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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, 06 Dec 2009 03:44:58 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/06/t1260096489s412n4v3e0m2bxr.htm/, Retrieved Wed, 01 May 2024 23:20:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64347, Retrieved Wed, 01 May 2024 23:20:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws10af1
Estimated Impact208

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Forecasting] [] [2009-12-06 10:44:58] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
-   PD    [ARIMA Forecasting] [ws 10 deel 2 prblm] [2009-12-09 19:29:01] [134dc66689e3d457a82860db6471d419]
- RMP       [(Partial) Autocorrelation Function] [WS 10 forum ACF] [2009-12-11 10:14:54] [83058a88a37d754675a5cd22dab372fc]
- RMP       [Standard Deviation-Mean Plot] [WS 10 Forum SMP] [2009-12-11 10:18:43] [83058a88a37d754675a5cd22dab372fc]
- RMP       [(Partial) Autocorrelation Function] [] [2009-12-11 10:27:22] [83058a88a37d754675a5cd22dab372fc]
- RM        [ARIMA Backward Selection] [WS 10 Forum ARIMA] [2009-12-11 10:33:01] [83058a88a37d754675a5cd22dab372fc]
-   P       [ARIMA Forecasting] [ws 10 deel 2 arim...] [2009-12-12 09:45:03] [134dc66689e3d457a82860db6471d419]
-    D        [ARIMA Forecasting] [WS 10 ] [2009-12-12 11:53:20] [3425351e86519d261a643e224a0c8ee1]
-   PD          [ARIMA Forecasting] [] [2009-12-19 16:24:22] [3425351e86519d261a643e224a0c8ee1]
-   P             [ARIMA Forecasting] [] [2009-12-20 10:24:37] [3425351e86519d261a643e224a0c8ee1]
-   PD              [ARIMA Forecasting] [ARIMA forecasting] [2009-12-21 15:59:35] [76ab39dc7a55316678260825bd5ad46c]
-   PD        [ARIMA Forecasting] [Forecasting] [2009-12-14 15:18:19] [24c4941ee50deadff4640c9c09cc70cb]
-   P         [ARIMA Forecasting] [Paper ARIMA F IGP] [2009-12-14 21:07:10] [134dc66689e3d457a82860db6471d419]
-   PD          [ARIMA Forecasting] [Paper ARIMA F ICP] [2009-12-15 20:21:11] [134dc66689e3d457a82860db6471d419]
-   P           [ARIMA Forecasting] [Paper ARIMA F IGP 12] [2009-12-15 20:24:19] [134dc66689e3d457a82860db6471d419]
- R PD            [ARIMA Forecasting] [Paper arima forec...] [2009-12-23 22:37:42] [62d3ced7fb1c10c35a82e9cb1d0d0e2b]
- R PD            [ARIMA Forecasting] [Paper arima forec...] [2009-12-23 23:25:41] [62d3ced7fb1c10c35a82e9cb1d0d0e2b]
-   P         [ARIMA Forecasting] [workshop 10] [2009-12-18 17:50:14] [28d531aeb5ea2ff1b676cbab66947a19]
- R P       [ARIMA Forecasting] [ws 10 deel 2 arim...] [2009-12-12 09:39:49] [134dc66689e3d457a82860db6471d419]
-    D        [ARIMA Forecasting] [WS 10] [2009-12-12 11:57:08] [3425351e86519d261a643e224a0c8ee1]
- R P         [ARIMA Forecasting] [] [2009-12-12 19:34:20] [b98453cac15ba1066b407e146608df68]
- R PD    [ARIMA Forecasting] [] [2009-12-10 15:50:22] [b7349fb284cae6f1172638396d27b11f]
-   PD    [ARIMA Forecasting] [arima forecast icp] [2009-12-10 18:43:40] [134dc66689e3d457a82860db6471d419]
-   PD    [ARIMA Forecasting] [review 3 ws 10 ar...] [2009-12-12 10:44:25] [134dc66689e3d457a82860db6471d419]
-   PD    [ARIMA Forecasting] [review 3 ws 10 ar...] [2009-12-12 10:45:51] [134dc66689e3d457a82860db6471d419]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2756,76
2849,27
2921,44
2981,85
3080,58
3106,22
3119,31
3061,26
3097,31
3161,69
3257,16
3277,01
3295,32
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45
1862,83
1905,41
1810,99
1670,07
1864,44
2052,02
2029,6
2070,83
2293,41
2443,27

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64347&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64347&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64347&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 time1 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[48])
364296.49-------
374435.23-------
384105.18-------
394116.68-------
403844.49-------
413720.98-------
423674.4-------
433857.62-------
443801.06-------
453504.37-------
463032.6-------
473047.03-------
482962.34-------
492197.822941.19362647.84693234.540400.443800.4438
502014.452935.91362466.40033405.42691e-040.99900.4561
511862.832934.59522327.48993541.70043e-040.99851e-040.4643
521905.412934.2662212.98463655.54740.00260.99820.00670.4696
531810.992934.18382113.9363754.43160.00360.9930.030.4732
541670.072934.16332025.54433842.78230.00320.99230.05520.4758
551864.442934.15811945.00393923.31240.0170.99390.03360.4777
562052.022934.15691870.54153997.77220.0520.97570.05510.4793
572029.62934.15661800.96084067.35230.05880.93650.1620.4806
582070.832934.15651735.4124132.9010.0790.93040.43610.4816
592293.412934.15651673.26614195.04680.15960.91020.43040.4825
602443.272934.15641614.04264254.27030.23310.82930.48330.4833

\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[48]) \tabularnewline
36 & 4296.49 & - & - & - & - & - & - & - \tabularnewline
37 & 4435.23 & - & - & - & - & - & - & - \tabularnewline
38 & 4105.18 & - & - & - & - & - & - & - \tabularnewline
39 & 4116.68 & - & - & - & - & - & - & - \tabularnewline
40 & 3844.49 & - & - & - & - & - & - & - \tabularnewline
41 & 3720.98 & - & - & - & - & - & - & - \tabularnewline
42 & 3674.4 & - & - & - & - & - & - & - \tabularnewline
43 & 3857.62 & - & - & - & - & - & - & - \tabularnewline
44 & 3801.06 & - & - & - & - & - & - & - \tabularnewline
45 & 3504.37 & - & - & - & - & - & - & - \tabularnewline
46 & 3032.6 & - & - & - & - & - & - & - \tabularnewline
47 & 3047.03 & - & - & - & - & - & - & - \tabularnewline
48 & 2962.34 & - & - & - & - & - & - & - \tabularnewline
49 & 2197.82 & 2941.1936 & 2647.8469 & 3234.5404 & 0 & 0.4438 & 0 & 0.4438 \tabularnewline
50 & 2014.45 & 2935.9136 & 2466.4003 & 3405.4269 & 1e-04 & 0.999 & 0 & 0.4561 \tabularnewline
51 & 1862.83 & 2934.5952 & 2327.4899 & 3541.7004 & 3e-04 & 0.9985 & 1e-04 & 0.4643 \tabularnewline
52 & 1905.41 & 2934.266 & 2212.9846 & 3655.5474 & 0.0026 & 0.9982 & 0.0067 & 0.4696 \tabularnewline
53 & 1810.99 & 2934.1838 & 2113.936 & 3754.4316 & 0.0036 & 0.993 & 0.03 & 0.4732 \tabularnewline
54 & 1670.07 & 2934.1633 & 2025.5443 & 3842.7823 & 0.0032 & 0.9923 & 0.0552 & 0.4758 \tabularnewline
55 & 1864.44 & 2934.1581 & 1945.0039 & 3923.3124 & 0.017 & 0.9939 & 0.0336 & 0.4777 \tabularnewline
56 & 2052.02 & 2934.1569 & 1870.5415 & 3997.7722 & 0.052 & 0.9757 & 0.0551 & 0.4793 \tabularnewline
57 & 2029.6 & 2934.1566 & 1800.9608 & 4067.3523 & 0.0588 & 0.9365 & 0.162 & 0.4806 \tabularnewline
58 & 2070.83 & 2934.1565 & 1735.412 & 4132.901 & 0.079 & 0.9304 & 0.4361 & 0.4816 \tabularnewline
59 & 2293.41 & 2934.1565 & 1673.2661 & 4195.0468 & 0.1596 & 0.9102 & 0.4304 & 0.4825 \tabularnewline
60 & 2443.27 & 2934.1564 & 1614.0426 & 4254.2703 & 0.2331 & 0.8293 & 0.4833 & 0.4833 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64347&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[48])[/C][/ROW]
[ROW][C]36[/C][C]4296.49[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]4435.23[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]4105.18[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]4116.68[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]3844.49[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]3720.98[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]3674.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]3857.62[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]3801.06[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]3504.37[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]3032.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]3047.03[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]2962.34[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]2197.82[/C][C]2941.1936[/C][C]2647.8469[/C][C]3234.5404[/C][C]0[/C][C]0.4438[/C][C]0[/C][C]0.4438[/C][/ROW]
[ROW][C]50[/C][C]2014.45[/C][C]2935.9136[/C][C]2466.4003[/C][C]3405.4269[/C][C]1e-04[/C][C]0.999[/C][C]0[/C][C]0.4561[/C][/ROW]
[ROW][C]51[/C][C]1862.83[/C][C]2934.5952[/C][C]2327.4899[/C][C]3541.7004[/C][C]3e-04[/C][C]0.9985[/C][C]1e-04[/C][C]0.4643[/C][/ROW]
[ROW][C]52[/C][C]1905.41[/C][C]2934.266[/C][C]2212.9846[/C][C]3655.5474[/C][C]0.0026[/C][C]0.9982[/C][C]0.0067[/C][C]0.4696[/C][/ROW]
[ROW][C]53[/C][C]1810.99[/C][C]2934.1838[/C][C]2113.936[/C][C]3754.4316[/C][C]0.0036[/C][C]0.993[/C][C]0.03[/C][C]0.4732[/C][/ROW]
[ROW][C]54[/C][C]1670.07[/C][C]2934.1633[/C][C]2025.5443[/C][C]3842.7823[/C][C]0.0032[/C][C]0.9923[/C][C]0.0552[/C][C]0.4758[/C][/ROW]
[ROW][C]55[/C][C]1864.44[/C][C]2934.1581[/C][C]1945.0039[/C][C]3923.3124[/C][C]0.017[/C][C]0.9939[/C][C]0.0336[/C][C]0.4777[/C][/ROW]
[ROW][C]56[/C][C]2052.02[/C][C]2934.1569[/C][C]1870.5415[/C][C]3997.7722[/C][C]0.052[/C][C]0.9757[/C][C]0.0551[/C][C]0.4793[/C][/ROW]
[ROW][C]57[/C][C]2029.6[/C][C]2934.1566[/C][C]1800.9608[/C][C]4067.3523[/C][C]0.0588[/C][C]0.9365[/C][C]0.162[/C][C]0.4806[/C][/ROW]
[ROW][C]58[/C][C]2070.83[/C][C]2934.1565[/C][C]1735.412[/C][C]4132.901[/C][C]0.079[/C][C]0.9304[/C][C]0.4361[/C][C]0.4816[/C][/ROW]
[ROW][C]59[/C][C]2293.41[/C][C]2934.1565[/C][C]1673.2661[/C][C]4195.0468[/C][C]0.1596[/C][C]0.9102[/C][C]0.4304[/C][C]0.4825[/C][/ROW]
[ROW][C]60[/C][C]2443.27[/C][C]2934.1564[/C][C]1614.0426[/C][C]4254.2703[/C][C]0.2331[/C][C]0.8293[/C][C]0.4833[/C][C]0.4833[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64347&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64347&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[48])
364296.49-------
374435.23-------
384105.18-------
394116.68-------
403844.49-------
413720.98-------
423674.4-------
433857.62-------
443801.06-------
453504.37-------
463032.6-------
473047.03-------
482962.34-------
492197.822941.19362647.84693234.540400.443800.4438
502014.452935.91362466.40033405.42691e-040.99900.4561
511862.832934.59522327.48993541.70043e-040.99851e-040.4643
521905.412934.2662212.98463655.54740.00260.99820.00670.4696
531810.992934.18382113.9363754.43160.00360.9930.030.4732
541670.072934.16332025.54433842.78230.00320.99230.05520.4758
551864.442934.15811945.00393923.31240.0170.99390.03360.4777
562052.022934.15691870.54153997.77220.0520.97570.05510.4793
572029.62934.15661800.96084067.35230.05880.93650.1620.4806
582070.832934.15651735.4124132.9010.0790.93040.43610.4816
592293.412934.15651673.26614195.04680.15960.91020.43040.4825
602443.272934.15641614.04264254.27030.23310.82930.48330.4833






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.0509-0.25270.0211552604.36246050.3635214.5935
500.0816-0.31390.0262849095.111270757.9259266.0036
510.1056-0.36520.03041148680.608195723.384309.392
520.1254-0.35060.02921058544.655288212.0546297.0051
530.1426-0.38280.03191261564.3069105130.3589324.2381
540.158-0.43080.03591597931.8053133160.9838364.9123
550.172-0.36460.03041144296.919195358.0766308.801
560.1849-0.30060.0251778165.457164847.1214254.651
570.197-0.30830.0257818222.552868185.2127261.123
580.2084-0.29420.0245745332.594862111.0496249.2209
590.2192-0.21840.0182410556.01434213.0012184.9676
600.2295-0.16730.0139240969.502520080.7919141.7067

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0509 & -0.2527 & 0.0211 & 552604.362 & 46050.3635 & 214.5935 \tabularnewline
50 & 0.0816 & -0.3139 & 0.0262 & 849095.1112 & 70757.9259 & 266.0036 \tabularnewline
51 & 0.1056 & -0.3652 & 0.0304 & 1148680.6081 & 95723.384 & 309.392 \tabularnewline
52 & 0.1254 & -0.3506 & 0.0292 & 1058544.6552 & 88212.0546 & 297.0051 \tabularnewline
53 & 0.1426 & -0.3828 & 0.0319 & 1261564.3069 & 105130.3589 & 324.2381 \tabularnewline
54 & 0.158 & -0.4308 & 0.0359 & 1597931.8053 & 133160.9838 & 364.9123 \tabularnewline
55 & 0.172 & -0.3646 & 0.0304 & 1144296.9191 & 95358.0766 & 308.801 \tabularnewline
56 & 0.1849 & -0.3006 & 0.0251 & 778165.4571 & 64847.1214 & 254.651 \tabularnewline
57 & 0.197 & -0.3083 & 0.0257 & 818222.5528 & 68185.2127 & 261.123 \tabularnewline
58 & 0.2084 & -0.2942 & 0.0245 & 745332.5948 & 62111.0496 & 249.2209 \tabularnewline
59 & 0.2192 & -0.2184 & 0.0182 & 410556.014 & 34213.0012 & 184.9676 \tabularnewline
60 & 0.2295 & -0.1673 & 0.0139 & 240969.5025 & 20080.7919 & 141.7067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64347&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]49[/C][C]0.0509[/C][C]-0.2527[/C][C]0.0211[/C][C]552604.362[/C][C]46050.3635[/C][C]214.5935[/C][/ROW]
[ROW][C]50[/C][C]0.0816[/C][C]-0.3139[/C][C]0.0262[/C][C]849095.1112[/C][C]70757.9259[/C][C]266.0036[/C][/ROW]
[ROW][C]51[/C][C]0.1056[/C][C]-0.3652[/C][C]0.0304[/C][C]1148680.6081[/C][C]95723.384[/C][C]309.392[/C][/ROW]
[ROW][C]52[/C][C]0.1254[/C][C]-0.3506[/C][C]0.0292[/C][C]1058544.6552[/C][C]88212.0546[/C][C]297.0051[/C][/ROW]
[ROW][C]53[/C][C]0.1426[/C][C]-0.3828[/C][C]0.0319[/C][C]1261564.3069[/C][C]105130.3589[/C][C]324.2381[/C][/ROW]
[ROW][C]54[/C][C]0.158[/C][C]-0.4308[/C][C]0.0359[/C][C]1597931.8053[/C][C]133160.9838[/C][C]364.9123[/C][/ROW]
[ROW][C]55[/C][C]0.172[/C][C]-0.3646[/C][C]0.0304[/C][C]1144296.9191[/C][C]95358.0766[/C][C]308.801[/C][/ROW]
[ROW][C]56[/C][C]0.1849[/C][C]-0.3006[/C][C]0.0251[/C][C]778165.4571[/C][C]64847.1214[/C][C]254.651[/C][/ROW]
[ROW][C]57[/C][C]0.197[/C][C]-0.3083[/C][C]0.0257[/C][C]818222.5528[/C][C]68185.2127[/C][C]261.123[/C][/ROW]
[ROW][C]58[/C][C]0.2084[/C][C]-0.2942[/C][C]0.0245[/C][C]745332.5948[/C][C]62111.0496[/C][C]249.2209[/C][/ROW]
[ROW][C]59[/C][C]0.2192[/C][C]-0.2184[/C][C]0.0182[/C][C]410556.014[/C][C]34213.0012[/C][C]184.9676[/C][/ROW]
[ROW][C]60[/C][C]0.2295[/C][C]-0.1673[/C][C]0.0139[/C][C]240969.5025[/C][C]20080.7919[/C][C]141.7067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64347&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64347&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
490.0509-0.25270.0211552604.36246050.3635214.5935
500.0816-0.31390.0262849095.111270757.9259266.0036
510.1056-0.36520.03041148680.608195723.384309.392
520.1254-0.35060.02921058544.655288212.0546297.0051
530.1426-0.38280.03191261564.3069105130.3589324.2381
540.158-0.43080.03591597931.8053133160.9838364.9123
550.172-0.36460.03041144296.919195358.0766308.801
560.1849-0.30060.0251778165.457164847.1214254.651
570.197-0.30830.0257818222.552868185.2127261.123
580.2084-0.29420.0245745332.594862111.0496249.2209
590.2192-0.21840.0182410556.01434213.0012184.9676
600.2295-0.16730.0139240969.502520080.7919141.7067


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; 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,fx))
(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.se <- array(0, dim=fx)
perf.mse <- 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$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
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 = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
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[1:12] <- 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.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[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')