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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Jan 2011 00:36:45 +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/2011/Jan/17/t12952244751yji5ybo7rbcwfb.htm/, Retrieved Sun, 19 May 2024 00:26:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117500, Retrieved Sun, 19 May 2024 00:26:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2010-12-12 16:16:55] [cdbe0c453eb9effe5ed0ab336cdc30fc]
- RM    [Classical Decomposition] [] [2011-01-17 00:15:44] [cdbe0c453eb9effe5ed0ab336cdc30fc]
- RM D      [Exponential Smoothing] [] [2011-01-17 00:36:45] [49c40d716750d950b45a50638ed38982] [Current]
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Dataseries X:
1590
1798
1935
1887
2027
2080
1556
1682
1785
1869
1781
2082
2571
1862
1938
1505
1767
1607
1578
1495
1615
1700
1337
1531
1623
1543
1640
1524
1429
1827
1603
1351
1267
1742
1384
1392
1649
1665
1526
1717
1391
1790
1472
1350
1704
1391
1190
1351
1160
1236
1444
1257
1193
1701
1428
1611
1431
1472
1240
1276




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117500&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117500&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117500&T=0

As an alternative you can also use a 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 time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.164888600957893
beta0
gamma0.935831558446131

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.164888600957893 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.935831558446131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117500&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]0.164888600957893[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.935831558446131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117500&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117500&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.164888600957893
beta0
gamma0.935831558446131







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325712727.36765770059-156.367657700595
1418621947.59613217641-85.5961321764082
1519382011.76874730217-73.7687473021747
1615051551.61727961216-46.617279612163
1717671822.83793193396-55.8379319339645
1816071674.0136952126-67.0136952125954
1915781469.81426637944108.185733620563
2014951557.69931261097-62.6993126109683
2116151624.878224738-9.87822473800361
2217001697.998406739632.00159326036805
2313371626.18292959689-289.182929596887
2415311857.66913594275-326.66913594275
2516232127.0337177642-504.033717764204
2615431486.6238634066256.3761365933808
2716401562.4806152650677.519384734936
2815241226.45824506152297.541754938476
2914291502.8230712347-73.8230712347004
3018271363.14446839862463.855531601378
3116031386.97522905345216.024770946554
3213511363.54571120616-12.5457112061647
3312671468.06451244961-201.064512449613
3417421507.79397411524234.20602588476
3513841266.37601317584117.623986824156
3613921515.30572956633-123.305729566333
3716491657.14366050572-8.1436605057172
3816651535.83739880696129.162601193041
3915261640.84089407702-114.840894077023
4017171437.5603679682279.4396320318
4113911421.02264991676-30.0226499167643
4217901686.08073425484103.919265745155
4314721465.542616882296.45738311770879
4413501246.49527240177103.504727598233
4517041221.22122338486482.778776615138
4613911716.99787093542-325.997870935421
4711901304.43857637212-114.438576372124
4813511321.8632309272929.1367690727109
4911601564.97571868442-404.975718684415
5012361483.86560344915-247.865603449155
5114441346.8547867309897.1452132690233
5212571464.99408187112-207.994081871118
5311931172.3490245980120.6509754019937
5417011488.4625351671212.537464832899
5514281253.250997642174.749002357998
5616111153.58382086826457.41617913174
5714311438.69522909813-7.69522909813213
5814721243.30312460142228.696875398582
5912401102.68691746106137.313082538945
6012761264.0909385761111.9090614238919

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2571 & 2727.36765770059 & -156.367657700595 \tabularnewline
14 & 1862 & 1947.59613217641 & -85.5961321764082 \tabularnewline
15 & 1938 & 2011.76874730217 & -73.7687473021747 \tabularnewline
16 & 1505 & 1551.61727961216 & -46.617279612163 \tabularnewline
17 & 1767 & 1822.83793193396 & -55.8379319339645 \tabularnewline
18 & 1607 & 1674.0136952126 & -67.0136952125954 \tabularnewline
19 & 1578 & 1469.81426637944 & 108.185733620563 \tabularnewline
20 & 1495 & 1557.69931261097 & -62.6993126109683 \tabularnewline
21 & 1615 & 1624.878224738 & -9.87822473800361 \tabularnewline
22 & 1700 & 1697.99840673963 & 2.00159326036805 \tabularnewline
23 & 1337 & 1626.18292959689 & -289.182929596887 \tabularnewline
24 & 1531 & 1857.66913594275 & -326.66913594275 \tabularnewline
25 & 1623 & 2127.0337177642 & -504.033717764204 \tabularnewline
26 & 1543 & 1486.62386340662 & 56.3761365933808 \tabularnewline
27 & 1640 & 1562.48061526506 & 77.519384734936 \tabularnewline
28 & 1524 & 1226.45824506152 & 297.541754938476 \tabularnewline
29 & 1429 & 1502.8230712347 & -73.8230712347004 \tabularnewline
30 & 1827 & 1363.14446839862 & 463.855531601378 \tabularnewline
31 & 1603 & 1386.97522905345 & 216.024770946554 \tabularnewline
32 & 1351 & 1363.54571120616 & -12.5457112061647 \tabularnewline
33 & 1267 & 1468.06451244961 & -201.064512449613 \tabularnewline
34 & 1742 & 1507.79397411524 & 234.20602588476 \tabularnewline
35 & 1384 & 1266.37601317584 & 117.623986824156 \tabularnewline
36 & 1392 & 1515.30572956633 & -123.305729566333 \tabularnewline
37 & 1649 & 1657.14366050572 & -8.1436605057172 \tabularnewline
38 & 1665 & 1535.83739880696 & 129.162601193041 \tabularnewline
39 & 1526 & 1640.84089407702 & -114.840894077023 \tabularnewline
40 & 1717 & 1437.5603679682 & 279.4396320318 \tabularnewline
41 & 1391 & 1421.02264991676 & -30.0226499167643 \tabularnewline
42 & 1790 & 1686.08073425484 & 103.919265745155 \tabularnewline
43 & 1472 & 1465.54261688229 & 6.45738311770879 \tabularnewline
44 & 1350 & 1246.49527240177 & 103.504727598233 \tabularnewline
45 & 1704 & 1221.22122338486 & 482.778776615138 \tabularnewline
46 & 1391 & 1716.99787093542 & -325.997870935421 \tabularnewline
47 & 1190 & 1304.43857637212 & -114.438576372124 \tabularnewline
48 & 1351 & 1321.86323092729 & 29.1367690727109 \tabularnewline
49 & 1160 & 1564.97571868442 & -404.975718684415 \tabularnewline
50 & 1236 & 1483.86560344915 & -247.865603449155 \tabularnewline
51 & 1444 & 1346.85478673098 & 97.1452132690233 \tabularnewline
52 & 1257 & 1464.99408187112 & -207.994081871118 \tabularnewline
53 & 1193 & 1172.34902459801 & 20.6509754019937 \tabularnewline
54 & 1701 & 1488.4625351671 & 212.537464832899 \tabularnewline
55 & 1428 & 1253.250997642 & 174.749002357998 \tabularnewline
56 & 1611 & 1153.58382086826 & 457.41617913174 \tabularnewline
57 & 1431 & 1438.69522909813 & -7.69522909813213 \tabularnewline
58 & 1472 & 1243.30312460142 & 228.696875398582 \tabularnewline
59 & 1240 & 1102.68691746106 & 137.313082538945 \tabularnewline
60 & 1276 & 1264.09093857611 & 11.9090614238919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117500&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]13[/C][C]2571[/C][C]2727.36765770059[/C][C]-156.367657700595[/C][/ROW]
[ROW][C]14[/C][C]1862[/C][C]1947.59613217641[/C][C]-85.5961321764082[/C][/ROW]
[ROW][C]15[/C][C]1938[/C][C]2011.76874730217[/C][C]-73.7687473021747[/C][/ROW]
[ROW][C]16[/C][C]1505[/C][C]1551.61727961216[/C][C]-46.617279612163[/C][/ROW]
[ROW][C]17[/C][C]1767[/C][C]1822.83793193396[/C][C]-55.8379319339645[/C][/ROW]
[ROW][C]18[/C][C]1607[/C][C]1674.0136952126[/C][C]-67.0136952125954[/C][/ROW]
[ROW][C]19[/C][C]1578[/C][C]1469.81426637944[/C][C]108.185733620563[/C][/ROW]
[ROW][C]20[/C][C]1495[/C][C]1557.69931261097[/C][C]-62.6993126109683[/C][/ROW]
[ROW][C]21[/C][C]1615[/C][C]1624.878224738[/C][C]-9.87822473800361[/C][/ROW]
[ROW][C]22[/C][C]1700[/C][C]1697.99840673963[/C][C]2.00159326036805[/C][/ROW]
[ROW][C]23[/C][C]1337[/C][C]1626.18292959689[/C][C]-289.182929596887[/C][/ROW]
[ROW][C]24[/C][C]1531[/C][C]1857.66913594275[/C][C]-326.66913594275[/C][/ROW]
[ROW][C]25[/C][C]1623[/C][C]2127.0337177642[/C][C]-504.033717764204[/C][/ROW]
[ROW][C]26[/C][C]1543[/C][C]1486.62386340662[/C][C]56.3761365933808[/C][/ROW]
[ROW][C]27[/C][C]1640[/C][C]1562.48061526506[/C][C]77.519384734936[/C][/ROW]
[ROW][C]28[/C][C]1524[/C][C]1226.45824506152[/C][C]297.541754938476[/C][/ROW]
[ROW][C]29[/C][C]1429[/C][C]1502.8230712347[/C][C]-73.8230712347004[/C][/ROW]
[ROW][C]30[/C][C]1827[/C][C]1363.14446839862[/C][C]463.855531601378[/C][/ROW]
[ROW][C]31[/C][C]1603[/C][C]1386.97522905345[/C][C]216.024770946554[/C][/ROW]
[ROW][C]32[/C][C]1351[/C][C]1363.54571120616[/C][C]-12.5457112061647[/C][/ROW]
[ROW][C]33[/C][C]1267[/C][C]1468.06451244961[/C][C]-201.064512449613[/C][/ROW]
[ROW][C]34[/C][C]1742[/C][C]1507.79397411524[/C][C]234.20602588476[/C][/ROW]
[ROW][C]35[/C][C]1384[/C][C]1266.37601317584[/C][C]117.623986824156[/C][/ROW]
[ROW][C]36[/C][C]1392[/C][C]1515.30572956633[/C][C]-123.305729566333[/C][/ROW]
[ROW][C]37[/C][C]1649[/C][C]1657.14366050572[/C][C]-8.1436605057172[/C][/ROW]
[ROW][C]38[/C][C]1665[/C][C]1535.83739880696[/C][C]129.162601193041[/C][/ROW]
[ROW][C]39[/C][C]1526[/C][C]1640.84089407702[/C][C]-114.840894077023[/C][/ROW]
[ROW][C]40[/C][C]1717[/C][C]1437.5603679682[/C][C]279.4396320318[/C][/ROW]
[ROW][C]41[/C][C]1391[/C][C]1421.02264991676[/C][C]-30.0226499167643[/C][/ROW]
[ROW][C]42[/C][C]1790[/C][C]1686.08073425484[/C][C]103.919265745155[/C][/ROW]
[ROW][C]43[/C][C]1472[/C][C]1465.54261688229[/C][C]6.45738311770879[/C][/ROW]
[ROW][C]44[/C][C]1350[/C][C]1246.49527240177[/C][C]103.504727598233[/C][/ROW]
[ROW][C]45[/C][C]1704[/C][C]1221.22122338486[/C][C]482.778776615138[/C][/ROW]
[ROW][C]46[/C][C]1391[/C][C]1716.99787093542[/C][C]-325.997870935421[/C][/ROW]
[ROW][C]47[/C][C]1190[/C][C]1304.43857637212[/C][C]-114.438576372124[/C][/ROW]
[ROW][C]48[/C][C]1351[/C][C]1321.86323092729[/C][C]29.1367690727109[/C][/ROW]
[ROW][C]49[/C][C]1160[/C][C]1564.97571868442[/C][C]-404.975718684415[/C][/ROW]
[ROW][C]50[/C][C]1236[/C][C]1483.86560344915[/C][C]-247.865603449155[/C][/ROW]
[ROW][C]51[/C][C]1444[/C][C]1346.85478673098[/C][C]97.1452132690233[/C][/ROW]
[ROW][C]52[/C][C]1257[/C][C]1464.99408187112[/C][C]-207.994081871118[/C][/ROW]
[ROW][C]53[/C][C]1193[/C][C]1172.34902459801[/C][C]20.6509754019937[/C][/ROW]
[ROW][C]54[/C][C]1701[/C][C]1488.4625351671[/C][C]212.537464832899[/C][/ROW]
[ROW][C]55[/C][C]1428[/C][C]1253.250997642[/C][C]174.749002357998[/C][/ROW]
[ROW][C]56[/C][C]1611[/C][C]1153.58382086826[/C][C]457.41617913174[/C][/ROW]
[ROW][C]57[/C][C]1431[/C][C]1438.69522909813[/C][C]-7.69522909813213[/C][/ROW]
[ROW][C]58[/C][C]1472[/C][C]1243.30312460142[/C][C]228.696875398582[/C][/ROW]
[ROW][C]59[/C][C]1240[/C][C]1102.68691746106[/C][C]137.313082538945[/C][/ROW]
[ROW][C]60[/C][C]1276[/C][C]1264.09093857611[/C][C]11.9090614238919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117500&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117500&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325712727.36765770059-156.367657700595
1418621947.59613217641-85.5961321764082
1519382011.76874730217-73.7687473021747
1615051551.61727961216-46.617279612163
1717671822.83793193396-55.8379319339645
1816071674.0136952126-67.0136952125954
1915781469.81426637944108.185733620563
2014951557.69931261097-62.6993126109683
2116151624.878224738-9.87822473800361
2217001697.998406739632.00159326036805
2313371626.18292959689-289.182929596887
2415311857.66913594275-326.66913594275
2516232127.0337177642-504.033717764204
2615431486.6238634066256.3761365933808
2716401562.4806152650677.519384734936
2815241226.45824506152297.541754938476
2914291502.8230712347-73.8230712347004
3018271363.14446839862463.855531601378
3116031386.97522905345216.024770946554
3213511363.54571120616-12.5457112061647
3312671468.06451244961-201.064512449613
3417421507.79397411524234.20602588476
3513841266.37601317584117.623986824156
3613921515.30572956633-123.305729566333
3716491657.14366050572-8.1436605057172
3816651535.83739880696129.162601193041
3915261640.84089407702-114.840894077023
4017171437.5603679682279.4396320318
4113911421.02264991676-30.0226499167643
4217901686.08073425484103.919265745155
4314721465.542616882296.45738311770879
4413501246.49527240177103.504727598233
4517041221.22122338486482.778776615138
4613911716.99787093542-325.997870935421
4711901304.43857637212-114.438576372124
4813511321.8632309272929.1367690727109
4911601564.97571868442-404.975718684415
5012361483.86560344915-247.865603449155
5114441346.8547867309897.1452132690233
5212571464.99408187112-207.994081871118
5311931172.3490245980120.6509754019937
5417011488.4625351671212.537464832899
5514281253.250997642174.749002357998
5616111153.58382086826457.41617913174
5714311438.69522909813-7.69522909813213
5814721243.30312460142228.696875398582
5912401102.68691746106137.313082538945
6012761264.0909385761111.9090614238919







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
611157.25632836129764.2234696207141550.28918710186
621257.78117658554857.5982000737751657.9641530973
631431.673813217041021.523272893081841.824353541
641292.04092888945879.9005625834121704.18129519548
651211.11628185114795.7238839211021626.50867978118
661677.706125238041231.323069317722124.08918115836
671376.85871814492942.527679295521811.18975699431
681444.72916648403999.3514955919841890.10683737607
691303.14915896263861.5283538826171744.76996404265
701288.30397275952841.2427262946371735.3652192244
711064.31959077632628.9226835794371499.71649797319
721097.47385209602887.7631119255161307.18459226653

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1157.25632836129 & 764.223469620714 & 1550.28918710186 \tabularnewline
62 & 1257.78117658554 & 857.598200073775 & 1657.9641530973 \tabularnewline
63 & 1431.67381321704 & 1021.52327289308 & 1841.824353541 \tabularnewline
64 & 1292.04092888945 & 879.900562583412 & 1704.18129519548 \tabularnewline
65 & 1211.11628185114 & 795.723883921102 & 1626.50867978118 \tabularnewline
66 & 1677.70612523804 & 1231.32306931772 & 2124.08918115836 \tabularnewline
67 & 1376.85871814492 & 942.52767929552 & 1811.18975699431 \tabularnewline
68 & 1444.72916648403 & 999.351495591984 & 1890.10683737607 \tabularnewline
69 & 1303.14915896263 & 861.528353882617 & 1744.76996404265 \tabularnewline
70 & 1288.30397275952 & 841.242726294637 & 1735.3652192244 \tabularnewline
71 & 1064.31959077632 & 628.922683579437 & 1499.71649797319 \tabularnewline
72 & 1097.47385209602 & 887.763111925516 & 1307.18459226653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117500&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]61[/C][C]1157.25632836129[/C][C]764.223469620714[/C][C]1550.28918710186[/C][/ROW]
[ROW][C]62[/C][C]1257.78117658554[/C][C]857.598200073775[/C][C]1657.9641530973[/C][/ROW]
[ROW][C]63[/C][C]1431.67381321704[/C][C]1021.52327289308[/C][C]1841.824353541[/C][/ROW]
[ROW][C]64[/C][C]1292.04092888945[/C][C]879.900562583412[/C][C]1704.18129519548[/C][/ROW]
[ROW][C]65[/C][C]1211.11628185114[/C][C]795.723883921102[/C][C]1626.50867978118[/C][/ROW]
[ROW][C]66[/C][C]1677.70612523804[/C][C]1231.32306931772[/C][C]2124.08918115836[/C][/ROW]
[ROW][C]67[/C][C]1376.85871814492[/C][C]942.52767929552[/C][C]1811.18975699431[/C][/ROW]
[ROW][C]68[/C][C]1444.72916648403[/C][C]999.351495591984[/C][C]1890.10683737607[/C][/ROW]
[ROW][C]69[/C][C]1303.14915896263[/C][C]861.528353882617[/C][C]1744.76996404265[/C][/ROW]
[ROW][C]70[/C][C]1288.30397275952[/C][C]841.242726294637[/C][C]1735.3652192244[/C][/ROW]
[ROW][C]71[/C][C]1064.31959077632[/C][C]628.922683579437[/C][C]1499.71649797319[/C][/ROW]
[ROW][C]72[/C][C]1097.47385209602[/C][C]887.763111925516[/C][C]1307.18459226653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117500&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117500&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
611157.25632836129764.2234696207141550.28918710186
621257.78117658554857.5982000737751657.9641530973
631431.673813217041021.523272893081841.824353541
641292.04092888945879.9005625834121704.18129519548
651211.11628185114795.7238839211021626.50867978118
661677.706125238041231.323069317722124.08918115836
671376.85871814492942.527679295521811.18975699431
681444.72916648403999.3514955919841890.10683737607
691303.14915896263861.5283538826171744.76996404265
701288.30397275952841.2427262946371735.3652192244
711064.31959077632628.9226835794371499.71649797319
721097.47385209602887.7631119255161307.18459226653



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')