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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: Sat, 19 Dec 2009 10:25:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/19/t1261243554hdh7dvah3ad90tr.htm/, Retrieved Sat, 19 Dec 2009 18:25:56 +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/19/t1261243554hdh7dvah3ad90tr.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 «

128.7 136.9 156.9 109.1 122.3 123.9 90.9 77.9 120.3 118.9 125.5 98.9 102.9 105.9 117.6 113.6 115.9 118.9 77.6 81.2 123.1 136.6 112.1 95.1 96.3 105.7 115.8 105.7 105.7 111.1 82.4 60 107.3 99.3 113.5 108.9 100.2 103.9 138.7 120.2 100.2 143.2 70.9 85.2 133 136.6 117.9 106.3 122.3 125.5 148.4 126.3 99.6 140.4 80.3 92.6 138.5 110.9 119.6 105 109 129.4 148.6 101.4 134.8 143.7 81.6 90.3 141.5 140.7 140.2 100.2 125.7 119.6 134.7 109 116.3 146.9 97.4 89.4 132.1 139.8 129 112.5 121.9 121.7 123.1 131.6 119.3 132.5 98.3 85.1 131.7 129.3 90.7 78.6 68.9 79.1 83.5 74.1 59.7 93.3 61.3 56.6 98.5

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	-0.481223	-4.6157	6e-06
2	0.002865	0.0275	0.489069
3	0.023865	0.2289	0.409725
4	-0.039069	-0.3747	0.354358
5	0.067323	0.6457	0.260027
6	0.135359	1.2983	0.098712
7	-0.236807	-2.2714	0.012728
8	0.042099	0.4038	0.343648
9	0.009009	0.0864	0.465662
10	0.026298	0.2522	0.400709
11	0.174114	1.67	0.049155
12	-0.380274	-3.6475	0.000219
13	0.133061	1.2763	0.102535
14	0.038032	0.3648	0.358054
15	0.081282	0.7796	0.218805
16	-0.103933	-0.9969	0.160717
17	0.017483	0.1677	0.433596
18	-0.066047	-0.6335	0.263989
19	0.044297	0.4249	0.335956
20	0.106732	1.0237	0.154322
21	0.019648	0.1885	0.425466
22	-0.245535	-2.3551	0.010322
23	0.223276	2.1416	0.017434
24	0.015143	0.1453	0.442415
25	-0.141633	-1.3585	0.088813
26	0.192946	1.8507	0.033713
27	-0.176342	-1.6914	0.047072
28	0.022996	0.2206	0.412957
29	0.15188	1.4568	0.074291
30	-0.108612	-1.0418	0.150124
31	-0.028624	-0.2746	0.392138
32	-0.027477	-0.2635	0.39636
33	-0.042527	-0.4079	0.342146
34	0.203109	1.9482	0.027222
35	-0.095217	-0.9133	0.181738
36	-0.087953	-0.8436	0.200535
37	0.065564	0.6289	0.265498
38	-0.058527	-0.5614	0.287955
39	0.058267	0.5589	0.288802
40	0.063892	0.6128	0.27075
41	-0.119823	-1.1493	0.126705
42	-0.017804	-0.1708	0.43239
43	0.134229	1.2875	0.100578
44	-0.008468	-0.0812	0.467721
45	-0.05554	-0.5327	0.297754
46	-0.015602	-0.1497	0.440683
47	0.029892	0.2867	0.38749
48	-0.084195	-0.8076	0.210709
49	0.236319	2.2667	0.012876
50	-0.152553	-1.4632	0.073405
51	-0.036462	-0.3497	0.363671
52	0.016433	0.1576	0.437552
53	0.030337	0.291	0.385859
54	0.046374	0.4448	0.328754
55	-0.069853	-0.67	0.252266
56	-0.069175	-0.6635	0.254332
57	0.08235	0.7899	0.215817
58	0.008988	0.0862	0.465743
59	-0.084254	-0.8081	0.210548
60	0.077703	0.7453	0.228996

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.481223	-4.6157	6e-06
2	-0.297636	-2.8548	0.00266
3	-0.167881	-1.6103	0.055384
4	-0.15076	-1.446	0.075782
5	-0.03118	-0.2991	0.382782
6	0.235709	2.2608	0.013063
7	-0.011815	-0.1133	0.455009
8	-0.097979	-0.9398	0.174896
9	-0.117001	-1.1222	0.132342
10	-0.063013	-0.6044	0.273533
11	0.226289	2.1705	0.016272
12	-0.23305	-2.2353	0.013907
13	-0.177157	-1.6992	0.046328
14	-0.110431	-1.0592	0.146136
15	0.104111	0.9986	0.160304
16	-0.049065	-0.4706	0.319516
17	-0.060554	-0.5808	0.281393
18	0.059238	0.5682	0.285645
19	-0.09587	-0.9196	0.180106
20	0.018306	0.1756	0.430501
21	0.143239	1.3739	0.086405
22	-0.130194	-1.2488	0.107457
23	0.175274	1.6812	0.048061
24	0.103683	0.9945	0.161296
25	-0.172484	-1.6544	0.050726
26	0.055854	0.5357	0.296717
27	0.083248	0.7985	0.213321
28	-0.006165	-0.0591	0.476488
29	0.062355	0.5981	0.275624
30	0.054681	0.5245	0.300604
31	-0.081365	-0.7804	0.218572
32	-0.1582	-1.5174	0.066297
33	-0.005469	-0.0525	0.47914
34	0.002236	0.0214	0.491469
35	0.147341	1.4132	0.08048
36	0.11653	1.1177	0.133299
37	-0.128808	-1.2355	0.109899
38	-0.082594	-0.7922	0.215136
39	-0.006176	-0.0592	0.476447
40	0.011967	0.1148	0.454432
41	0.013616	0.1306	0.448187
42	0.029998	0.2877	0.387101
43	0.065905	0.6321	0.264433
44	-0.058473	-0.5608	0.288132
45	0.008031	0.077	0.469385
46	-0.013274	-0.1273	0.449484
47	0.063997	0.6138	0.270417
48	-0.050175	-0.4813	0.315736
49	0.056675	0.5436	0.294013
50	-0.007312	-0.0701	0.472119
51	0.057899	0.5553	0.290004
52	0.002307	0.0221	0.491197
53	-0.010987	-0.1054	0.45815
54	0.073578	0.7057	0.241069
55	-0.089375	-0.8573	0.196767
56	-0.08979	-0.8612	0.195675
57	-0.025627	-0.2458	0.403189
58	0.025795	0.2474	0.402567
59	-0.029936	-0.2871	0.387326
60	-0.162251	-1.5563	0.06154

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261243554hdh7dvah3ad90tr/1u1aw1261243528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261243554hdh7dvah3ad90tr/1u1aw1261243528.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261243554hdh7dvah3ad90tr/2ftnt1261243528.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261243554hdh7dvah3ad90tr/2ftnt1261243528.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 = 1 ; 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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