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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 04:45:30 -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/t1263296828xc33zhldkoaqpn3.htm/, Retrieved Tue, 12 Jan 2010 12:47:10 +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/t1263296828xc33zhldkoaqpn3.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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.504969	6.661	0
2	0.478931	6.3175	0
3	0.326982	4.3132	1.3e-05
4	0.275766	3.6376	0.000181
5	0.170767	2.2526	0.012768
6	0.187767	2.4768	0.007106
7	0.159328	2.1017	0.018511
8	0.106797	1.4087	0.080347
9	0.008628	0.1138	0.45476
10	-0.105876	-1.3966	0.082157
11	-0.0871	-1.1489	0.126082
12	-0.32447	-4.28	1.5e-05
13	-0.105134	-1.3868	0.083637
14	-0.117873	-1.5549	0.060899
15	0.057316	0.7561	0.225319
16	-0.048377	-0.6381	0.26211
17	-0.076092	-1.0037	0.158454
18	-0.067675	-0.8927	0.186627
19	-0.07832	-1.0331	0.151493
20	-0.11377	-1.5007	0.067619
21	-0.058951	-0.7776	0.218924
22	-0.012772	-0.1685	0.433204
23	-0.06358	-0.8387	0.201401
24	-0.013276	-0.1751	0.430595
25	-0.106541	-1.4054	0.080848
26	-0.07271	-0.9591	0.169417
27	-0.195998	-2.5854	0.005273
28	-0.129572	-1.7092	0.044601
29	-0.032823	-0.433	0.332789
30	-0.082944	-1.0941	0.137711
31	-0.034951	-0.461	0.322676
32	-0.026539	-0.3501	0.363354
33	-0.054425	-0.7179	0.236886
34	-0.06796	-0.8965	0.185625
35	-0.058153	-0.7671	0.222034
36	-0.084101	-1.1094	0.1344
37	-0.024653	-0.3252	0.372712
38	-0.084604	-1.116	0.132979
39	-0.026396	-0.3482	0.364062
40	-0.008579	-0.1132	0.455013
41	-0.082573	-1.0892	0.138783
42	-0.075353	-0.994	0.160806
43	-0.099261	-1.3093	0.096072
44	-0.054031	-0.7127	0.238488
45	-0.099706	-1.3152	0.095085
46	-0.068477	-0.9033	0.183813
47	-0.033235	-0.4384	0.330818
48	-0.069753	-0.9201	0.179397
49	-0.076052	-1.0032	0.158578
50	-0.037513	-0.4948	0.310672
51	-0.068859	-0.9083	0.182484
52	-0.086521	-1.1413	0.127658
53	-0.005083	-0.067	0.47331
54	-0.034758	-0.4585	0.323585
55	0.069754	0.9201	0.179392
56	-0.018989	-0.2505	0.401255
57	-0.008268	-0.1091	0.456641
58	-0.016965	-0.2238	0.411595
59	-0.021533	-0.284	0.388361
60	-0.010227	-0.1349	0.446421

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.504969	6.661	0
2	0.300584	3.965	5.4e-05
3	0.008921	0.1177	0.453232
4	0.020961	0.2765	0.39125
5	-0.047824	-0.6308	0.264488
6	0.071722	0.9461	0.172712
7	0.048676	0.6421	0.260834
8	-0.04916	-0.6485	0.258768
9	-0.128794	-1.6989	0.045561
10	-0.178383	-2.353	0.009869
11	0.031917	0.421	0.337134
12	-0.30737	-4.0545	3.8e-05
13	0.237159	3.1283	0.001031
14	0.100839	1.3302	0.092603
15	0.221464	2.9213	0.001974
16	-0.100428	-1.3247	0.093499
17	-0.20857	-2.7512	0.003283
18	0.077389	1.0208	0.154376
19	-0.010736	-0.1416	0.443774
20	-0.039824	-0.5253	0.300016
21	-0.069729	-0.9198	0.179477
22	-0.049661	-0.6551	0.256644
23	-0.012429	-0.164	0.434979
24	-0.077014	-1.0159	0.155547
25	0.043824	0.5781	0.281979
26	0.008442	0.1114	0.45573
27	0.007433	0.0981	0.461002
28	-0.058404	-0.7704	0.221055
29	0.073204	0.9656	0.167787
30	-0.106848	-1.4094	0.080248
31	0.072928	0.962	0.168696
32	0.021625	0.2853	0.387893
33	-0.090481	-1.1935	0.117143
34	-0.012414	-0.1637	0.43506
35	-0.061388	-0.8098	0.209592
36	-0.036219	-0.4778	0.31671
37	-0.030342	-0.4002	0.344738
38	-0.047188	-0.6225	0.267228
39	0.008599	0.1134	0.454908
40	0.05173	0.6824	0.247958
41	-0.002767	-0.0365	0.485464
42	-0.086566	-1.1419	0.127537
43	0.007086	0.0935	0.462817
44	-0.006154	-0.0812	0.467698
45	-0.064722	-0.8537	0.19721
46	-0.022256	-0.2936	0.384714
47	0.0017	0.0224	0.491065
48	-0.103304	-1.3627	0.087374
49	0.025292	0.3336	0.369533
50	-0.030161	-0.3978	0.345616
51	-0.024409	-0.322	0.373931
52	-0.006887	-0.0908	0.463859
53	0.077812	1.0264	0.153063
54	-0.056749	-0.7486	0.227563
55	0.066812	0.8813	0.189682
56	-0.058173	-0.7674	0.221956
57	-0.103315	-1.3628	0.087351
58	-0.023122	-0.305	0.380363
59	0.011901	0.157	0.437721
60	-0.012599	-0.1662	0.4341

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263296828xc33zhldkoaqpn3/1dgf21263296728.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263296828xc33zhldkoaqpn3/1dgf21263296728.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263296828xc33zhldkoaqpn3/2ea7a1263296728.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263296828xc33zhldkoaqpn3/2ea7a1263296728.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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