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autocorrelation

*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 04:01:23 -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/t12295118329r83bm3fveto3s1.htm/, Retrieved Wed, 17 Dec 2008 12:03:57 +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/t12295118329r83bm3fveto3s1.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 «

117.09 116.77 119.39 122.49 124.08 118.29 112.94 113.79 114.43 118.70 120.36 118.27 118.34 117.82 117.65 118.18 121.02 124.78 131.16 130.14 131.75 134.73 135.35 140.32 136.35 131.60 128.90 133.89 138.25 146.23 144.76 149.30 156.80 159.08 165.12 163.14 153.43 151.01 154.72 154.58 155.63 161.67 163.51 162.91 164.80 164.98 154.54 148.60 149.19 150.61

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	0.321024	2.2472	0.014583
2	-0.101803	-0.7126	0.239731
3	-0.117669	-0.8237	0.207056
4	-0.186907	-1.3083	0.09843
5	-0.135948	-0.9516	0.172976
6	0.001031	0.0072	0.497137
7	-0.1112	-0.7784	0.220037
8	-0.195597	-1.3692	0.088593
9	0.034449	0.2411	0.405225
10	0.243427	1.704	0.047359
11	0.341643	2.3915	0.010332
12	0.016626	0.1164	0.453914
13	-0.045847	-0.3209	0.374815
14	-0.020142	-0.141	0.444226
15	-0.135102	-0.9457	0.174467
16	-0.077737	-0.5442	0.2944
17	-0.146452	-1.0252	0.15516
18	-0.155451	-1.0882	0.140925
19	-0.060228	-0.4216	0.337582
20	0.088358	0.6185	0.269552
21	0.077561	0.5429	0.294822
22	0.040498	0.2835	0.388998
23	-0.05242	-0.3669	0.357621
24	-0.00065	-0.0046	0.498194
25	0.051528	0.3607	0.35994
26	-0.099792	-0.6985	0.24407
27	-0.112816	-0.7897	0.21675
28	-0.131842	-0.9229	0.180292
29	-0.077451	-0.5422	0.295083
30	0.043718	0.306	0.380439
31	0.114098	0.7987	0.214163
32	0.040226	0.2816	0.389724
33	-0.042565	-0.298	0.383498
34	-0.007144	-0.05	0.480159
35	0.019235	0.1346	0.446721
36	-0.038632	-0.2704	0.393985
37	-0.058443	-0.4091	0.342124
38	-0.011597	-0.0812	0.467815
39	0.0074	0.0518	0.47945
40	0.086816	0.6077	0.273092
41	0.143977	1.0078	0.159242
42	0.046674	0.3267	0.372635
43	-0.050562	-0.3539	0.362452
44	-0.054447	-0.3811	0.352378
45	-0.001579	-0.0111	0.495612
46	0.010721	0.075	0.470241
47	0.001975	0.0138	0.494513
48	-0.000961	-0.0067	0.497331
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.321024	2.2472	0.014583
2	-0.228397	-1.5988	0.05815
3	-0.004943	-0.0346	0.486269
4	-0.19068	-1.3348	0.094062
5	-0.031754	-0.2223	0.412512
6	0.003471	0.0243	0.490358
7	-0.19766	-1.3836	0.086373
8	-0.150186	-1.0513	0.149139
9	0.094583	0.6621	0.25551
10	0.156307	1.0942	0.139619
11	0.229524	1.6067	0.057277
12	-0.245928	-1.7215	0.045735
13	0.159841	1.1189	0.134321
14	0.027399	0.1918	0.424349
15	-0.092414	-0.6469	0.26036
16	-0.015213	-0.1065	0.457815
17	-0.229571	-1.607	0.057241
18	0.133418	0.9339	0.177462
19	-0.072888	-0.5102	0.306096
20	-0.07212	-0.5048	0.307967
21	-0.057036	-0.3993	0.34572
22	-0.109439	-0.7661	0.223654
23	0.023361	0.1635	0.435388
24	-0.044054	-0.3084	0.37955
25	-0.041245	-0.2887	0.387009
26	-0.074711	-0.523	0.301674
27	-0.082968	-0.5808	0.282026
28	0.022678	0.1587	0.43726
29	-0.086122	-0.6029	0.274693
30	-0.000903	-0.0063	0.497491
31	0.018446	0.1291	0.448894
32	-0.043966	-0.3078	0.379785
33	-0.031304	-0.2191	0.413731
34	-0.057447	-0.4021	0.34467
35	-0.030649	-0.2145	0.415508
36	-0.116027	-0.8122	0.210305
37	0.038214	0.2675	0.395103
38	-0.027539	-0.1928	0.423967
39	0.048124	0.3369	0.368828
40	0.050575	0.354	0.362419
41	0.002137	0.015	0.494063
42	0.021644	0.1515	0.440097
43	-0.097018	-0.6791	0.250128
44	-0.02014	-0.141	0.444232
45	0.001523	0.0107	0.49577
46	-0.012276	-0.0859	0.465937
47	0.058857	0.412	0.341069
48	-0.067586	-0.4731	0.319121
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t12295118329r83bm3fveto3s1/1vpq11229511681.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t12295118329r83bm3fveto3s1/1vpq11229511681.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t12295118329r83bm3fveto3s1/2c4yk1229511681.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/17/t12295118329r83bm3fveto3s1/2c4yk1229511681.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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