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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: Thu, 17 Dec 2009 20:22:52 +0100

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/17/t1261077796ihrorppqtbkcaif.htm/, Retrieved Thu, 17 Dec 2009 20:23:18 +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/2009/Dec/17/t1261077796ihrorppqtbkcaif.htm/},
    year = {2009},
}
@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 = {2009},
    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	7 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.790824	10.7854	0
2	0.734747	10.0206	0
3	0.630802	8.603	0
4	0.660364	9.0062	0
5	0.70893	9.6685	0
6	0.770407	10.5069	0
7	0.667777	9.1073	0
8	0.588332	8.0238	0
9	0.517054	7.0517	0
10	0.589295	8.0369	0
11	0.621529	8.4765	0
12	0.781232	10.6546	0
13	0.599594	8.1774	0
14	0.555437	7.5752	0
15	0.46065	6.2824	0
16	0.487249	6.6452	0
17	0.539832	7.3623	0
18	0.594738	8.1112	0
19	0.503804	6.871	0
20	0.436467	5.9526	0
21	0.372236	5.0766	0
22	0.446357	6.0875	0
23	0.474272	6.4682	0
24	0.627313	8.5554	0
25	0.460955	6.2866	0
26	0.420334	5.7326	0
27	0.328687	4.4827	6e-06
28	0.352179	4.8031	2e-06
29	0.407197	5.5534	0
30	0.45322	6.1811	0
31	0.375134	5.1161	0
32	0.314507	4.2893	1.4e-05
33	0.245535	3.3486	0.000491
34	0.31191	4.2539	1.7e-05
35	0.343212	4.6808	3e-06
36	0.481808	6.571	0
37	0.335283	4.5726	4e-06
38	0.298932	4.0769	3.4e-05
39	0.216144	2.9478	0.001805
40	0.23725	3.2357	0.000718
41	0.287992	3.9277	6e-05
42	0.330729	4.5105	6e-06
43	0.255736	3.4878	0.000304
44	0.202486	2.7615	0.003165
45	0.135292	1.8451	0.033304
46	0.19785	2.6983	0.003805
47	0.226521	3.0893	0.001157
48	0.349903	4.772	2e-06
49	0.217962	2.9726	0.001672
50	0.189772	2.5882	0.005206
51	0.113244	1.5444	0.06209
52	0.126334	1.723	0.043279
53	0.182188	2.4847	0.006924
54	0.21869	2.9825	0.001621
55	0.15034	2.0504	0.020866
56	0.102401	1.3966	0.082104
57	0.040049	0.5462	0.292794
58	0.095428	1.3015	0.097354
59	0.126225	1.7215	0.043413
60	0.236811	3.2297	0.000733

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.790824	10.7854	0
2	0.291899	3.981	4.9e-05
3	-0.033516	-0.4571	0.324067
4	0.289802	3.9524	5.5e-05
5	0.33121	4.5171	6e-06
6	0.272449	3.7157	0.000134
7	-0.245094	-3.3426	0.000502
8	-0.182078	-2.4832	0.006953
9	0.004895	0.0668	0.473425
10	0.29366	4.005	4.5e-05
11	0.024925	0.3399	0.367147
12	0.499698	6.815	0
13	-0.548126	-7.4754	0
14	-0.084651	-1.1545	0.12489
15	-0.005796	-0.0791	0.468539
16	-0.040258	-0.549	0.291816
17	0.014693	0.2004	0.420701
18	-0.002759	-0.0376	0.485012
19	0.098004	1.3366	0.091494
20	0.033932	0.4628	0.322036
21	0.086372	1.178	0.120158
22	0.045667	0.6228	0.267083
23	-0.06068	-0.8276	0.20449
24	0.150667	2.0548	0.020647
25	-0.219883	-2.9988	0.001541
26	-0.119558	-1.6306	0.052339
27	-0.05466	-0.7455	0.228465
28	0.013698	0.1868	0.426002
29	0.05668	0.773	0.220249
30	-0.031038	-0.4233	0.336284
31	0.152137	2.0749	0.019687
32	0.027061	0.3691	0.356252
33	-0.028913	-0.3943	0.346896
34	-0.06094	-0.8311	0.203488
35	0.025456	0.3472	0.364426
36	-0.029974	-0.4088	0.34158
37	-0.069795	-0.9519	0.171197
38	-0.034814	-0.4748	0.317742
39	0.029625	0.404	0.343328
40	0.043336	0.591	0.27761
41	-0.051903	-0.7079	0.239958
42	0.037989	0.5181	0.302504
43	-0.036677	-0.5002	0.308759
44	0.048792	0.6654	0.253299
45	0.002253	0.0307	0.487762
46	-0.065798	-0.8974	0.185341
47	0.010244	0.1397	0.444522
48	-0.042695	-0.5823	0.280539
49	0.010221	0.1394	0.444646
50	0.010448	0.1425	0.44342
51	0.004238	0.0578	0.476983
52	-0.051428	-0.7014	0.241969
53	0.044852	0.6117	0.270743
54	0.014926	0.2036	0.419457
55	-0.036777	-0.5016	0.308281
56	-0.023131	-0.3155	0.376382
57	0.03487	0.4756	0.317471
58	-0.013919	-0.1898	0.424826
59	-0.001684	-0.023	0.490851
60	-0.022367	-0.305	0.380337

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261077796ihrorppqtbkcaif/1kaxv1261077763.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261077796ihrorppqtbkcaif/1kaxv1261077763.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261077796ihrorppqtbkcaif/20y3b1261077763.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261077796ihrorppqtbkcaif/20y3b1261077763.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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