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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: Tue, 08 Dec 2009 10:32:48 -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/08/t1260293665ugx6624h6uz2xtf.htm/, Retrieved Tue, 08 Dec 2009 18:34:27 +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/08/t1260293665ugx6624h6uz2xtf.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 «

87.28 87.09 86.92 87.59 90.72 90.69 90.3 89.55 88.94 88.41 87.82 87.07 86.82 86.4 86.02 85.66 85.32 85 84.67 83.94 82.83 81.95 81.19 80.48 78.86 69.47 68.77 70.06 73.95 75.8 77.79 81.57 83.07 84.34 85.1 85.25 84.26 83.63 86.44 85.3 84.1 83.36 82.48 81.58 80.47 79.34 82.13 81.69 80.7 79.88 79.16 78.38 77.42 76.47 75.46 74.48 78.27 80.7 79.91 78.75 77.78 81.14 81.08 80.03 78.91 78.01 76.9 75.97 81.93 80.27 78.67 77.42 76.16 74.7 76.39 76.04 74.65 73.29 71.79 74.39 74.91 74.54 73.08 72.75 71.32 70.38 70.35 70.01 69.36 67.77 69.26 69.8 68.38 67.62 68.39 66.95 65.21 66.64 63.45 60.66 62.34 60.32 58.64 60.46 58.59 61.87 61.85 67.44 77.06 91.74 93.15 94.15 93.11 91.51 89.96 88.16 86.98 88.03 86.24 84.65 83.23 81.7 80.25 78.8 77.51 76.2 75.04 74 75.49 77.14 76.15 76.27 78.19 76.49 77.31 76.65 74.99 73.51 72.07 70.59 71.96 76.29 74.86 74.93 71.9 71.01 77.47 75.78 76.6 76. etc...

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	0.120181	2.2739	0.011781
2	-0.01047	-0.1981	0.421537
3	0.072501	1.3718	0.085496
4	-0.214934	-4.0667	2.9e-05
5	-0.160308	-3.0332	0.001298
6	0.043568	0.8243	0.205146
7	0.077151	1.4598	0.072616
8	0.019017	0.3598	0.359595
9	0.037014	0.7003	0.242086
10	0.047179	0.8927	0.186317
11	0.036405	0.6888	0.245696
12	-0.084928	-1.6069	0.054478
13	-0.004423	-0.0837	0.466676
14	-0.049981	-0.9457	0.172476
15	-0.085608	-1.6198	0.05308
16	-0.029284	-0.5541	0.289936
17	-0.013512	-0.2557	0.399179
18	-0.049324	-0.9332	0.175661
19	-0.124429	-2.3543	0.009548
20	-0.007686	-0.1454	0.442225
21	0.008889	0.1682	0.433267
22	0.059737	1.1303	0.129559
23	0.049545	0.9374	0.174584
24	0.080777	1.5284	0.063653
25	-0.011023	-0.2086	0.417456
26	-0.03657	-0.6919	0.24471
27	-0.032254	-0.6103	0.271032
28	-0.066908	-1.266	0.103177
29	0.014725	0.2786	0.390353
30	0.149543	2.8295	0.002462
31	0.08278	1.5663	0.059084
32	0.003179	0.0601	0.476037
33	0.147908	2.7985	0.002706
34	-0.069774	-1.3202	0.093808
35	-0.051901	-0.982	0.163377
36	0.076488	1.4472	0.074356
37	-0.002989	-0.0565	0.477469
38	0.02625	0.4967	0.309865
39	-0.003792	-0.0717	0.471422
40	-0.041201	-0.7796	0.218082
41	-0.039275	-0.7431	0.228949
42	-0.029664	-0.5613	0.287481
43	0.018594	0.3518	0.362589
44	-0.081008	-1.5328	0.06311
45	-0.037842	-0.716	0.237229
46	-0.001805	-0.0341	0.48639
47	0.022164	0.4194	0.337604
48	-0.055181	-1.0441	0.148576
49	-0.023893	-0.4521	0.325747
50	0.02071	0.3919	0.347701
51	-0.044276	-0.8377	0.201367
52	-0.037604	-0.7115	0.238618
53	-0.022911	-0.4335	0.332455
54	-0.038207	-0.7229	0.235103
55	-0.078554	-1.4863	0.069038
56	-0.025122	-0.4753	0.317419
57	0.004429	0.0838	0.466633
58	-0.00338	-0.064	0.474521
59	-0.010997	-0.2081	0.417648
60	0.043239	0.8181	0.206919

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.120181	2.2739	0.011781
2	-0.025279	-0.4783	0.316365
3	0.078004	1.4759	0.070423
4	-0.238781	-4.5179	4e-06
5	-0.104469	-1.9766	0.024425
6	0.064043	1.2118	0.113203
7	0.106518	2.0154	0.022304
8	-0.027529	-0.5209	0.301389
9	-0.033929	-0.642	0.260651
10	0.03705	0.701	0.241871
11	0.091218	1.7259	0.042612
12	-0.087668	-1.6588	0.04902
13	-0.004979	-0.0942	0.462499
14	-0.058711	-1.1109	0.133685
15	-0.018115	-0.3427	0.365994
16	-0.046404	-0.878	0.190265
17	-0.033658	-0.6368	0.262318
18	-0.063666	-1.2046	0.114572
19	-0.142947	-2.7047	0.003582
20	-0.001338	-0.0253	0.489911
21	0.017156	0.3246	0.372833
22	0.080856	1.5299	0.063466
23	-0.025857	-0.4892	0.312487
24	0.048733	0.9221	0.178554
25	0.001278	0.0242	0.49036
26	0.028223	0.534	0.296838
27	-0.03096	-0.5858	0.279192
28	-0.047034	-0.8899	0.187051
29	0.033513	0.6341	0.263211
30	0.162465	3.074	0.001137
31	0.012122	0.2294	0.409357
32	-0.067512	-1.2774	0.101145
33	0.110513	2.091	0.018616
34	-0.042407	-0.8024	0.211432
35	0.021855	0.4135	0.339739
36	0.048272	0.9133	0.180838
37	0.019994	0.3783	0.352715
38	0.033735	0.6383	0.261842
39	-0.055107	-1.0427	0.148902
40	-0.041262	-0.7807	0.217745
41	0.002916	0.0552	0.478019
42	0.000519	0.0098	0.496086
43	0.025584	0.4841	0.314318
44	-0.145846	-2.7595	0.003043
45	0.022213	0.4203	0.337263
46	-0.026074	-0.4933	0.311039
47	0.067543	1.278	0.101043
48	-0.0904	-1.7104	0.044025
49	-0.002916	-0.0552	0.478015
50	0.06494	1.2287	0.109991
51	0.003653	0.0691	0.472465
52	-0.030005	-0.5677	0.285288
53	-0.097911	-1.8526	0.032384
54	-0.036613	-0.6928	0.244455
55	-0.057534	-1.0886	0.138533
56	-0.028766	-0.5443	0.293297
57	-0.023137	-0.4378	0.330906
58	-0.029666	-0.5613	0.287471
59	-0.069204	-1.3094	0.095618
60	-0.01408	-0.2664	0.395042

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260293665ugx6624h6uz2xtf/16b7b1260293566.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260293665ugx6624h6uz2xtf/16b7b1260293566.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260293665ugx6624h6uz2xtf/2jsje1260293566.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/08/t1260293665ugx6624h6uz2xtf/2jsje1260293566.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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