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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: Wed, 17 Dec 2008 12:00:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/17/t122954044799l8k5kd905s0m3.htm/, Retrieved Wed, 17 Dec 2008 20:00:49 +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/2008/Dec/17/t122954044799l8k5kd905s0m3.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

1721 1476 1842 2171 1670 1540 1266 897 1266 1519 1074 1435 1385 1440 1883 1822 1661 1774 1133 1361 1688 2216 2896 1382 1330 1419 1662 2040 2126 1649 1610 1952 2102 1749 2091 3036 2414 2097 2705 2431 4192 3990 2854 1966 2431 2763 2831 2023 2934 2489 3252 3018 3193 3976 2584 2512 2169 2504 1843 1408 2179 3690 2372 2494 3872 2786 2312 1599 3167 3433 2648 1978 1947 3113 2856 3174 3507 4174 2978 4428 2832 2930 3681 3253 1660 2208 3139 3409 3445 2410 3262 2897 2526 3982 4097 3403 3362 2708 3129 3550 2696 2885 2945 3600 3808 3671 4005

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	-0.251187	-2.5861	0.005531
2	-0.250183	-2.5758	0.005689
3	-0.038911	-0.4006	0.344755
4	0.064082	0.6598	0.25542
5	0.074347	0.7654	0.222853
6	-0.075594	-0.7783	0.219068
7	-0.091927	-0.9464	0.173036
8	0.126636	1.3038	0.097563
9	-0.018995	-0.1956	0.422661
10	-0.193644	-1.9937	0.024378
11	0.139195	1.4331	0.077386
12	-0.061728	-0.6355	0.263226
13	0.255253	2.628	0.004932
14	-0.121819	-1.2542	0.106263
15	-0.058519	-0.6025	0.274066
16	0.01695	0.1745	0.430899
17	-0.059021	-0.6077	0.272357
18	0.127476	1.3124	0.096103
19	-0.038059	-0.3918	0.347983
20	0.013994	0.1441	0.442855
21	-0.09333	-0.9609	0.169396
22	0.016533	0.1702	0.43258
23	-0.093835	-0.9661	0.168098
24	0.110706	1.1398	0.128472
25	-0.028651	-0.295	0.384293
26	0.142403	1.4661	0.072787
27	-0.123551	-1.272	0.103073
28	-0.122052	-1.2566	0.10583
29	0.22679	2.3349	0.010715
30	-0.00809	-0.0833	0.466887
31	-0.062056	-0.6389	0.262132
32	-0.11871	-1.2222	0.112172
33	0.143004	1.4723	0.071949
34	-0.088035	-0.9064	0.183397
35	0.068142	0.7016	0.242246
36	-0.099899	-1.0285	0.153024
37	0.060706	0.625	0.266654
38	0.049538	0.51	0.305546
39	-0.00987	-0.1016	0.459627
40	-0.120434	-1.2399	0.108868
41	0.04764	0.4905	0.312402
42	0.188205	1.9377	0.027661
43	-0.061315	-0.6313	0.264609
44	-0.075586	-0.7782	0.219089
45	-0.074111	-0.763	0.223574
46	0.015917	0.1639	0.43507
47	0.070944	0.7304	0.233375
48	0.055839	0.5749	0.283288
49	-0.070907	-0.73	0.23349
50	-0.028771	-0.2962	0.383821
51	-0.018225	-0.1876	0.425759
52	-0.013756	-0.1416	0.44382
53	0.080554	0.8294	0.204383
54	-0.040914	-0.4212	0.337218
55	0.101083	1.0407	0.150189
56	-0.082329	-0.8476	0.199277
57	-0.055508	-0.5715	0.284438
58	0.057272	0.5896	0.27834
59	0.006386	0.0657	0.473851
60	-0.012819	-0.132	0.447626

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.251187	-2.5861	0.005531
2	-0.334375	-3.4426	0.000413
3	-0.248461	-2.5581	0.005969
4	-0.152531	-1.5704	0.059651
5	-0.04142	-0.4264	0.335323
6	-0.099504	-1.0245	0.153976
7	-0.160831	-1.6559	0.050354
8	-0.000573	-0.0059	0.497653
9	-0.070904	-0.73	0.233498
10	-0.276421	-2.8459	0.002659
11	-0.068188	-0.702	0.242097
12	-0.256577	-2.6416	0.00475
13	0.144435	1.487	0.069985
14	-0.032763	-0.3373	0.368274
15	0.073975	0.7616	0.22399
16	0.003658	0.0377	0.485013
17	-0.127092	-1.3085	0.096768
18	0.102847	1.0589	0.146032
19	-0.045345	-0.4669	0.320781
20	0.140184	1.4433	0.075945
21	-0.061136	-0.6294	0.265211
22	0.000257	0.0026	0.498949
23	-0.10113	-1.0412	0.150077
24	-0.109199	-1.1243	0.131719
25	-0.045084	-0.4642	0.32174
26	0.024488	0.2521	0.40072
27	-0.070125	-0.722	0.235948
28	-0.16362	-1.6846	0.047506
29	0.093879	0.9665	0.167986
30	0.064986	0.6691	0.252451
31	-0.071618	-0.7373	0.23127
32	-0.11082	-1.141	0.128227
33	-0.009322	-0.096	0.461861
34	-0.147763	-1.5213	0.065579
35	0.066683	0.6865	0.246936
36	0.000156	0.0016	0.499362
37	-0.048477	-0.4991	0.309372
38	-0.026655	-0.2744	0.392146
39	0.030724	0.3163	0.376188
40	-0.142207	-1.4641	0.073061
41	-0.005744	-0.0591	0.476479
42	0.086517	0.8907	0.187542
43	0.105144	1.0825	0.140738
44	-0.030192	-0.3108	0.378263
45	0.067176	0.6916	0.245343
46	-0.17922	-1.8452	0.033902
47	0.022519	0.2318	0.408552
48	0.04836	0.4979	0.309794
49	0.03955	0.4072	0.342342
50	0.024285	0.25	0.401526
51	-0.067022	-0.69	0.245842
52	-0.033728	-0.3472	0.364547
53	-0.058731	-0.6047	0.273345
54	-0.035677	-0.3673	0.357057
55	-0.039259	-0.4042	0.343442
56	-0.100308	-1.0327	0.152041
57	-0.019256	-0.1983	0.421614
58	0.046671	0.4805	0.315928
59	-0.046637	-0.4802	0.316054
60	-0.010935	-0.1126	0.455287

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122954044799l8k5kd905s0m3/153111229540403.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122954044799l8k5kd905s0m3/153111229540403.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122954044799l8k5kd905s0m3/2q2l71229540403.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t122954044799l8k5kd905s0m3/2q2l71229540403.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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