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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: Fri, 19 Dec 2008 19:26:02 -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/20/t1229740141qvzou5x94x32el4.htm/, Retrieved Sat, 20 Dec 2008 03:29:01 +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/20/t1229740141qvzou5x94x32el4.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 «

99.2 93.6 104.2 95.3 102.7 103.1 100 107.2 107 119 110.4 101.7 102.4 98.8 105.6 104.4 106.3 107.2 108.5 106.9 114.2 125.9 110.6 110.5 106.7 104.7 107.4 109.8 103.4 114.8 114.3 109.6 118.3 127.3 112.3 114.9 108.2 105.4 122.1 113.5 110 125.3 114.3 115.6 127.1 123 122.2 126.4 112.7 105.8 120.9 116.3 115.7 127.9 108.3 121.1 128.6 123.1 127.7 126.6 118.4 110 129.6 115.8 125.9 128.4 114 125.6 128.5 136.6 133.1 124.6

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.254583	-1.972	0.026613
2	-0.000801	-0.0062	0.497536
3	0.23727	1.8379	0.035516
4	-0.176	-1.3633	0.088943
5	0.134742	1.0437	0.150403
6	0.125607	0.9729	0.167243
7	-0.234871	-1.8193	0.036928
8	0.070907	0.5492	0.292439
9	0.266905	2.0674	0.021507
10	-0.353542	-2.7385	0.004056
11	0.006469	0.0501	0.4801
12	0.003223	0.025	0.490081
13	-0.275709	-2.1356	0.0184
14	0.220822	1.7105	0.046172
15	-0.047357	-0.3668	0.35752
16	-0.255007	-1.9753	0.026421
17	0.265814	2.059	0.021922
18	0.047243	0.3659	0.357847
19	-0.258656	-2.0035	0.024821
20	0.141879	1.099	0.138082
21	0.010047	0.0778	0.469115
22	-0.000482	-0.0037	0.498518
23	0.360269	2.7906	0.003521
24	-0.172728	-1.3379	0.092981
25	-0.093754	-0.7262	0.235265
26	0.310121	2.4022	0.009705
27	-0.254472	-1.9711	0.026663
28	0.095051	0.7363	0.23222
29	0.072051	0.5581	0.289424
30	-0.180848	-1.4008	0.083206
31	0.111357	0.8626	0.195904
32	0.009601	0.0744	0.470483
33	-0.142076	-1.1005	0.137751
34	-0.050089	-0.388	0.3497
35	0.08747	0.6775	0.250333
36	-0.199486	-1.5452	0.063776
37	0.107552	0.8331	0.204047
38	-0.070431	-0.5456	0.293697
39	-0.065123	-0.5044	0.307899
40	0.066005	0.5113	0.305519
41	-0.091374	-0.7078	0.240912
42	-0.054052	-0.4187	0.33847
43	0.030925	0.2395	0.405749
44	0.006043	0.0468	0.481411
45	-0.039615	-0.3069	0.380008
46	0.075955	0.5883	0.279255
47	-0.039081	-0.3027	0.381574
48	-0.067721	-0.5246	0.30091
49	0.122944	0.9523	0.172378
50	-0.119406	-0.9249	0.179357
51	0.053232	0.4123	0.340781
52	0.013002	0.1007	0.460056
53	-0.05795	-0.4489	0.327567
54	0.055179	0.4274	0.335304
55	-0.027886	-0.216	0.414858
56	-0.023362	-0.181	0.428504
57	0.013886	0.1076	0.457351
58	-0.016356	-0.1267	0.449803
59	0.001245	0.0096	0.496167
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.254583	-1.972	0.026613
2	-0.07016	-0.5435	0.294413
3	0.23554	1.8245	0.036529
4	-0.062936	-0.4875	0.313839
5	0.089064	0.6899	0.246463
6	0.141871	1.0989	0.138095
7	-0.144055	-1.1158	0.134469
8	-0.088558	-0.686	0.247688
9	0.288918	2.238	0.014474
10	-0.200973	-1.5567	0.062397
11	-0.247673	-1.9185	0.029907
12	-0.07986	-0.6186	0.269262
13	-0.147066	-1.1392	0.129581
14	0.016206	0.1255	0.450262
15	0.090651	0.7022	0.242642
16	-0.070928	-0.5494	0.292383
17	0.082827	0.6416	0.261795
18	0.205471	1.5916	0.058369
19	-0.108517	-0.8406	0.201964
20	-0.141453	-1.0957	0.138796
21	0.160285	1.2416	0.109615
22	0.14445	1.1189	0.13382
23	0.126978	0.9836	0.164638
24	0.015622	0.121	0.452046
25	-0.119432	-0.9251	0.179306
26	-0.02239	-0.1734	0.431449
27	-0.168125	-1.3023	0.098897
28	0.126047	0.9764	0.166403
29	0.027361	0.2119	0.416436
30	-0.063229	-0.4898	0.313041
31	-0.08008	-0.6203	0.268704
32	-0.153373	-1.188	0.119753
33	0.176232	1.3651	0.088661
34	0.040326	0.3124	0.377922
35	-0.020128	-0.1559	0.438312
36	0.001601	0.0124	0.495074
37	0.017028	0.1319	0.447754
38	-0.158635	-1.2288	0.111976
39	0.031831	0.2466	0.403045
40	-0.132599	-1.0271	0.154247
41	-0.083337	-0.6455	0.260525
42	0.088676	0.6869	0.247403
43	-0.059835	-0.4635	0.322347
44	-0.150821	-1.1683	0.123663
45	-0.016015	-0.1241	0.450844
46	-0.053241	-0.4124	0.340756
47	0.045725	0.3542	0.36222
48	0.037824	0.293	0.385274
49	0.101388	0.7853	0.217671
50	-0.136956	-1.0609	0.146504
51	-0.10653	-0.8252	0.206269
52	0.024031	0.1861	0.426479
53	0.057597	0.4461	0.32855
54	-0.014715	-0.114	0.454818
55	0.034984	0.271	0.393667
56	-0.108343	-0.8392	0.202338
57	-0.050975	-0.3948	0.347177
58	0.05521	0.4277	0.335215
59	0.001493	0.0116	0.495405
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229740141qvzou5x94x32el4/1qrb41229739957.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229740141qvzou5x94x32el4/1qrb41229739957.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229740141qvzou5x94x32el4/2gok11229739957.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t1229740141qvzou5x94x32el4/2gok11229739957.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 60 ; par2 = -0.7 ; par3 = 0 ; 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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