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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, 15 Dec 2008 07:12:30 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/15/t1229350400ux9w6wterxq7tub.htm/, Retrieved Mon, 15 Dec 2008 15:13:22 +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/15/t1229350400ux9w6wterxq7tub.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 «

6392.3 8686.4 9244.7 8182.7 7451.4 7988.8 8243.5 8843 9092.7 8246.7 9311.7 8341.2 7116.7 9635.7 9815.4 8611.3 8297.8 8715.1 8919.9 10085.8 9511.7 8991.3 10311.2 8895.4 7449.8 10084 9859.4 9100.1 8920.8 8502.7 8599.6 10394.4 9290.4 8742.2 10217.3 8639 8139.6 10779.1 10427.7 10349.1 10036.4 9492.1 10638.8 12054.5 10324.7 11817.3 11008.9 9996.6 9419.5 11958.8 12594.6 11890.6 10871.7 11835.7 11542.2 13093.7 11180.2 12035.7 12112 10875.2 9897.3 11672.1 12385.7 11405.6 9830.9 11025.1 10853.8 12252.6 11839.4 11669.1 11601.4 11178.4 9516.4 12102.8 12989 11610.2 10205.5 11356.2 11307.1 12648.6 11947.2 11714.1 12192.5 11268.8 9097.4 12639.8 13040.1 11687.3 11191.7 11391.9 11793.1 13933.2 12778.1 11810.3 13698.4 11956.6 10723.8 13938.9 13979.8 13807.4 12973.9 12509.8 12934.1 14908.3 13772.1 13012.6 14049.9 11816.5 11593.2 14466.2 13615.9 14733.9 13880.7 13527.5 13584 16170.2 13260.6 14741.9 15486.5 13154.5 12621.2

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	-0.531843	-5.5271	0
2	-0.046275	-0.4809	0.315779
3	0.327557	3.4041	0.000466
4	-0.280207	-2.912	0.002182
5	0.060111	0.6247	0.266746
6	0.257999	2.6812	0.004243
7	-0.375075	-3.8979	8.4e-05
8	0.146112	1.5184	0.065913
9	0.150336	1.5623	0.060566
10	-0.190516	-1.9799	0.025129
11	0.037674	0.3915	0.348093
12	-0.009661	-0.1004	0.460108
13	-0.106133	-1.103	0.136246
14	0.120929	1.2567	0.105781
15	0.056335	0.5855	0.279733
16	-0.25696	-2.6704	0.004373
17	0.164806	1.7127	0.044818
18	0.080356	0.8351	0.202757
19	-0.210748	-2.1902	0.015332
20	0.127252	1.3224	0.094408
21	0.043018	0.4471	0.327865
22	-0.286375	-2.9761	0.001802
23	0.396123	4.1166	3.8e-05
24	-0.161227	-1.6755	0.048362
25	-0.190878	-1.9837	0.024916
26	0.301489	3.1332	0.001113
27	-0.171573	-1.783	0.038694
28	-0.027528	-0.2861	0.387683
29	0.154068	1.6011	0.056135
30	-0.150432	-1.5633	0.06045
31	0.005093	0.0529	0.478945
32	0.189694	1.9714	0.02562
33	-0.171695	-1.7843	0.038591
34	0.021262	0.221	0.412768
35	0.06125	0.6365	0.262888
36	-0.135509	-1.4083	0.080964
37	0.130815	1.3595	0.088414
38	0.024118	0.2506	0.401284
39	-0.18236	-1.8951	0.030374
40	0.126541	1.3151	0.095639
41	0.090346	0.9389	0.174939
42	-0.21086	-2.1913	0.015288
43	0.161422	1.6775	0.048163
44	-0.020154	-0.2094	0.417249
45	-0.154681	-1.6075	0.055433
46	0.23429	2.4348	0.008269
47	-0.006675	-0.0694	0.472413
48	-0.280731	-2.9174	0.002147
49	0.311698	3.2393	0.000796
50	-0.139988	-1.4548	0.074313
51	-0.004178	-0.0434	0.482723
52	0.124668	1.2956	0.09894
53	-0.157218	-1.6339	0.0526
54	0.037262	0.3872	0.349669
55	0.135542	1.4086	0.080915
56	-0.140703	-1.4622	0.073291
57	0.020593	0.214	0.415474
58	0.035037	0.3641	0.358242
59	-0.051554	-0.5358	0.296611
60	0.092183	0.958	0.170102

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.531843	-5.5271	0
2	-0.45895	-4.7695	3e-06
3	0.084018	0.8731	0.192261
4	-0.021726	-0.2258	0.410899
5	-0.040266	-0.4185	0.33822
6	0.266607	2.7707	0.003294
7	-0.044275	-0.4601	0.323177
8	-0.131899	-1.3707	0.086649
9	0.018344	0.1906	0.424585
10	0.123254	1.2809	0.101488
11	-0.063428	-0.6592	0.255598
12	-0.250125	-2.5994	0.005322
13	-0.21223	-2.2056	0.014767
14	-0.108007	-1.1224	0.132082
15	0.135614	1.4093	0.080803
16	-0.089733	-0.9325	0.176571
17	-0.08514	-0.8848	0.189115
18	0.12895	1.3401	0.091514
19	-0.01193	-0.124	0.450781
20	-0.136023	-1.4136	0.080178
21	0.065978	0.6857	0.247198
22	-0.16357	-1.6999	0.046017
23	-0.008588	-0.0893	0.464523
24	-0.028439	-0.2956	0.38407
25	-0.084236	-0.8754	0.191648
26	-0.012121	-0.126	0.449995
27	-0.06546	-0.6803	0.248892
28	-0.020247	-0.2104	0.416869
29	-0.113147	-1.1759	0.121119
30	0.053244	0.5533	0.290593
31	-0.012905	-0.1341	0.44678
32	-0.004611	-0.0479	0.480935
33	0.032079	0.3334	0.369748
34	0.009699	0.1008	0.459952
35	-0.065003	-0.6755	0.25039
36	-0.253998	-2.6396	0.004764
37	-0.04929	-0.5122	0.304766
38	0.017353	0.1803	0.428613
39	-0.079879	-0.8301	0.204149
40	-0.130205	-1.3531	0.089421
41	0.054041	0.5616	0.287771
42	0.025273	0.2626	0.396663
43	0.015094	0.1569	0.437825
44	-0.009553	-0.0993	0.460551
45	-0.007355	-0.0764	0.469607
46	-0.018659	-0.1939	0.423305
47	0.064492	0.6702	0.252075
48	-0.163884	-1.7031	0.04571
49	-0.084724	-0.8805	0.190277
50	-0.091497	-0.9509	0.171899
51	0.030694	0.319	0.375177
52	0.036557	0.3799	0.352377
53	-0.006582	-0.0684	0.472796
54	0.089086	0.9258	0.178306
55	-0.016466	-0.1711	0.432227
56	-0.018195	-0.1891	0.425189
57	0.031631	0.3287	0.371504
58	-0.038848	-0.4037	0.343609
59	0.005276	0.0548	0.47819
60	-0.014096	-0.1465	0.441905

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229350400ux9w6wterxq7tub/1x4lx1229350348.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229350400ux9w6wterxq7tub/1x4lx1229350348.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229350400ux9w6wterxq7tub/2tguu1229350348.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229350400ux9w6wterxq7tub/2tguu1229350348.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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