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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 28 Nov 2010 09:11:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/28/t1290935422ag48sowosq2v1g9.htm/, Retrieved Sat, 04 May 2024 16:08:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102455, Retrieved Sat, 04 May 2024 16:08:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact218

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Workshop 8 Regres...] [2010-11-27 09:22:21] [87d60b8864dc39f7ed759c345edfb471]
- RMP   [Spectral Analysis] [Workshop 8 Regres...] [2010-11-27 12:28:23] [87d60b8864dc39f7ed759c345edfb471]
- RMP     [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:02:33] [87d60b8864dc39f7ed759c345edfb471]
-   P       [Exponential Smoothing] [Workshop 8 Regres...] [2010-11-27 13:15:31] [87d60b8864dc39f7ed759c345edfb471]
- R  D          [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:11:22] [a948b7c78e10e31abd3f68e640bbd8ba] [Current]
-   P             [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:21:35] [033eb2749a430605d9b2be7c4aac4a0c]
-   P               [Exponential Smoothing] [ws 8 - exponentia...] [2010-11-28 09:23:28] [033eb2749a430605d9b2be7c4aac4a0c]
- RMP             [Multiple Regression] [ws 8 - werklooshe...] [2010-11-29 10:16:03] [033eb2749a430605d9b2be7c4aac4a0c]
- R  D              [Multiple Regression] [ws 8 multiple regr] [2010-11-30 16:05:15] [4eaa304e6a28c475ba490fccf4c01ad3]
- R  D            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:56:04] [48146708a479232c43a8f6e52fbf83b4]
- R PD            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:57:52] [48146708a479232c43a8f6e52fbf83b4]
- R PD            [Exponential Smoothing] [W8-exponentieel s...] [2010-11-29 11:59:42] [48146708a479232c43a8f6e52fbf83b4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
444
454
469
471
443
437
444
451
457
460
454
439
441
446
459
456
433
424
430
428
424
419
409
397
397
413
413
390
385
397
398
406
412
409
404
412
418
434
431
406
416
424
427
401

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time69 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 69 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102455&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]69 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102455&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time69 seconds
R Server'George Udny Yule' @ 72.249.76.132






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99991938208817
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99991938208817 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102455&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.99991938208817[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102455&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99991938208817
betaFALSE
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
245444410
3469453.99919382088215.0008061791183
4471468.998790666332.00120933366998
5443470.999838666682-27.9998386666824
6437443.002257288525-6.0022572885249
7444437.0004838894496.99951611055116
8451443.9994357136277.00056428637265
9457450.9994356291266.00056437087443
10460456.9995162470313.00048375296933
11454459.999758107265-5.99975810726534
12439454.00048368797-15.0004836879701
13441439.0012093076711.99879069232867
14446440.9998388616685.00016113833180
15459445.9995968974513.0004031025498
16456458.998951934649-2.99895193464891
17433456.000241769243-23.0002417692427
18424433.001854231463-9.00185423146303
19430424.0007257106915.99927428930926
20428429.999516351034-1.99951635103429
21424428.000161196833-4.00016119683289
22419424.000322484643-5.00032248464271
23409419.000403115557-10.0004031155572
24397409.000806211617-12.0008062116166
25397397.000967479937-0.000967479937060034
26413397.00000007799615.9999999220038
27413412.9987101134170.00128988658303797
28390412.999999896012-22.999999896012
29385390.001854211964-5.00185421196369
30397385.00040323904211.9995967609582
31398396.9990326175661.00096738243366
32406397.99991930418.00008069590018
33412405.99935505026.00064494980018
34409411.999516240535-2.99951624053455
35404409.000241814736-5.00024181473583
36412404.0004031090547.99959689094624
37418411.9993550892036.00064491079684
38434417.99951624053816.0004837594623
39431433.998710074411-2.99871007441101
40406431.000241749744-25.0002417497444
41416406.0020154672859.9979845327149
42424415.9991939833648.00080601663552
43427423.9993549917263.00064500827398
44401426.999758094265-25.9997580942652

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 454 & 444 & 10 \tabularnewline
3 & 469 & 453.999193820882 & 15.0008061791183 \tabularnewline
4 & 471 & 468.99879066633 & 2.00120933366998 \tabularnewline
5 & 443 & 470.999838666682 & -27.9998386666824 \tabularnewline
6 & 437 & 443.002257288525 & -6.0022572885249 \tabularnewline
7 & 444 & 437.000483889449 & 6.99951611055116 \tabularnewline
8 & 451 & 443.999435713627 & 7.00056428637265 \tabularnewline
9 & 457 & 450.999435629126 & 6.00056437087443 \tabularnewline
10 & 460 & 456.999516247031 & 3.00048375296933 \tabularnewline
11 & 454 & 459.999758107265 & -5.99975810726534 \tabularnewline
12 & 439 & 454.00048368797 & -15.0004836879701 \tabularnewline
13 & 441 & 439.001209307671 & 1.99879069232867 \tabularnewline
14 & 446 & 440.999838861668 & 5.00016113833180 \tabularnewline
15 & 459 & 445.99959689745 & 13.0004031025498 \tabularnewline
16 & 456 & 458.998951934649 & -2.99895193464891 \tabularnewline
17 & 433 & 456.000241769243 & -23.0002417692427 \tabularnewline
18 & 424 & 433.001854231463 & -9.00185423146303 \tabularnewline
19 & 430 & 424.000725710691 & 5.99927428930926 \tabularnewline
20 & 428 & 429.999516351034 & -1.99951635103429 \tabularnewline
21 & 424 & 428.000161196833 & -4.00016119683289 \tabularnewline
22 & 419 & 424.000322484643 & -5.00032248464271 \tabularnewline
23 & 409 & 419.000403115557 & -10.0004031155572 \tabularnewline
24 & 397 & 409.000806211617 & -12.0008062116166 \tabularnewline
25 & 397 & 397.000967479937 & -0.000967479937060034 \tabularnewline
26 & 413 & 397.000000077996 & 15.9999999220038 \tabularnewline
27 & 413 & 412.998710113417 & 0.00128988658303797 \tabularnewline
28 & 390 & 412.999999896012 & -22.999999896012 \tabularnewline
29 & 385 & 390.001854211964 & -5.00185421196369 \tabularnewline
30 & 397 & 385.000403239042 & 11.9995967609582 \tabularnewline
31 & 398 & 396.999032617566 & 1.00096738243366 \tabularnewline
32 & 406 & 397.9999193041 & 8.00008069590018 \tabularnewline
33 & 412 & 405.9993550502 & 6.00064494980018 \tabularnewline
34 & 409 & 411.999516240535 & -2.99951624053455 \tabularnewline
35 & 404 & 409.000241814736 & -5.00024181473583 \tabularnewline
36 & 412 & 404.000403109054 & 7.99959689094624 \tabularnewline
37 & 418 & 411.999355089203 & 6.00064491079684 \tabularnewline
38 & 434 & 417.999516240538 & 16.0004837594623 \tabularnewline
39 & 431 & 433.998710074411 & -2.99871007441101 \tabularnewline
40 & 406 & 431.000241749744 & -25.0002417497444 \tabularnewline
41 & 416 & 406.002015467285 & 9.9979845327149 \tabularnewline
42 & 424 & 415.999193983364 & 8.00080601663552 \tabularnewline
43 & 427 & 423.999354991726 & 3.00064500827398 \tabularnewline
44 & 401 & 426.999758094265 & -25.9997580942652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102455&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]454[/C][C]444[/C][C]10[/C][/ROW]
[ROW][C]3[/C][C]469[/C][C]453.999193820882[/C][C]15.0008061791183[/C][/ROW]
[ROW][C]4[/C][C]471[/C][C]468.99879066633[/C][C]2.00120933366998[/C][/ROW]
[ROW][C]5[/C][C]443[/C][C]470.999838666682[/C][C]-27.9998386666824[/C][/ROW]
[ROW][C]6[/C][C]437[/C][C]443.002257288525[/C][C]-6.0022572885249[/C][/ROW]
[ROW][C]7[/C][C]444[/C][C]437.000483889449[/C][C]6.99951611055116[/C][/ROW]
[ROW][C]8[/C][C]451[/C][C]443.999435713627[/C][C]7.00056428637265[/C][/ROW]
[ROW][C]9[/C][C]457[/C][C]450.999435629126[/C][C]6.00056437087443[/C][/ROW]
[ROW][C]10[/C][C]460[/C][C]456.999516247031[/C][C]3.00048375296933[/C][/ROW]
[ROW][C]11[/C][C]454[/C][C]459.999758107265[/C][C]-5.99975810726534[/C][/ROW]
[ROW][C]12[/C][C]439[/C][C]454.00048368797[/C][C]-15.0004836879701[/C][/ROW]
[ROW][C]13[/C][C]441[/C][C]439.001209307671[/C][C]1.99879069232867[/C][/ROW]
[ROW][C]14[/C][C]446[/C][C]440.999838861668[/C][C]5.00016113833180[/C][/ROW]
[ROW][C]15[/C][C]459[/C][C]445.99959689745[/C][C]13.0004031025498[/C][/ROW]
[ROW][C]16[/C][C]456[/C][C]458.998951934649[/C][C]-2.99895193464891[/C][/ROW]
[ROW][C]17[/C][C]433[/C][C]456.000241769243[/C][C]-23.0002417692427[/C][/ROW]
[ROW][C]18[/C][C]424[/C][C]433.001854231463[/C][C]-9.00185423146303[/C][/ROW]
[ROW][C]19[/C][C]430[/C][C]424.000725710691[/C][C]5.99927428930926[/C][/ROW]
[ROW][C]20[/C][C]428[/C][C]429.999516351034[/C][C]-1.99951635103429[/C][/ROW]
[ROW][C]21[/C][C]424[/C][C]428.000161196833[/C][C]-4.00016119683289[/C][/ROW]
[ROW][C]22[/C][C]419[/C][C]424.000322484643[/C][C]-5.00032248464271[/C][/ROW]
[ROW][C]23[/C][C]409[/C][C]419.000403115557[/C][C]-10.0004031155572[/C][/ROW]
[ROW][C]24[/C][C]397[/C][C]409.000806211617[/C][C]-12.0008062116166[/C][/ROW]
[ROW][C]25[/C][C]397[/C][C]397.000967479937[/C][C]-0.000967479937060034[/C][/ROW]
[ROW][C]26[/C][C]413[/C][C]397.000000077996[/C][C]15.9999999220038[/C][/ROW]
[ROW][C]27[/C][C]413[/C][C]412.998710113417[/C][C]0.00128988658303797[/C][/ROW]
[ROW][C]28[/C][C]390[/C][C]412.999999896012[/C][C]-22.999999896012[/C][/ROW]
[ROW][C]29[/C][C]385[/C][C]390.001854211964[/C][C]-5.00185421196369[/C][/ROW]
[ROW][C]30[/C][C]397[/C][C]385.000403239042[/C][C]11.9995967609582[/C][/ROW]
[ROW][C]31[/C][C]398[/C][C]396.999032617566[/C][C]1.00096738243366[/C][/ROW]
[ROW][C]32[/C][C]406[/C][C]397.9999193041[/C][C]8.00008069590018[/C][/ROW]
[ROW][C]33[/C][C]412[/C][C]405.9993550502[/C][C]6.00064494980018[/C][/ROW]
[ROW][C]34[/C][C]409[/C][C]411.999516240535[/C][C]-2.99951624053455[/C][/ROW]
[ROW][C]35[/C][C]404[/C][C]409.000241814736[/C][C]-5.00024181473583[/C][/ROW]
[ROW][C]36[/C][C]412[/C][C]404.000403109054[/C][C]7.99959689094624[/C][/ROW]
[ROW][C]37[/C][C]418[/C][C]411.999355089203[/C][C]6.00064491079684[/C][/ROW]
[ROW][C]38[/C][C]434[/C][C]417.999516240538[/C][C]16.0004837594623[/C][/ROW]
[ROW][C]39[/C][C]431[/C][C]433.998710074411[/C][C]-2.99871007441101[/C][/ROW]
[ROW][C]40[/C][C]406[/C][C]431.000241749744[/C][C]-25.0002417497444[/C][/ROW]
[ROW][C]41[/C][C]416[/C][C]406.002015467285[/C][C]9.9979845327149[/C][/ROW]
[ROW][C]42[/C][C]424[/C][C]415.999193983364[/C][C]8.00080601663552[/C][/ROW]
[ROW][C]43[/C][C]427[/C][C]423.999354991726[/C][C]3.00064500827398[/C][/ROW]
[ROW][C]44[/C][C]401[/C][C]426.999758094265[/C][C]-25.9997580942652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102455&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
245444410
3469453.99919382088215.0008061791183
4471468.998790666332.00120933366998
5443470.999838666682-27.9998386666824
6437443.002257288525-6.0022572885249
7444437.0004838894496.99951611055116
8451443.9994357136277.00056428637265
9457450.9994356291266.00056437087443
10460456.9995162470313.00048375296933
11454459.999758107265-5.99975810726534
12439454.00048368797-15.0004836879701
13441439.0012093076711.99879069232867
14446440.9998388616685.00016113833180
15459445.9995968974513.0004031025498
16456458.998951934649-2.99895193464891
17433456.000241769243-23.0002417692427
18424433.001854231463-9.00185423146303
19430424.0007257106915.99927428930926
20428429.999516351034-1.99951635103429
21424428.000161196833-4.00016119683289
22419424.000322484643-5.00032248464271
23409419.000403115557-10.0004031155572
24397409.000806211617-12.0008062116166
25397397.000967479937-0.000967479937060034
26413397.00000007799615.9999999220038
27413412.9987101134170.00128988658303797
28390412.999999896012-22.999999896012
29385390.001854211964-5.00185421196369
30397385.00040323904211.9995967609582
31398396.9990326175661.00096738243366
32406397.99991930418.00008069590018
33412405.99935505026.00064494980018
34409411.999516240535-2.99951624053455
35404409.000241814736-5.00024181473583
36412404.0004031090547.99959689094624
37418411.9993550892036.00064491079684
38434417.99951624053816.0004837594623
39431433.998710074411-2.99871007441101
40406431.000241749744-25.0002417497444
41416406.0020154672859.9979845327149
42424415.9991939833648.00080601663552
43427423.9993549917263.00064500827398
44401426.999758094265-25.9997580942652






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
45401.002096046206378.410552230622423.593639861790
46401.002096046206369.054116202926432.950075889486
47401.002096046206361.874497344499440.129694747912
48401.002096046206355.821740312137446.182451780274
49401.002096046206350.48912634186451.515065750552
50401.002096046206345.668058849853456.336133242558
51401.002096046206341.23461963518460.769572457232
52401.002096046206337.108068151279464.896123941133
53401.002096046206333.2323213326468.771870759811
54401.002096046206329.566545171112472.437646921299
55401.002096046206326.079913130041475.92427896237
56401.002096046206322.748475957302479.255716135109

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
45 & 401.002096046206 & 378.410552230622 & 423.593639861790 \tabularnewline
46 & 401.002096046206 & 369.054116202926 & 432.950075889486 \tabularnewline
47 & 401.002096046206 & 361.874497344499 & 440.129694747912 \tabularnewline
48 & 401.002096046206 & 355.821740312137 & 446.182451780274 \tabularnewline
49 & 401.002096046206 & 350.48912634186 & 451.515065750552 \tabularnewline
50 & 401.002096046206 & 345.668058849853 & 456.336133242558 \tabularnewline
51 & 401.002096046206 & 341.23461963518 & 460.769572457232 \tabularnewline
52 & 401.002096046206 & 337.108068151279 & 464.896123941133 \tabularnewline
53 & 401.002096046206 & 333.2323213326 & 468.771870759811 \tabularnewline
54 & 401.002096046206 & 329.566545171112 & 472.437646921299 \tabularnewline
55 & 401.002096046206 & 326.079913130041 & 475.92427896237 \tabularnewline
56 & 401.002096046206 & 322.748475957302 & 479.255716135109 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102455&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]45[/C][C]401.002096046206[/C][C]378.410552230622[/C][C]423.593639861790[/C][/ROW]
[ROW][C]46[/C][C]401.002096046206[/C][C]369.054116202926[/C][C]432.950075889486[/C][/ROW]
[ROW][C]47[/C][C]401.002096046206[/C][C]361.874497344499[/C][C]440.129694747912[/C][/ROW]
[ROW][C]48[/C][C]401.002096046206[/C][C]355.821740312137[/C][C]446.182451780274[/C][/ROW]
[ROW][C]49[/C][C]401.002096046206[/C][C]350.48912634186[/C][C]451.515065750552[/C][/ROW]
[ROW][C]50[/C][C]401.002096046206[/C][C]345.668058849853[/C][C]456.336133242558[/C][/ROW]
[ROW][C]51[/C][C]401.002096046206[/C][C]341.23461963518[/C][C]460.769572457232[/C][/ROW]
[ROW][C]52[/C][C]401.002096046206[/C][C]337.108068151279[/C][C]464.896123941133[/C][/ROW]
[ROW][C]53[/C][C]401.002096046206[/C][C]333.2323213326[/C][C]468.771870759811[/C][/ROW]
[ROW][C]54[/C][C]401.002096046206[/C][C]329.566545171112[/C][C]472.437646921299[/C][/ROW]
[ROW][C]55[/C][C]401.002096046206[/C][C]326.079913130041[/C][C]475.92427896237[/C][/ROW]
[ROW][C]56[/C][C]401.002096046206[/C][C]322.748475957302[/C][C]479.255716135109[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102455&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102455&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
45401.002096046206378.410552230622423.593639861790
46401.002096046206369.054116202926432.950075889486
47401.002096046206361.874497344499440.129694747912
48401.002096046206355.821740312137446.182451780274
49401.002096046206350.48912634186451.515065750552
50401.002096046206345.668058849853456.336133242558
51401.002096046206341.23461963518460.769572457232
52401.002096046206337.108068151279464.896123941133
53401.002096046206333.2323213326468.771870759811
54401.002096046206329.566545171112472.437646921299
55401.002096046206326.079913130041475.92427896237
56401.002096046206322.748475957302479.255716135109


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')