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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationSun, 26 Dec 2010 17:15:25 +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/Dec/26/t1293383606w0nl9lfhprbiuqq.htm/, Retrieved Mon, 06 May 2024 18:15:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115734, Retrieved Mon, 06 May 2024 18:15:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
-   PD      [ARIMA Forecasting] [ARIMA Model] [2010-12-07 16:48:47] [1c68a339ea090fe045c8010fcdb839f1]
-   PD        [ARIMA Forecasting] [Paper ARIMA Model] [2010-12-17 12:22:16] [1c68a339ea090fe045c8010fcdb839f1]
-   PD          [ARIMA Forecasting] [paper voorspellin...] [2010-12-26 16:46:25] [eeb33d252044f8583501f5ba0605ad6d]
-    D              [ARIMA Forecasting] [paper arima forec...] [2010-12-26 17:15:25] [6df2229e3f2091de42c4a9cf9a617420] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10554,27
10532,54
10324,31
10695,25
10827,81
10872,48
10971,19
11145,65
11234,68
11333,88
10997,97
11036,89
11257,35
11533,59
11963,12
12185,15
12377,62
12512,89
12631,48
12268,53
12754,8
13407,75
13480,21
13673,28
13239,71
13557,69
13901,28
13200,58
13406,97
12538,12
12419,57
12193,88
12656,63
12812,48
12056,67
11322,38
11530,75
11114,08
9181,73
8614,55
8595,56
8396,2
7690,5
7235,47
7992,12
8398,37
8593
8679,75
9374,63
9634,97
9857,34
10238,83
10433,44
10471,24
10214,51
10677,52
11052,15
10500,19
10159,27
10222,24
10350,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115734&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115734&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[49])
3711530.75-------
3811114.08-------
399181.73-------
408614.55-------
418595.56-------
428396.2-------
437690.5-------
447235.47-------
457992.12-------
468398.37-------
478593-------
488679.75-------
499374.63-------
509634.979364.31718251.618710379.9430.30070.49214e-040.4921
519857.349320.41047702.927410738.74480.2290.33190.5760.4701
5210238.839308.7797286.706311027.04270.14440.26570.78580.4701
5310433.449308.39976932.386711273.57740.13090.17670.76140.4737
5410471.249304.4576603.017611484.20870.14710.1550.79290.4748
5510214.519291.08926280.098211663.83550.22280.16480.90690.4725
5610677.529282.96335976.895411830.53080.14170.23680.94240.4719
5711052.159296.68975714.651712001.37020.10170.15850.82780.4775
5810500.199304.49955451.490912155.98060.20560.11480.73330.4808
5910159.279308.34865187.234812297.95340.28850.21730.68050.4827
6010222.249310.08644922.287712430.25670.28330.29690.65390.4838
6110350.49324.49824680.169712565.66870.26750.29360.48790.4879

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[49]) \tabularnewline
37 & 11530.75 & - & - & - & - & - & - & - \tabularnewline
38 & 11114.08 & - & - & - & - & - & - & - \tabularnewline
39 & 9181.73 & - & - & - & - & - & - & - \tabularnewline
40 & 8614.55 & - & - & - & - & - & - & - \tabularnewline
41 & 8595.56 & - & - & - & - & - & - & - \tabularnewline
42 & 8396.2 & - & - & - & - & - & - & - \tabularnewline
43 & 7690.5 & - & - & - & - & - & - & - \tabularnewline
44 & 7235.47 & - & - & - & - & - & - & - \tabularnewline
45 & 7992.12 & - & - & - & - & - & - & - \tabularnewline
46 & 8398.37 & - & - & - & - & - & - & - \tabularnewline
47 & 8593 & - & - & - & - & - & - & - \tabularnewline
48 & 8679.75 & - & - & - & - & - & - & - \tabularnewline
49 & 9374.63 & - & - & - & - & - & - & - \tabularnewline
50 & 9634.97 & 9364.3171 & 8251.6187 & 10379.943 & 0.3007 & 0.4921 & 4e-04 & 0.4921 \tabularnewline
51 & 9857.34 & 9320.4104 & 7702.9274 & 10738.7448 & 0.229 & 0.3319 & 0.576 & 0.4701 \tabularnewline
52 & 10238.83 & 9308.779 & 7286.7063 & 11027.0427 & 0.1444 & 0.2657 & 0.7858 & 0.4701 \tabularnewline
53 & 10433.44 & 9308.3997 & 6932.3867 & 11273.5774 & 0.1309 & 0.1767 & 0.7614 & 0.4737 \tabularnewline
54 & 10471.24 & 9304.457 & 6603.0176 & 11484.2087 & 0.1471 & 0.155 & 0.7929 & 0.4748 \tabularnewline
55 & 10214.51 & 9291.0892 & 6280.0982 & 11663.8355 & 0.2228 & 0.1648 & 0.9069 & 0.4725 \tabularnewline
56 & 10677.52 & 9282.9633 & 5976.8954 & 11830.5308 & 0.1417 & 0.2368 & 0.9424 & 0.4719 \tabularnewline
57 & 11052.15 & 9296.6897 & 5714.6517 & 12001.3702 & 0.1017 & 0.1585 & 0.8278 & 0.4775 \tabularnewline
58 & 10500.19 & 9304.4995 & 5451.4909 & 12155.9806 & 0.2056 & 0.1148 & 0.7333 & 0.4808 \tabularnewline
59 & 10159.27 & 9308.3486 & 5187.2348 & 12297.9534 & 0.2885 & 0.2173 & 0.6805 & 0.4827 \tabularnewline
60 & 10222.24 & 9310.0864 & 4922.2877 & 12430.2567 & 0.2833 & 0.2969 & 0.6539 & 0.4838 \tabularnewline
61 & 10350.4 & 9324.4982 & 4680.1697 & 12565.6687 & 0.2675 & 0.2936 & 0.4879 & 0.4879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115734&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[49])[/C][/ROW]
[ROW][C]37[/C][C]11530.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]11114.08[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]9181.73[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]8614.55[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]8595.56[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]8396.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]7690.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]7235.47[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]7992.12[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]8398.37[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]8593[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]8679.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]9374.63[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]9634.97[/C][C]9364.3171[/C][C]8251.6187[/C][C]10379.943[/C][C]0.3007[/C][C]0.4921[/C][C]4e-04[/C][C]0.4921[/C][/ROW]
[ROW][C]51[/C][C]9857.34[/C][C]9320.4104[/C][C]7702.9274[/C][C]10738.7448[/C][C]0.229[/C][C]0.3319[/C][C]0.576[/C][C]0.4701[/C][/ROW]
[ROW][C]52[/C][C]10238.83[/C][C]9308.779[/C][C]7286.7063[/C][C]11027.0427[/C][C]0.1444[/C][C]0.2657[/C][C]0.7858[/C][C]0.4701[/C][/ROW]
[ROW][C]53[/C][C]10433.44[/C][C]9308.3997[/C][C]6932.3867[/C][C]11273.5774[/C][C]0.1309[/C][C]0.1767[/C][C]0.7614[/C][C]0.4737[/C][/ROW]
[ROW][C]54[/C][C]10471.24[/C][C]9304.457[/C][C]6603.0176[/C][C]11484.2087[/C][C]0.1471[/C][C]0.155[/C][C]0.7929[/C][C]0.4748[/C][/ROW]
[ROW][C]55[/C][C]10214.51[/C][C]9291.0892[/C][C]6280.0982[/C][C]11663.8355[/C][C]0.2228[/C][C]0.1648[/C][C]0.9069[/C][C]0.4725[/C][/ROW]
[ROW][C]56[/C][C]10677.52[/C][C]9282.9633[/C][C]5976.8954[/C][C]11830.5308[/C][C]0.1417[/C][C]0.2368[/C][C]0.9424[/C][C]0.4719[/C][/ROW]
[ROW][C]57[/C][C]11052.15[/C][C]9296.6897[/C][C]5714.6517[/C][C]12001.3702[/C][C]0.1017[/C][C]0.1585[/C][C]0.8278[/C][C]0.4775[/C][/ROW]
[ROW][C]58[/C][C]10500.19[/C][C]9304.4995[/C][C]5451.4909[/C][C]12155.9806[/C][C]0.2056[/C][C]0.1148[/C][C]0.7333[/C][C]0.4808[/C][/ROW]
[ROW][C]59[/C][C]10159.27[/C][C]9308.3486[/C][C]5187.2348[/C][C]12297.9534[/C][C]0.2885[/C][C]0.2173[/C][C]0.6805[/C][C]0.4827[/C][/ROW]
[ROW][C]60[/C][C]10222.24[/C][C]9310.0864[/C][C]4922.2877[/C][C]12430.2567[/C][C]0.2833[/C][C]0.2969[/C][C]0.6539[/C][C]0.4838[/C][/ROW]
[ROW][C]61[/C][C]10350.4[/C][C]9324.4982[/C][C]4680.1697[/C][C]12565.6687[/C][C]0.2675[/C][C]0.2936[/C][C]0.4879[/C][C]0.4879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115734&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:

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[49])
3711530.75-------
3811114.08-------
399181.73-------
408614.55-------
418595.56-------
428396.2-------
437690.5-------
447235.47-------
457992.12-------
468398.37-------
478593-------
488679.75-------
499374.63-------
509634.979364.31718251.618710379.9430.30070.49214e-040.4921
519857.349320.41047702.927410738.74480.2290.33190.5760.4701
5210238.839308.7797286.706311027.04270.14440.26570.78580.4701
5310433.449308.39976932.386711273.57740.13090.17670.76140.4737
5410471.249304.4576603.017611484.20870.14710.1550.79290.4748
5510214.519291.08926280.098211663.83550.22280.16480.90690.4725
5610677.529282.96335976.895411830.53080.14170.23680.94240.4719
5711052.159296.68975714.651712001.37020.10170.15850.82780.4775
5810500.199304.49955451.490912155.98060.20560.11480.73330.4808
5910159.279308.34865187.234812297.95340.28850.21730.68050.4827
6010222.249310.08644922.287712430.25670.28330.29690.65390.4838
6110350.49324.49824680.169712565.66870.26750.29360.48790.4879






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
500.05530.0289073253.003700
510.07760.05760.0433288293.4089180773.2063425.1743
520.09420.09990.0621864994.8688408847.0938639.4115
530.10770.12090.07681265715.7867623064.267789.3442
540.11950.12540.08651361382.6249770727.9386877.9111
550.13030.09940.0887852705.9378784390.9385885.6585
560.140.15020.09751944788.3763950162.001974.7625
570.14840.18880.10893081640.96721216596.87181102.9945
580.15640.12850.11111429675.77221240272.30521113.6751
590.16390.09140.1091724067.29261188651.80391090.2531
600.1710.0980.1081832024.12441156231.10581075.2819
610.17730.110.10831052474.49741147584.72171071.2538

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
50 & 0.0553 & 0.0289 & 0 & 73253.0037 & 0 & 0 \tabularnewline
51 & 0.0776 & 0.0576 & 0.0433 & 288293.4089 & 180773.2063 & 425.1743 \tabularnewline
52 & 0.0942 & 0.0999 & 0.0621 & 864994.8688 & 408847.0938 & 639.4115 \tabularnewline
53 & 0.1077 & 0.1209 & 0.0768 & 1265715.7867 & 623064.267 & 789.3442 \tabularnewline
54 & 0.1195 & 0.1254 & 0.0865 & 1361382.6249 & 770727.9386 & 877.9111 \tabularnewline
55 & 0.1303 & 0.0994 & 0.0887 & 852705.9378 & 784390.9385 & 885.6585 \tabularnewline
56 & 0.14 & 0.1502 & 0.0975 & 1944788.3763 & 950162.001 & 974.7625 \tabularnewline
57 & 0.1484 & 0.1888 & 0.1089 & 3081640.9672 & 1216596.8718 & 1102.9945 \tabularnewline
58 & 0.1564 & 0.1285 & 0.1111 & 1429675.7722 & 1240272.3052 & 1113.6751 \tabularnewline
59 & 0.1639 & 0.0914 & 0.1091 & 724067.2926 & 1188651.8039 & 1090.2531 \tabularnewline
60 & 0.171 & 0.098 & 0.1081 & 832024.1244 & 1156231.1058 & 1075.2819 \tabularnewline
61 & 0.1773 & 0.11 & 0.1083 & 1052474.4974 & 1147584.7217 & 1071.2538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115734&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]50[/C][C]0.0553[/C][C]0.0289[/C][C]0[/C][C]73253.0037[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]0.0776[/C][C]0.0576[/C][C]0.0433[/C][C]288293.4089[/C][C]180773.2063[/C][C]425.1743[/C][/ROW]
[ROW][C]52[/C][C]0.0942[/C][C]0.0999[/C][C]0.0621[/C][C]864994.8688[/C][C]408847.0938[/C][C]639.4115[/C][/ROW]
[ROW][C]53[/C][C]0.1077[/C][C]0.1209[/C][C]0.0768[/C][C]1265715.7867[/C][C]623064.267[/C][C]789.3442[/C][/ROW]
[ROW][C]54[/C][C]0.1195[/C][C]0.1254[/C][C]0.0865[/C][C]1361382.6249[/C][C]770727.9386[/C][C]877.9111[/C][/ROW]
[ROW][C]55[/C][C]0.1303[/C][C]0.0994[/C][C]0.0887[/C][C]852705.9378[/C][C]784390.9385[/C][C]885.6585[/C][/ROW]
[ROW][C]56[/C][C]0.14[/C][C]0.1502[/C][C]0.0975[/C][C]1944788.3763[/C][C]950162.001[/C][C]974.7625[/C][/ROW]
[ROW][C]57[/C][C]0.1484[/C][C]0.1888[/C][C]0.1089[/C][C]3081640.9672[/C][C]1216596.8718[/C][C]1102.9945[/C][/ROW]
[ROW][C]58[/C][C]0.1564[/C][C]0.1285[/C][C]0.1111[/C][C]1429675.7722[/C][C]1240272.3052[/C][C]1113.6751[/C][/ROW]
[ROW][C]59[/C][C]0.1639[/C][C]0.0914[/C][C]0.1091[/C][C]724067.2926[/C][C]1188651.8039[/C][C]1090.2531[/C][/ROW]
[ROW][C]60[/C][C]0.171[/C][C]0.098[/C][C]0.1081[/C][C]832024.1244[/C][C]1156231.1058[/C][C]1075.2819[/C][/ROW]
[ROW][C]61[/C][C]0.1773[/C][C]0.11[/C][C]0.1083[/C][C]1052474.4974[/C][C]1147584.7217[/C][C]1071.2538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115734&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:

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
500.05530.0289073253.003700
510.07760.05760.0433288293.4089180773.2063425.1743
520.09420.09990.0621864994.8688408847.0938639.4115
530.10770.12090.07681265715.7867623064.267789.3442
540.11950.12540.08651361382.6249770727.9386877.9111
550.13030.09940.0887852705.9378784390.9385885.6585
560.140.15020.09751944788.3763950162.001974.7625
570.14840.18880.10893081640.96721216596.87181102.9945
580.15640.12850.11111429675.77221240272.30521113.6751
590.16390.09140.1091724067.29261188651.80391090.2531
600.1710.0980.1081832024.12441156231.10581075.2819
610.17730.110.10831052474.49741147584.72171071.2538


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 0.3 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,par1))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:par1] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
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,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')