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Paper: ACF (min18 gediff.)

*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: Wed, 29 Dec 2010 10:17:18 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t12936178639j4941prqzmxok2.htm/, Retrieved Wed, 29 Dec 2010 11:17:46 +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/Dec/29/t12936178639j4941prqzmxok2.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 «

3065 2997 2901 2815 2709 2711 3509 3369 3596 3448 3160 2934 2534 2266 2088 1932 1784 1851 2700 2580 2829 2298 2045 1824 1872 1801 1735 1639 1521 1758 2603 2540 3103 2801 2590 2324 2424 2288 2163 2082 1937 2155 2874 2836 3439 3278 3129 2959 3060 2898 2783 2632 2465 2689 3321 3359 4108 3407 3241 3013 3067 2965 2823 2718 2567 2658 3436 3375 3931 3371 3038

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	0.090712	0.6908	0.246211
2	0.095273	0.7256	0.235507
3	0.037467	0.2853	0.388199
4	-0.124142	-0.9454	0.17418
5	0.086269	0.657	0.256889
6	0.044586	0.3396	0.367707
7	0.098359	0.7491	0.228418
8	0.23491	1.789	0.039417
9	-0.054672	-0.4164	0.339337
10	-0.051821	-0.3947	0.347271
11	-0.099107	-0.7548	0.226719
12	-0.22812	-1.7373	0.04382
13	0.026895	0.2048	0.419212
14	0.010001	0.0762	0.469775
15	0.023995	0.1827	0.427818
16	0.031223	0.2378	0.406443
17	-0.004921	-0.0375	0.485117
18	-0.112092	-0.8537	0.198401
19	-0.008949	-0.0682	0.472949
20	0.004508	0.0343	0.486366
21	0.056572	0.4308	0.334091
22	0.040648	0.3096	0.378999
23	0.020219	0.154	0.439079
24	-0.117475	-0.8947	0.187333
25	-0.182098	-1.3868	0.085403
26	-0.056596	-0.431	0.334024
27	-0.012419	-0.0946	0.462488
28	-0.042716	-0.3253	0.373056
29	-0.002899	-0.0221	0.491231
30	0.002906	0.0221	0.49121
31	-0.026696	-0.2033	0.419802
32	-0.09112	-0.694	0.245241
33	-0.192176	-1.4636	0.074355
34	-0.06249	-0.4759	0.317962
35	-0.126905	-0.9665	0.168909
36	0.119935	0.9134	0.182408
37	0.035129	0.2675	0.395003
38	-0.019659	-0.1497	0.440752
39	-0.015972	-0.1216	0.451804
40	-0.046037	-0.3506	0.363577
41	-0.036432	-0.2775	0.391208
42	0.01549	0.118	0.453251
43	-0.05387	-0.4103	0.341563
44	0.085343	0.65	0.259144
45	-0.01782	-0.1357	0.446258
46	-0.019539	-0.1488	0.441112
47	0.069221	0.5272	0.300042
48	-0.063858	-0.4863	0.314283
49	0.066301	0.5049	0.30776
50	-0.018033	-0.1373	0.445621
51	-0.003131	-0.0238	0.49053
52	0.028348	0.2159	0.414914
53	-0.017911	-0.1364	0.445987
54	0.030968	0.2358	0.407192
55	0.035269	0.2686	0.394594
56	-0.010652	-0.0811	0.467813
57	0.02978	0.2268	0.410691
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.090712	0.6908	0.246211
2	0.087767	0.6684	0.253261
3	0.021971	0.1673	0.433849
4	-0.139633	-1.0634	0.146
5	0.106287	0.8095	0.210781
6	0.053949	0.4109	0.341342
7	0.083406	0.6352	0.263897
8	0.195211	1.4867	0.071257
9	-0.092872	-0.7073	0.241108
10	-0.090257	-0.6874	0.247294
11	-0.079593	-0.6062	0.273385
12	-0.178245	-1.3575	0.089945
13	0.021157	0.1611	0.436277
14	0.029367	0.2237	0.411906
15	-0.008393	-0.0639	0.474627
16	-0.032117	-0.2446	0.403815
17	0.087703	0.6679	0.253415
18	-0.080422	-0.6125	0.271308
19	0.066781	0.5086	0.306486
20	0.095234	0.7253	0.235598
21	0.007085	0.054	0.478577
22	-0.036867	-0.2808	0.389944
23	-0.000818	-0.0062	0.497524
24	-0.191237	-1.4564	0.075335
25	-0.193341	-1.4724	0.073154
26	0.038016	0.2895	0.386606
27	0.000482	0.0037	0.498542
28	-0.097137	-0.7398	0.23121
29	0.017354	0.1322	0.447656
30	0.026902	0.2049	0.419192
31	0.038593	0.2939	0.384936
32	0.04448	0.3387	0.368012
33	-0.124901	-0.9512	0.17272
34	-0.087012	-0.6627	0.255086
35	-0.134158	-1.0217	0.155579
36	0.079806	0.6078	0.272851
37	-0.067149	-0.5114	0.30551
38	-0.014406	-0.1097	0.456508
39	-0.028816	-0.2195	0.413532
40	0.012222	0.0931	0.463081
41	0.05794	0.4413	0.330333
42	0.058146	0.4428	0.329768
43	-0.087969	-0.67	0.252774
44	0.020595	0.1568	0.437955
45	-0.056072	-0.427	0.33547
46	-0.067593	-0.5148	0.304334
47	0.039289	0.2992	0.382923
48	-0.016773	-0.1277	0.449398
49	-0.017875	-0.1361	0.446094
50	-0.04976	-0.379	0.353051
51	0.031678	0.2413	0.405104
52	-0.006702	-0.051	0.479735
53	-0.012632	-0.0962	0.461845
54	0.090126	0.6864	0.247604
55	0.00973	0.0741	0.470591
56	-0.014524	-0.1106	0.456153
57	-0.086336	-0.6575	0.256725
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936178639j4941prqzmxok2/1kqvy1293617832.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936178639j4941prqzmxok2/1kqvy1293617832.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936178639j4941prqzmxok2/2c0u11293617832.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936178639j4941prqzmxok2/2c0u11293617832.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936178639j4941prqzmxok2/3c0u11293617832.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t12936178639j4941prqzmxok2/3c0u11293617832.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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