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Data:
679 687 638 628 604 713 712 693 697 555 486 470 465 426 384 379 381 380 351 346 339 336 333 324 324 321 304 343 407 389 361 353 361 387 692 704 742 721 843 847 945 946 946 945 1082 1075 820 832 851 1090 1203 1239 1535 1527 1480 1452 1383 1381 1429 1376 1602 1597 2003 1958 1997 1986 2129 2115 2297 2250 2309 2648 2627 2711 2732 2825 2932 2910 2969 2999 2965 2846 2847 2751

Seasonal period


Type of Exponential Smoothing (?)


Type of seasonality (?)


Number of Forecasts


Chart options



R Code
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')

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	Big Analytics Cloud Computing Center

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	465	598.841346153846	-133.841346153846
14	426	427.057687387911	-1.0576873879109
15	384	381.20724153046	2.79275846953982
16	379	370.944860608865	8.05513939113467
17	381	364.768837550719	16.2311624492806
18	380	361.530832563602	18.4691674363975
19	351	437.348300583388	-86.3483005833878
20	346	319.38740446655	26.6125955334498
21	339	337.628844540714	1.371155459286
22	336	184.911205735496	151.088794264504
23	333	259.072386900193	73.927613099807
24	324	319.384708149638	4.61529185036153
25	324	326.583347633019	-2.583347633019
26	321	298.686681408879	22.3133185911205
27	304	290.63760524724	13.3623947527595
28	343	306.426999695684	36.5730003043158
29	407	345.624219845033	61.3757801549669
30	389	406.667757603906	-17.6677576039059
31	361	463.231357474279	-102.231357474279
32	353	349.186058707009	3.81394129299053
33	361	360.329468422363	0.670531577637178
34	387	225.558114524352	161.441885475648
35	692	324.403341714824	367.596658285176
36	704	703.687577729366	0.31242227063376
37	742	741.100942183417	0.899057816583081
38	721	751.870850931483	-30.8708509314827
39	843	723.315216968824	119.684783031176
40	847	881.111610369959	-34.111610369959
41	945	885.737576110281	59.2624238897188
42	946	976.621408986531	-30.6214089865315
43	946	1051.54895219416	-105.548952194158
44	945	968.949363229293	-23.9493632292928
45	1082	983.759920130717	98.2400798692831
46	1075	984.092880381738	90.9071196182623
47	820	1051.03201176764	-231.032011767637
48	832	835.120171937197	-3.12017193719703
49	851	863.485776372326	-12.4857763723262
50	1090	854.015705244038	235.984294755962
51	1203	1098.4065598651	104.593440134902
52	1239	1247.75274082412	-8.7527408241217
53	1535	1289.95696615988	245.043033840122
54	1527	1582.42764176639	-55.427641766385
55	1480	1652.89237188297	-172.892371882967
56	1452	1523.41604587513	-71.4160458751298
57	1383	1508.50504393859	-125.505043938592
58	1381	1290.84638763246	90.1536123675392
59	1429	1350.12141152128	78.8785884787169
60	1376	1459.6085067455	-83.6085067454967
61	1602	1423.74625883425	178.253741165747
62	1597	1631.19937532066	-34.1993753206605
63	2003	1619.34683503134	383.653164968659
64	1958	2064.62186675385	-106.621866753849
65	1997	2037.56038568497	-40.5603856849671
66	1986	2048.69525362654	-62.6952536265408
67	2129	2111.79577703464	17.2042229653571
68	2115	2183.43673986881	-68.4367398688082
69	2297	2184.66944002171	112.330559978286
70	2250	2232.1666458201	17.8333541799011
71	2309	2245.73359338986	63.2664066101388
72	2648	2360.55763393387	287.442366066128
73	2627	2738.29421082746	-111.294210827462
74	2711	2688.83450406193	22.1654959380662
75	2732	2772.99224228435	-40.9922422843515
76	2825	2800.91735585442	24.0826441455838
77	2932	2916.28655396746	15.7134460325428
78	2910	2999.22489286581	-89.2248928658109
79	2969	3054.02422888183	-85.0242288818263
80	2999	3033.86459966955	-34.8645996695459
81	2965	3082.96495334929	-117.964953349292
82	2846	2901.4700843197	-55.4700843197006
83	2847	2836.94367838674	10.0563216132564
84	2751	2893.5184093159	-142.5184093159

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	2806.56349585787	2586.10600545056	3027.02098626518
86	2836.75919527386	2519.34900811621	3154.1693824315
87	2865.33941967837	2465.99623323892	3264.68260611783
88	2904.34144233821	2429.82128549948	3378.86159917693
89	2964.46792626507	2418.36991654484	3510.56593598531
90	2997.31928714772	2381.66795342454	3612.97062087091
91	3111.98028219989	2427.89653150301	3796.06403289677
92	3153.93276876137	2401.97154022988	3905.89399729285
93	3215.83608309015	2396.17608547321	4035.49608070709
94	3138.42841837354	2250.98734503906	4025.86949170801
95	3120.79490131633	2165.30353908716	4076.28626354551
96	3155.41686040399	2131.46892281584	4179.36479799213

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.972448439054055
beta	0.0651879070466909
gamma	0.746729979627399