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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 04 Dec 2009 03:28:02 -0700

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/04/t1259922624eli1c3u3c4ca528.htm/, Retrieved Fri, 04 Dec 2009 11:30:26 +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/04/t1259922624eli1c3u3c4ca528.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 «

462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446

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	0.935977	7.25	0
2	0.852066	6.6001	0
3	0.799646	6.194	0
4	0.774288	5.9976	0
5	0.758976	5.879	0
6	0.721206	5.5864	0
7	0.646132	5.0049	3e-06
8	0.550092	4.261	3.6e-05
9	0.470132	3.6416	0.000283
10	0.417344	3.2327	0.000997
11	0.401568	3.1105	0.001428
12	0.363149	2.8129	0.003313
13	0.254784	1.9735	0.026522
14	0.145805	1.1294	0.131612
15	0.067951	0.5263	0.300295
16	0.017348	0.1344	0.446778
17	-0.016106	-0.1248	0.450566
18	-0.058613	-0.454	0.325728
19	-0.12403	-0.9607	0.170271
20	-0.208225	-1.6129	0.056007
21	-0.268956	-2.0833	0.020745
22	-0.302886	-2.3461	0.011145
23	-0.311426	-2.4123	0.009463
24	-0.336165	-2.6039	0.0058
25	-0.394857	-3.0585	0.001661
26	-0.445895	-3.4539	0.00051
27	-0.464463	-3.5977	0.000325
28	-0.460553	-3.5674	0.000358
29	-0.440402	-3.4113	0.000581
30	-0.419206	-3.2472	0.000955
31	-0.412944	-3.1987	0.001103
32	-0.416555	-3.2266	0.001015
33	-0.39446	-3.0555	0.001675
34	-0.364271	-2.8216	0.003235
35	-0.330425	-2.5595	0.006511
36	-0.303192	-2.3485	0.011081
37	-0.299563	-2.3204	0.011868
38	-0.294937	-2.2846	0.012945
39	-0.280159	-2.1701	0.016984
40	-0.254479	-1.9712	0.02666
41	-0.221593	-1.7164	0.04562
42	-0.188573	-1.4607	0.07466
43	-0.168018	-1.3015	0.099038
44	-0.148544	-1.1506	0.127228
45	-0.122749	-0.9508	0.172758
46	-0.101149	-0.7835	0.218209
47	-0.077965	-0.6039	0.274088
48	-0.054532	-0.4224	0.33712
49	-0.041139	-0.3187	0.375545
50	-0.029881	-0.2315	0.408874
51	-0.018055	-0.1399	0.444622
52	-0.004428	-0.0343	0.486376
53	0.007109	0.0551	0.478134
54	0.014397	0.1115	0.455788
55	0.01656	0.1283	0.449181
56	0.020838	0.1614	0.436156
57	0.023726	0.1838	0.427404
58	0.015602	0.1209	0.452106
59	0.004694	0.0364	0.485558
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.935977	7.25	0
2	-0.193531	-1.4991	0.069548
3	0.242476	1.8782	0.032607
4	0.10879	0.8427	0.201377
5	0.076844	0.5952	0.276964
6	-0.151818	-1.176	0.122125
7	-0.234042	-1.8129	0.037426
8	-0.213774	-1.6559	0.051483
9	-0.036167	-0.2801	0.390165
10	-0.003349	-0.0259	0.489694
11	0.273837	2.1211	0.019026
12	-0.1811	-1.4028	0.082916
13	-0.425171	-3.2934	0.000832
14	0.084682	0.6559	0.257184
15	-0.028948	-0.2242	0.411669
16	-0.051981	-0.4026	0.344322
17	0.0474	0.3672	0.357396
18	0.017286	0.1339	0.446968
19	0.048404	0.3749	0.354514
20	-0.158285	-1.2261	0.112481
21	0.093192	0.7219	0.236592
22	-0.11994	-0.929	0.178293
23	-0.096207	-0.7452	0.229526
24	0.008827	0.0684	0.472857
25	0.026969	0.2089	0.417617
26	-0.00044	-0.0034	0.498645
27	0.143569	1.1121	0.13527
28	-0.035565	-0.2755	0.391946
29	0.094746	0.7339	0.232935
30	0.005317	0.0412	0.483643
31	0.087067	0.6744	0.251317
32	-0.01072	-0.083	0.46705
33	0.067141	0.5201	0.302463
34	-0.206214	-1.5973	0.057723
35	-0.06715	-0.5201	0.30244
36	0.013073	0.1013	0.459839
37	-0.07277	-0.5637	0.287538
38	-0.120512	-0.9335	0.177156
39	-0.070117	-0.5431	0.294529
40	-0.000221	-0.0017	0.49932
41	0.029227	0.2264	0.410833
42	-0.014722	-0.114	0.454796
43	0.148688	1.1517	0.127
44	0.025465	0.1972	0.422149
45	-0.13175	-1.0205	0.155788
46	0.041595	0.3222	0.374212
47	0.003866	0.0299	0.488104
48	-0.081364	-0.6302	0.265463
49	0.031014	0.2402	0.405485
50	-0.043622	-0.3379	0.368312
51	0.035272	0.2732	0.392812
52	-0.091471	-0.7085	0.240679
53	0.015124	0.1172	0.453566
54	-0.053075	-0.4111	0.341226
55	-0.053582	-0.415	0.339795
56	0.051077	0.3956	0.346887
57	0.07637	0.5916	0.278184
58	-0.04107	-0.3181	0.375747
59	0.001663	0.0129	0.494881
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922624eli1c3u3c4ca528/1e82n1259922480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922624eli1c3u3c4ca528/1e82n1259922480.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922624eli1c3u3c4ca528/23uz81259922480.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259922624eli1c3u3c4ca528/23uz81259922480.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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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