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TIJDREEKS B - STAP 27

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 17 Aug 2010 19:46:19 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/17/t1282074372axp61eec88rkzs4.htm/, Retrieved Tue, 17 Aug 2010 21:46:17 +0200

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/2010/Aug/17/t1282074372axp61eec88rkzs4.htm/},
    year = {2010},
}
@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 = {2010},
    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:

Schrauwen Nathalie

Dataseries X:

» Textbox « » Textfile « » CSV «

162 161 160 158 156 155 156 158 159 159 160 162 168 177 174 169 169 160 168 172 173 175 170 177 187 201 188 179 176 170 179 183 174 177 170 166 171 178 165 162 159 149 153 156 149 150 139 131 141 150 128 124 120 113 120 121 115 119 106 98 106 116 93 94 90 93 100 99 90 91 83 83 92 104 71 69 67 75 86 81 88 87 77 70

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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.807164232749437
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	160	160	0
4	158	159	-1
5	156	157.192835767251	-1.19283576725056
6	155	155.230021400382	-0.230021400381673
7	156	154.044356353227	1.95564364677335
8	158	154.622881956906	3.37711804309421
9	159	156.348770851064	2.65122914893578
10	159	157.488748192908	1.51125180709209
11	160	157.708576598271	2.29142340172939
12	162	158.558131610232	3.44186838976836
13	168	160.336284668284	7.66371533171645
14	177	165.522161574019	11.4778384259814
15	174	173.786662220748	0.213337779252129
16	169	172.958860845654	-3.95886084565439
17	169	168.76340996861	0.236590031390023
18	160	167.954376979773	-7.95437697977309
19	168	160.533888387895	7.46611161210524
20	172	165.560266638901	6.43973336109866
21	173	169.758189076423	3.24181092357651
22	175	171.374862903271	3.62513709672913
23	170	173.300943906564	-3.30094390656376
24	177	169.636540050873	7.36345994912671
25	187	174.580061551091	12.4199384489086
26	201	183.60499164	17.3950083600001
27	188	196.645620216569	-8.64562021656943
28	179	188.667184807819	-9.66718480781915
29	176	179.864178999569	-3.86417899956879
30	170	175.745151922175	-5.74515192217535
31	179	170.107870778884	8.89212922111628
32	183	176.285279439155	6.71472056084508
33	174	180.705161708776	-6.7051617087763
34	177	174.292995002651	2.70700499734903
35	170	175.477992614385	-5.47799261438507
36	166	170.056352908788	-4.05635290878786
37	171	165.782209925405	5.21779007459486
38	178	168.993823447613	9.00617655238688
39	165	175.263287034526	-10.2632870345265
40	162	165.979128829816	-3.97912882981564
41	159	161.767318360886	-2.76731836088632
42	149	158.533637959348	-9.53363795934808
43	153	149.83842639058	3.16157360942003
44	156	151.390335527308	4.60966447269163
45	149	154.111091814641	-5.11109181464084
46	150	148.985601311564	1.01439868843568
47	139	148.804387650618	-9.80438765061754
48	131	139.890636615029	-8.89063661502877
49	141	131.714432733005	9.28556726699497
50	150	138.209410511712	11.7905894882877
51	128	146.726352629690	-18.7263526296896
52	124	130.611110577151	-6.61111057715078
53	120	124.274858580523	-4.27485858052319
54	113	119.824345634263	-6.82434563426284
55	120	113.315977926366	6.6840220736339
56	121	117.711081475111	3.28891852488889
57	115	119.365778872828	-4.36577887282846
58	119	114.841878318588	4.15812168141183
59	106	117.198165415244	-11.1981654152437
60	98	107.159406819647	-9.15940681964724
61	106	98.7662612416267	7.2337387583733
62	116	103.605076436439	12.3949235635611
63	93	112.609815404609	-19.6098154046086
64	94	95.7814737991896	-1.78147379918960
65	90	93.3435318669035	-3.34353186690350
66	93	89.644752532881	3.35524746711897
67	100	91.3529882803626	8.6470117196374
68	99	97.3325468606191	1.66745313938088
69	90	97.6784553945131	-7.67845539451314
70	91	90.4806808373002	0.519319162699844
71	83	89.8998566908129	-6.89985669081285
72	83	83.3305391588918	-0.330539158891824
73	92	82.0637397723113	9.93626022768875
74	104	89.0839336353924	14.9160663646076
75	71	100.123648898221	-29.1236488982206
76	69	75.6160811804244	-6.61608118042437
77	67	69.2758170906191	-2.27581709061914
78	75	66.4388589347915	8.56114106520852
79	86	72.3491057941502	13.6508942058498
80	81	82.3676193421587	-1.36761934215869
81	88	80.2637259251519	7.73627407484813
82	87	85.508169653116	1.49183034688397
83	77	85.712321750451	-8.71232175045097
84	70	77.680047249282	-7.68004724928198

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	70.4809878038359	54.4496506679007	86.512324939771
86	69.4809878038359	48.878916302151	90.0830593055207
87	68.4809878038359	44.1522613687127	92.809714238959
88	67.4809878038359	39.9250717466698	95.0369038610019
89	66.4809878038359	36.0380889677509	96.9238866399208
90	65.4809878038359	32.4021173675796	98.559858240092
91	64.4809878038359	28.9612292301469	100.000746377525
92	63.4809878038359	25.6776172011016	101.28435840657
93	62.4809878038359	22.5243061507982	102.437669456873
94	61.4809878038359	19.481249846121	103.480725761551
95	60.4809878038359	16.5330689872271	104.428906620445
96	59.4809878038359	13.6676584322899	105.294317175382

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282074372axp61eec88rkzs4/1nhd21282074376.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282074372axp61eec88rkzs4/1nhd21282074376.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282074372axp61eec88rkzs4/2nhd21282074376.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282074372axp61eec88rkzs4/2nhd21282074376.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282074372axp61eec88rkzs4/3a5ny1282074376.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282074372axp61eec88rkzs4/3a5ny1282074376.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)

if (par2 == 'Single') K <- 1

if (par2 == 'Double') K <- 2

if (par2 == 'Triple') K <- par1

nx <- length(x)

nxmK <- nx - K

x <- ts(x, frequency = par1)

if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)

if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)

fit

myresid <- x - fit$fitted[,'xhat']

bitmap(file='test1.png')

op <- par(mfrow=c(2,1))

plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')

plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')

par(op)

dev.off()

bitmap(file='test2.png')

p <- predict(fit, par1, prediction.interval=TRUE)

np <- length(p[,1])

plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')

spectrum(myresid,main='Residals Periodogram')

cpgram(myresid,main='Residal Cumulative Periodogram')

qqnorm(myresid,main='Residual Normal QQ Plot')

qqline(myresid)

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'Value',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'alpha',header=TRUE)

a<-table.element(a,fit$alpha)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'beta',header=TRUE)

a<-table.element(a,fit$beta)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'gamma',header=TRUE)

a<-table.element(a,fit$gamma)

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,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Observed',header=TRUE)

a<-table.element(a,'Fitted',header=TRUE)

a<-table.element(a,'Residuals',header=TRUE)

a<-table.row.end(a)

for (i in 1:nxmK) {

a<-table.row.start(a)

a<-table.element(a,i+K,header=TRUE)

a<-table.element(a,x[i+K])

a<-table.element(a,fit$fitted[i,'xhat'])

a<-table.element(a,myresid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Forecast',header=TRUE)

a<-table.element(a,'95% Lower Bound',header=TRUE)

a<-table.element(a,'95% Upper Bound',header=TRUE)

a<-table.row.end(a)

for (i in 1:np) {

a<-table.row.start(a)

a<-table.element(a,nx+i,header=TRUE)

a<-table.element(a,p[i,'fit'])

a<-table.element(a,p[i,'lwr'])

a<-table.element(a,p[i,'upr'])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.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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