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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: Mon, 27 Dec 2010 13:32:05 +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/27/t1293456706ywmixefjkac95fz.htm/, Retrieved Mon, 27 Dec 2010 14:31:46 +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/27/t1293456706ywmixefjkac95fz.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 «

35.36 31.19 35.29 33.80 36.38 37.77 34.88 37.07 35.56 34.18 32.05 32.35 34.79 33.75 33.76 36.80 36.57 34.14 33.85 35.10 33.92 33.34 30.69 32.32 32.47 34.71 37.19 35.58 36.04 35.63 32.74 33.31 28.40 27.37 28.20 29.23 28.05 27.70 28.05 28.01 30.73 30.82 30.48 30.92 31.20 31.41 31.96 36.95 35.64 37.18 38.69 39.97 40.36 40.79 42.92 41.21 44.15 44.70 47.42 45.14 46.08 50.59 48.63 47.46 47.30 49.02 51.77 54.15 56.10 52.58 52.56 51.27 57.72 53.46 55.48 59.33 57.32 56.44 58.80 55.64 53.62 54.87 56.15 55.35 52.38 51.27 53.95 56.09 56.34 60.65 58.35 57.18 58.87 66.20 62.25 62.62 54.73 56.20 52.54 63.06 63.53 60.95 53.83 51.20 44.57 44.15 44.04 42.28 38.42 35.41 37.01 39.19 46.50 44.79 47.01 49.15 50.85 54.09 55.40 56.16 54.37 52.34 56.13 51.29 42.95 28.88 38.47 34.83 41.17 40.80 40.00 44.00

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.095563	-1.0938	0.138031
2	0.114898	1.3151	0.095392
3	-0.198624	-2.2734	0.012316
4	0.056881	0.651	0.258084
5	-0.037057	-0.4241	0.33608
6	0.08526	0.9758	0.165471
7	0.006402	0.0733	0.470851
8	-0.125389	-1.4351	0.076816
9	-0.170042	-1.9462	0.026885
10	-0.040494	-0.4635	0.321898
11	0.043746	0.5007	0.308713
12	0.014424	0.1651	0.434562
13	-0.11289	-1.2921	0.099302
14	0.049533	0.5669	0.285867
15	-0.091818	-1.0509	0.147619
16	0.021882	0.2504	0.401317
17	0.080712	0.9238	0.178646
18	0.002816	0.0322	0.48717
19	0.065642	0.7513	0.226907
20	-0.047319	-0.5416	0.29451
21	0.176555	2.0208	0.022671
22	-0.019615	-0.2245	0.411358
23	0.135544	1.5514	0.061613
24	-0.111148	-1.2721	0.102788
25	0.071263	0.8156	0.208094
26	-0.165652	-1.896	0.030083
27	0.14136	1.6179	0.05404
28	-0.039979	-0.4576	0.324007
29	0.137669	1.5757	0.058755
30	-0.190526	-2.1807	0.015497
31	0.052155	0.5969	0.27579
32	-0.095311	-1.0909	0.138663
33	0.059941	0.6861	0.246944
34	-0.051222	-0.5863	0.279352
35	0.010529	0.1205	0.452132
36	-0.106263	-1.2162	0.113041
37	-0.032354	-0.3703	0.355875
38	-0.051835	-0.5933	0.277009
39	0.03745	0.4286	0.334445
40	0.040175	0.4598	0.323201
41	0.014336	0.1641	0.434959
42	0.013088	0.1498	0.440575
43	-0.032184	-0.3684	0.3566
44	-0.019297	-0.2209	0.41277
45	0.052381	0.5995	0.274929
46	0.013164	0.1507	0.440235
47	-0.011248	-0.1287	0.448881
48	-0.025915	-0.2966	0.383619
49	-0.018595	-0.2128	0.415894
50	-0.036339	-0.4159	0.339075
51	-0.010455	-0.1197	0.452465
52	0.0346	0.396	0.346369
53	-0.087261	-0.9988	0.159878
54	0.098368	1.1259	0.131139
55	-0.110275	-1.2622	0.104567
56	0.073782	0.8445	0.199972
57	-0.122466	-1.4017	0.081686
58	-0.041136	-0.4708	0.319273
59	-0.005751	-0.0658	0.473812
60	-0.003875	-0.0443	0.482347

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.095563	-1.0938	0.138031
2	0.106741	1.2217	0.112007
3	-0.182339	-2.087	0.019415
4	0.01678	0.1921	0.423999
5	0.007129	0.0816	0.467545
6	0.042603	0.4876	0.313321
7	0.032423	0.3711	0.355582
8	-0.14921	-1.7078	0.045022
9	-0.18073	-2.0685	0.020278
10	-0.040464	-0.4631	0.322019
11	0.025097	0.2872	0.387188
12	-0.027659	-0.3166	0.376038
13	-0.148183	-1.696	0.046127
14	0.056156	0.6427	0.260762
15	-0.043696	-0.5001	0.308913
16	-0.056007	-0.641	0.261312
17	0.073222	0.8381	0.201761
18	-0.069603	-0.7966	0.21355
19	0.065387	0.7484	0.227784
20	-7.2e-05	-8e-04	0.499671
21	0.130948	1.4988	0.06817
22	0.015386	0.1761	0.430244
23	0.085379	0.9772	0.165134
24	-0.050489	-0.5779	0.28217
25	0.032334	0.3701	0.355959
26	-0.10118	-1.1581	0.124473
27	0.118903	1.3609	0.08794
28	0.002118	0.0242	0.490347
29	0.136116	1.5579	0.060832
30	-0.087519	-1.0017	0.159167
31	0.044292	0.5069	0.306523
32	0.010108	0.1157	0.454037
33	-0.013374	-0.1531	0.439289
34	-0.02578	-0.2951	0.384206
35	-0.045436	-0.52	0.301959
36	-0.049462	-0.5661	0.286142
37	-0.019486	-0.223	0.411933
38	-0.066901	-0.7657	0.222612
39	-0.050451	-0.5774	0.282316
40	0.036286	0.4153	0.339297
41	-0.017324	-0.1983	0.421566
42	0.007402	0.0847	0.466306
43	-0.075554	-0.8648	0.194378
44	-0.063569	-0.7276	0.234084
45	0.036935	0.4227	0.336589
46	-0.069113	-0.791	0.215177
47	0.000731	0.0084	0.496667
48	-0.096956	-1.1097	0.134577
49	0.028171	0.3224	0.373819
50	-0.123308	-1.4113	0.08026
51	0.00882	0.1009	0.459874
52	-0.047337	-0.5418	0.29444
53	-0.033659	-0.3853	0.350338
54	0.068944	0.7891	0.215739
55	-0.016206	-0.1855	0.426567
56	-0.053439	-0.6116	0.27092
57	-0.030351	-0.3474	0.364432
58	-0.145635	-1.6669	0.048965
59	0.052587	0.6019	0.274145
60	-0.075279	-0.8616	0.195239

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456706ywmixefjkac95fz/1ibqt1293456721.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456706ywmixefjkac95fz/1ibqt1293456721.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456706ywmixefjkac95fz/2lus91293456722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456706ywmixefjkac95fz/2lus91293456722.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456706ywmixefjkac95fz/3lus91293456722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456706ywmixefjkac95fz/3lus91293456722.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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 (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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