 232.3 294.1 267.5 309.7 280.7 287.3 235.7 256.4 289 290.8 321.9 291.8 241.4 295.5 258.2 306.1 281.5 283.1 237.4 274.8 299.3 300.4 340.9 318.8 265.7 322.7 281.6 323.5 312.6 310.8 262.8 273.8 320 310.3 342.2 320.1 265.6 327 300.7 346.4 317.3 326.2 270.7 278.2 324.6 321.8 343.5 354 278.2 330.2 307.3 375.9 335.3 339.3 280.3 293.7 341.2 345.1 368.7 369.4 288.4 341 319.1 374.2 344.5 337.3 281 282.2 321 325.4 366.3 380.3 300.7 359.3 327.6 383.6 352.4 329.4 294.5 333.5 334.3 358 396.1 387 307.2 363.9 344.7 397.6 376.8 337.1 299.3 323.1 329.1 347 462 436.5 360.4 415.5 382.1 432.2 424.3 386.7 354.5 375.8 368 402.4 426.5 433.3 338.5 416.8 381.1 445.7 412.4 394 348.2 380.1 373.7 393.6 434.2 430.7 344.5 411.9 370.5 437.3 411.3 385.5 341.3 384.2 373.2 415.8 448.6 454.3 350.3 419.1 398 456.1 430.1 399.8 362.7 384. etc...

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.683326	-9.2691	0
2	0.349009	4.7342	2e-06
3	-0.273852	-3.7147	0.000135
4	0.112362	1.5241	0.064594
5	-0.166118	-2.2533	0.012709
6	0.331996	4.5034	6e-06
7	-0.183269	-2.486	0.006905
8	0.13042	1.7691	0.039267
9	-0.273553	-3.7107	0.000137
10	0.311991	4.2321	1.8e-05
11	-0.581377	-7.8862	0
12	0.862242	11.696	0
13	-0.607994	-8.2472	0
14	0.32668	4.4313	8e-06
15	-0.244551	-3.3173	0.000548
16	0.079571	1.0794	0.140921
17	-0.129671	-1.7589	0.040125
18	0.296398	4.0205	4.2e-05
19	-0.177116	-2.4025	0.008638
20	0.139139	1.8874	0.030342
21	-0.276053	-3.7446	0.000121
22	0.314906	4.2716	1.6e-05
23	-0.561218	-7.6127	0
24	0.810439	10.9933	0
25	-0.573692	-7.7819	0
26	0.321323	4.3586	1.1e-05
27	-0.233778	-3.1711	0.00089
28	0.053374	0.724	0.234991
29	-0.086578	-1.1744	0.120876
30	0.246911	3.3493	0.000491
31	-0.158696	-2.1527	0.016324
32	0.147656	2.0029	0.023327
33	-0.26758	-3.6296	0.000184
34	0.276495	3.7506	0.000118
35	-0.489239	-6.6364	0
36	0.719257	9.7565	0
37	-0.508916	-6.9033	0
38	0.284028	3.8527	8.1e-05
39	-0.206372	-2.7994	0.002833
40	0.043814	0.5943	0.276515
41	-0.079325	-1.076	0.141664
42	0.233879	3.1725	0.000886
43	-0.162648	-2.2063	0.014302
44	0.158457	2.1494	0.016454
45	-0.26431	-3.5853	0.000216
46	0.259178	3.5157	0.000276
47	-0.441007	-5.9821	0
48	0.651899	8.8428	0
49	-0.47314	-6.418	0
50	0.270445	3.6685	0.00016
51	-0.175386	-2.379	0.009191
52	0.002641	0.0358	0.485732
53	-0.040206	-0.5454	0.293074
54	0.200641	2.7216	0.00356
55	-0.147537	-2.0013	0.023415
56	0.147025	1.9943	0.023796
57	-0.237732	-3.2248	0.000746
58	0.223485	3.0315	0.001392
59	-0.388407	-5.2686	0
60	0.585121	7.937	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.683326	-9.2691	0
2	-0.221223	-3.0008	0.001533
3	-0.263865	-3.5792	0.00022
4	-0.335819	-4.5553	5e-06
5	-0.597513	-8.1051	0
6	-0.362543	-4.9178	1e-06
7	-0.09525	-1.292	0.098982
8	0.17411	2.3617	0.009617
9	-0.119389	-1.6195	0.05353
10	0.344081	4.6673	3e-06
11	-0.689049	-9.3467	0
12	-0.043834	-0.5946	0.276425
13	0.128342	1.7409	0.041684
14	0.010931	0.1483	0.441142
15	0.085073	1.154	0.125001
16	0.058358	0.7916	0.214804
17	0.135091	1.8325	0.03425
18	0.04674	0.634	0.26343
19	-0.001306	-0.0177	0.492941
20	-0.006642	-0.0901	0.464155
21	-0.135096	-1.8325	0.034244
22	0.094067	1.276	0.101785
23	-0.208611	-2.8297	0.002588
24	-0.094515	-1.2821	0.100716
25	0.009039	0.1226	0.451275
26	0.076464	1.0372	0.150501
27	0.12301	1.6686	0.04845
28	-0.029521	-0.4004	0.344647
29	0.12192	1.6538	0.049936
30	-0.003116	-0.0423	0.483168
31	-0.085582	-1.1609	0.123595
32	-0.066904	-0.9075	0.182658
33	0.011913	0.1616	0.435901
34	-0.070298	-0.9536	0.170776
35	-0.013322	-0.1807	0.428397
36	0.013916	0.1888	0.42524
37	0.101978	1.3833	0.084124
38	0.026849	0.3642	0.358065
39	-0.061239	-0.8307	0.203615
40	0.064776	0.8787	0.190365
41	-0.044801	-0.6077	0.272063
42	0.030351	0.4117	0.340519
43	-0.0228	-0.3093	0.378732
44	-0.063242	-0.8579	0.196045
45	0.026736	0.3627	0.358633
46	-0.026248	-0.356	0.361107
47	0.026162	0.3549	0.361544
48	0.020093	0.2726	0.392752
49	-0.007902	-0.1072	0.457377
50	-0.015265	-0.2071	0.418093
51	0.064856	0.8797	0.190072
52	0.005991	0.0813	0.467662
53	-0.043175	-0.5857	0.279413
54	-0.031193	-0.4231	0.33635
55	0.040484	0.5491	0.291785
56	-0.026988	-0.3661	0.357361
57	-0.020097	-0.2726	0.392727
58	-0.008569	-0.1162	0.453794
59	-0.045063	-0.6113	0.270891
60	0.018378	0.2493	0.401705

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/12/t126329840660u4p0llv4s9owu/1g2k91263298193.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t126329840660u4p0llv4s9owu/1g2k91263298193.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t126329840660u4p0llv4s9owu/2n9uf1263298193.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t126329840660u4p0llv4s9owu/2n9uf1263298193.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

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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