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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 computationTue, 06 Dec 2011 04:14:29 -0500
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/Dec/06/t13231629213na6bfwuw68x5tk.htm/, Retrieved Sun, 28 Apr 2024 22:06:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151399, Retrieved Sun, 28 Apr 2024 22:06:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [] [2011-12-06 08:04:41] [80bca13c5f9401fbb753952fd2952f4a]
- RMP   [(Partial) Autocorrelation Function] [] [2011-12-06 08:29:14] [80bca13c5f9401fbb753952fd2952f4a]
-   P     [(Partial) Autocorrelation Function] [] [2011-12-06 08:31:19] [80bca13c5f9401fbb753952fd2952f4a]
- RMP       [Variance Reduction Matrix] [] [2011-12-06 08:45:18] [80bca13c5f9401fbb753952fd2952f4a]
- RM          [ARIMA Backward Selection] [] [2011-12-06 09:03:08] [80bca13c5f9401fbb753952fd2952f4a]
- RM              [ARIMA Forecasting] [] [2011-12-06 09:14:29] [204816f6f70a8d342ddc2b9d4f4a80d3] [Current]
-   PD              [ARIMA Forecasting] [Paper arima forec...] [2011-12-23 12:03:11] [805a2cd4f7b6665cd8870eed4006f53c]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.008
9.169
8.788
8.417
8.247
8.197
8.236
8.253
7.733
8.366
8.626
8.863
10.102
8.463
9.114
8.563
8.872
8.301
8.301
8.278
7.736
7.973
8.268
9.476
11.100
8.962
9.173
8.738
8.459
8.078
8.411
8.291
7.810
8.616
8.312
9.692
9.911
8.915
9.452
9.112
8.472
8.230
8.384
8.625
8.221
8.649
8.625
10.443
10.357
8.586
8.892
8.329
8.101
7.922
8.120
7.838
7.735
8.406
8.209
9.451
10.041
9.411
10.405
8.467
8.464
8.102
7.627
7.513
7.510
8.291
8.064
9.383
9.706
8.579
9.474
8.318
8.213
8.059
9.111
7.708
7.680
8.014
8.007
8.718
9.486
9.113
9.025
8.476
7.952
7.759
7.835
7.600
7.651
8.319
8.812
8.630

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151399&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151399&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151399&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






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[72])
609.451-------
6110.041-------
629.411-------
6310.405-------
648.467-------
658.464-------
668.102-------
677.627-------
687.513-------
697.51-------
708.291-------
718.064-------
729.383-------
739.70610.2129.423811.00030.10420.98040.66470.9804
748.5799.02588.14789.90370.15930.06440.19490.2126
759.4749.67748.782210.57260.3280.99190.05560.7404
768.3188.28627.38769.18490.47240.00480.34670.0084
778.2138.20337.30399.10270.49150.40130.2850.0051
788.0597.96467.0658.86410.41850.29420.38230.001
799.1117.79046.89088.68990.0020.27920.63913e-04
807.7087.53316.63368.43270.35163e-040.51750
817.687.51866.6198.41820.36260.33990.50750
828.0148.37447.47489.27390.21620.93490.57210.014
838.0078.06827.16878.96770.44690.5470.50370.0021
848.7189.18688.287610.0860.15340.99490.33440.3344
859.4869.84588.821110.87050.24560.98450.60540.812
869.1139.1958.142110.24780.43940.2940.87420.3632
879.02510.15839.099711.21690.01790.97350.89740.9244
888.4768.44617.38649.50580.4780.14220.59360.0416
897.9528.42077.36089.48070.1930.45930.64960.0376
907.7598.08237.02239.14230.2750.59520.51720.0081
917.8357.70196.64198.7620.40280.4580.00469e-04
927.67.57736.51738.63730.48330.31690.40454e-04
937.6517.55566.49568.61570.430.46730.40914e-04
948.3198.30137.24129.36130.48690.88540.70240.0227
958.8128.09387.03389.15380.09210.33860.56380.0086
968.639.42978.369710.48980.06960.87330.90590.5344

\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[72]) \tabularnewline
60 & 9.451 & - & - & - & - & - & - & - \tabularnewline
61 & 10.041 & - & - & - & - & - & - & - \tabularnewline
62 & 9.411 & - & - & - & - & - & - & - \tabularnewline
63 & 10.405 & - & - & - & - & - & - & - \tabularnewline
64 & 8.467 & - & - & - & - & - & - & - \tabularnewline
65 & 8.464 & - & - & - & - & - & - & - \tabularnewline
66 & 8.102 & - & - & - & - & - & - & - \tabularnewline
67 & 7.627 & - & - & - & - & - & - & - \tabularnewline
68 & 7.513 & - & - & - & - & - & - & - \tabularnewline
69 & 7.51 & - & - & - & - & - & - & - \tabularnewline
70 & 8.291 & - & - & - & - & - & - & - \tabularnewline
71 & 8.064 & - & - & - & - & - & - & - \tabularnewline
72 & 9.383 & - & - & - & - & - & - & - \tabularnewline
73 & 9.706 & 10.212 & 9.4238 & 11.0003 & 0.1042 & 0.9804 & 0.6647 & 0.9804 \tabularnewline
74 & 8.579 & 9.0258 & 8.1478 & 9.9037 & 0.1593 & 0.0644 & 0.1949 & 0.2126 \tabularnewline
75 & 9.474 & 9.6774 & 8.7822 & 10.5726 & 0.328 & 0.9919 & 0.0556 & 0.7404 \tabularnewline
76 & 8.318 & 8.2862 & 7.3876 & 9.1849 & 0.4724 & 0.0048 & 0.3467 & 0.0084 \tabularnewline
77 & 8.213 & 8.2033 & 7.3039 & 9.1027 & 0.4915 & 0.4013 & 0.285 & 0.0051 \tabularnewline
78 & 8.059 & 7.9646 & 7.065 & 8.8641 & 0.4185 & 0.2942 & 0.3823 & 0.001 \tabularnewline
79 & 9.111 & 7.7904 & 6.8908 & 8.6899 & 0.002 & 0.2792 & 0.6391 & 3e-04 \tabularnewline
80 & 7.708 & 7.5331 & 6.6336 & 8.4327 & 0.3516 & 3e-04 & 0.5175 & 0 \tabularnewline
81 & 7.68 & 7.5186 & 6.619 & 8.4182 & 0.3626 & 0.3399 & 0.5075 & 0 \tabularnewline
82 & 8.014 & 8.3744 & 7.4748 & 9.2739 & 0.2162 & 0.9349 & 0.5721 & 0.014 \tabularnewline
83 & 8.007 & 8.0682 & 7.1687 & 8.9677 & 0.4469 & 0.547 & 0.5037 & 0.0021 \tabularnewline
84 & 8.718 & 9.1868 & 8.2876 & 10.086 & 0.1534 & 0.9949 & 0.3344 & 0.3344 \tabularnewline
85 & 9.486 & 9.8458 & 8.8211 & 10.8705 & 0.2456 & 0.9845 & 0.6054 & 0.812 \tabularnewline
86 & 9.113 & 9.195 & 8.1421 & 10.2478 & 0.4394 & 0.294 & 0.8742 & 0.3632 \tabularnewline
87 & 9.025 & 10.1583 & 9.0997 & 11.2169 & 0.0179 & 0.9735 & 0.8974 & 0.9244 \tabularnewline
88 & 8.476 & 8.4461 & 7.3864 & 9.5058 & 0.478 & 0.1422 & 0.5936 & 0.0416 \tabularnewline
89 & 7.952 & 8.4207 & 7.3608 & 9.4807 & 0.193 & 0.4593 & 0.6496 & 0.0376 \tabularnewline
90 & 7.759 & 8.0823 & 7.0223 & 9.1423 & 0.275 & 0.5952 & 0.5172 & 0.0081 \tabularnewline
91 & 7.835 & 7.7019 & 6.6419 & 8.762 & 0.4028 & 0.458 & 0.0046 & 9e-04 \tabularnewline
92 & 7.6 & 7.5773 & 6.5173 & 8.6373 & 0.4833 & 0.3169 & 0.4045 & 4e-04 \tabularnewline
93 & 7.651 & 7.5556 & 6.4956 & 8.6157 & 0.43 & 0.4673 & 0.4091 & 4e-04 \tabularnewline
94 & 8.319 & 8.3013 & 7.2412 & 9.3613 & 0.4869 & 0.8854 & 0.7024 & 0.0227 \tabularnewline
95 & 8.812 & 8.0938 & 7.0338 & 9.1538 & 0.0921 & 0.3386 & 0.5638 & 0.0086 \tabularnewline
96 & 8.63 & 9.4297 & 8.3697 & 10.4898 & 0.0696 & 0.8733 & 0.9059 & 0.5344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151399&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[72])[/C][/ROW]
[ROW][C]60[/C][C]9.451[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]10.041[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]9.411[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]63[/C][C]10.405[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]64[/C][C]8.467[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]65[/C][C]8.464[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]66[/C][C]8.102[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]67[/C][C]7.627[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]68[/C][C]7.513[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]69[/C][C]7.51[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]70[/C][C]8.291[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]71[/C][C]8.064[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]72[/C][C]9.383[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]73[/C][C]9.706[/C][C]10.212[/C][C]9.4238[/C][C]11.0003[/C][C]0.1042[/C][C]0.9804[/C][C]0.6647[/C][C]0.9804[/C][/ROW]
[ROW][C]74[/C][C]8.579[/C][C]9.0258[/C][C]8.1478[/C][C]9.9037[/C][C]0.1593[/C][C]0.0644[/C][C]0.1949[/C][C]0.2126[/C][/ROW]
[ROW][C]75[/C][C]9.474[/C][C]9.6774[/C][C]8.7822[/C][C]10.5726[/C][C]0.328[/C][C]0.9919[/C][C]0.0556[/C][C]0.7404[/C][/ROW]
[ROW][C]76[/C][C]8.318[/C][C]8.2862[/C][C]7.3876[/C][C]9.1849[/C][C]0.4724[/C][C]0.0048[/C][C]0.3467[/C][C]0.0084[/C][/ROW]
[ROW][C]77[/C][C]8.213[/C][C]8.2033[/C][C]7.3039[/C][C]9.1027[/C][C]0.4915[/C][C]0.4013[/C][C]0.285[/C][C]0.0051[/C][/ROW]
[ROW][C]78[/C][C]8.059[/C][C]7.9646[/C][C]7.065[/C][C]8.8641[/C][C]0.4185[/C][C]0.2942[/C][C]0.3823[/C][C]0.001[/C][/ROW]
[ROW][C]79[/C][C]9.111[/C][C]7.7904[/C][C]6.8908[/C][C]8.6899[/C][C]0.002[/C][C]0.2792[/C][C]0.6391[/C][C]3e-04[/C][/ROW]
[ROW][C]80[/C][C]7.708[/C][C]7.5331[/C][C]6.6336[/C][C]8.4327[/C][C]0.3516[/C][C]3e-04[/C][C]0.5175[/C][C]0[/C][/ROW]
[ROW][C]81[/C][C]7.68[/C][C]7.5186[/C][C]6.619[/C][C]8.4182[/C][C]0.3626[/C][C]0.3399[/C][C]0.5075[/C][C]0[/C][/ROW]
[ROW][C]82[/C][C]8.014[/C][C]8.3744[/C][C]7.4748[/C][C]9.2739[/C][C]0.2162[/C][C]0.9349[/C][C]0.5721[/C][C]0.014[/C][/ROW]
[ROW][C]83[/C][C]8.007[/C][C]8.0682[/C][C]7.1687[/C][C]8.9677[/C][C]0.4469[/C][C]0.547[/C][C]0.5037[/C][C]0.0021[/C][/ROW]
[ROW][C]84[/C][C]8.718[/C][C]9.1868[/C][C]8.2876[/C][C]10.086[/C][C]0.1534[/C][C]0.9949[/C][C]0.3344[/C][C]0.3344[/C][/ROW]
[ROW][C]85[/C][C]9.486[/C][C]9.8458[/C][C]8.8211[/C][C]10.8705[/C][C]0.2456[/C][C]0.9845[/C][C]0.6054[/C][C]0.812[/C][/ROW]
[ROW][C]86[/C][C]9.113[/C][C]9.195[/C][C]8.1421[/C][C]10.2478[/C][C]0.4394[/C][C]0.294[/C][C]0.8742[/C][C]0.3632[/C][/ROW]
[ROW][C]87[/C][C]9.025[/C][C]10.1583[/C][C]9.0997[/C][C]11.2169[/C][C]0.0179[/C][C]0.9735[/C][C]0.8974[/C][C]0.9244[/C][/ROW]
[ROW][C]88[/C][C]8.476[/C][C]8.4461[/C][C]7.3864[/C][C]9.5058[/C][C]0.478[/C][C]0.1422[/C][C]0.5936[/C][C]0.0416[/C][/ROW]
[ROW][C]89[/C][C]7.952[/C][C]8.4207[/C][C]7.3608[/C][C]9.4807[/C][C]0.193[/C][C]0.4593[/C][C]0.6496[/C][C]0.0376[/C][/ROW]
[ROW][C]90[/C][C]7.759[/C][C]8.0823[/C][C]7.0223[/C][C]9.1423[/C][C]0.275[/C][C]0.5952[/C][C]0.5172[/C][C]0.0081[/C][/ROW]
[ROW][C]91[/C][C]7.835[/C][C]7.7019[/C][C]6.6419[/C][C]8.762[/C][C]0.4028[/C][C]0.458[/C][C]0.0046[/C][C]9e-04[/C][/ROW]
[ROW][C]92[/C][C]7.6[/C][C]7.5773[/C][C]6.5173[/C][C]8.6373[/C][C]0.4833[/C][C]0.3169[/C][C]0.4045[/C][C]4e-04[/C][/ROW]
[ROW][C]93[/C][C]7.651[/C][C]7.5556[/C][C]6.4956[/C][C]8.6157[/C][C]0.43[/C][C]0.4673[/C][C]0.4091[/C][C]4e-04[/C][/ROW]
[ROW][C]94[/C][C]8.319[/C][C]8.3013[/C][C]7.2412[/C][C]9.3613[/C][C]0.4869[/C][C]0.8854[/C][C]0.7024[/C][C]0.0227[/C][/ROW]
[ROW][C]95[/C][C]8.812[/C][C]8.0938[/C][C]7.0338[/C][C]9.1538[/C][C]0.0921[/C][C]0.3386[/C][C]0.5638[/C][C]0.0086[/C][/ROW]
[ROW][C]96[/C][C]8.63[/C][C]9.4297[/C][C]8.3697[/C][C]10.4898[/C][C]0.0696[/C][C]0.8733[/C][C]0.9059[/C][C]0.5344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151399&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151399&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[72])
609.451-------
6110.041-------
629.411-------
6310.405-------
648.467-------
658.464-------
668.102-------
677.627-------
687.513-------
697.51-------
708.291-------
718.064-------
729.383-------
739.70610.2129.423811.00030.10420.98040.66470.9804
748.5799.02588.14789.90370.15930.06440.19490.2126
759.4749.67748.782210.57260.3280.99190.05560.7404
768.3188.28627.38769.18490.47240.00480.34670.0084
778.2138.20337.30399.10270.49150.40130.2850.0051
788.0597.96467.0658.86410.41850.29420.38230.001
799.1117.79046.89088.68990.0020.27920.63913e-04
807.7087.53316.63368.43270.35163e-040.51750
817.687.51866.6198.41820.36260.33990.50750
828.0148.37447.47489.27390.21620.93490.57210.014
838.0078.06827.16878.96770.44690.5470.50370.0021
848.7189.18688.287610.0860.15340.99490.33440.3344
859.4869.84588.821110.87050.24560.98450.60540.812
869.1139.1958.142110.24780.43940.2940.87420.3632
879.02510.15839.099711.21690.01790.97350.89740.9244
888.4768.44617.38649.50580.4780.14220.59360.0416
897.9528.42077.36089.48070.1930.45930.64960.0376
907.7598.08237.02239.14230.2750.59520.51720.0081
917.8357.70196.64198.7620.40280.4580.00469e-04
927.67.57736.51738.63730.48330.31690.40454e-04
937.6517.55566.49568.61570.430.46730.40914e-04
948.3198.30137.24129.36130.48690.88540.70240.0227
958.8128.09387.03389.15380.09210.33860.56380.0086
968.639.42978.369710.48980.06960.87330.90590.5344






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
730.0394-0.049600.256100
740.0496-0.04950.04950.19960.22780.4773
750.0472-0.0210.040.04140.16570.407
760.05530.00380.0310.0010.12450.3529
770.05590.00120.0251e-040.09960.3156
780.05760.01190.02280.00890.08450.2907
790.05890.16950.04381.74410.32160.5671
800.06090.02320.04120.03060.28520.5341
810.0610.02150.0390.0260.25640.5064
820.0548-0.0430.03940.12990.24380.4937
830.0569-0.00760.03650.00370.22190.4711
840.0499-0.0510.03770.21970.22180.4709
850.0531-0.03650.03760.12950.21470.4633
860.0584-0.00890.03560.00670.19980.447
870.0532-0.11160.04071.28440.27210.5216
880.0640.00350.03839e-040.25520.5051
890.0642-0.05570.03940.21970.25310.5031
900.0669-0.040.03940.10450.24480.4948
910.07020.01730.03820.01770.23290.4826
920.07140.0030.03655e-040.22130.4704
930.07160.01260.03530.00910.21120.4595
940.06520.00210.03383e-040.20160.449
950.06680.08870.03620.51580.21520.4639
960.0574-0.08480.03820.63960.23290.4826

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
73 & 0.0394 & -0.0496 & 0 & 0.2561 & 0 & 0 \tabularnewline
74 & 0.0496 & -0.0495 & 0.0495 & 0.1996 & 0.2278 & 0.4773 \tabularnewline
75 & 0.0472 & -0.021 & 0.04 & 0.0414 & 0.1657 & 0.407 \tabularnewline
76 & 0.0553 & 0.0038 & 0.031 & 0.001 & 0.1245 & 0.3529 \tabularnewline
77 & 0.0559 & 0.0012 & 0.025 & 1e-04 & 0.0996 & 0.3156 \tabularnewline
78 & 0.0576 & 0.0119 & 0.0228 & 0.0089 & 0.0845 & 0.2907 \tabularnewline
79 & 0.0589 & 0.1695 & 0.0438 & 1.7441 & 0.3216 & 0.5671 \tabularnewline
80 & 0.0609 & 0.0232 & 0.0412 & 0.0306 & 0.2852 & 0.5341 \tabularnewline
81 & 0.061 & 0.0215 & 0.039 & 0.026 & 0.2564 & 0.5064 \tabularnewline
82 & 0.0548 & -0.043 & 0.0394 & 0.1299 & 0.2438 & 0.4937 \tabularnewline
83 & 0.0569 & -0.0076 & 0.0365 & 0.0037 & 0.2219 & 0.4711 \tabularnewline
84 & 0.0499 & -0.051 & 0.0377 & 0.2197 & 0.2218 & 0.4709 \tabularnewline
85 & 0.0531 & -0.0365 & 0.0376 & 0.1295 & 0.2147 & 0.4633 \tabularnewline
86 & 0.0584 & -0.0089 & 0.0356 & 0.0067 & 0.1998 & 0.447 \tabularnewline
87 & 0.0532 & -0.1116 & 0.0407 & 1.2844 & 0.2721 & 0.5216 \tabularnewline
88 & 0.064 & 0.0035 & 0.0383 & 9e-04 & 0.2552 & 0.5051 \tabularnewline
89 & 0.0642 & -0.0557 & 0.0394 & 0.2197 & 0.2531 & 0.5031 \tabularnewline
90 & 0.0669 & -0.04 & 0.0394 & 0.1045 & 0.2448 & 0.4948 \tabularnewline
91 & 0.0702 & 0.0173 & 0.0382 & 0.0177 & 0.2329 & 0.4826 \tabularnewline
92 & 0.0714 & 0.003 & 0.0365 & 5e-04 & 0.2213 & 0.4704 \tabularnewline
93 & 0.0716 & 0.0126 & 0.0353 & 0.0091 & 0.2112 & 0.4595 \tabularnewline
94 & 0.0652 & 0.0021 & 0.0338 & 3e-04 & 0.2016 & 0.449 \tabularnewline
95 & 0.0668 & 0.0887 & 0.0362 & 0.5158 & 0.2152 & 0.4639 \tabularnewline
96 & 0.0574 & -0.0848 & 0.0382 & 0.6396 & 0.2329 & 0.4826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151399&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]73[/C][C]0.0394[/C][C]-0.0496[/C][C]0[/C][C]0.2561[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]74[/C][C]0.0496[/C][C]-0.0495[/C][C]0.0495[/C][C]0.1996[/C][C]0.2278[/C][C]0.4773[/C][/ROW]
[ROW][C]75[/C][C]0.0472[/C][C]-0.021[/C][C]0.04[/C][C]0.0414[/C][C]0.1657[/C][C]0.407[/C][/ROW]
[ROW][C]76[/C][C]0.0553[/C][C]0.0038[/C][C]0.031[/C][C]0.001[/C][C]0.1245[/C][C]0.3529[/C][/ROW]
[ROW][C]77[/C][C]0.0559[/C][C]0.0012[/C][C]0.025[/C][C]1e-04[/C][C]0.0996[/C][C]0.3156[/C][/ROW]
[ROW][C]78[/C][C]0.0576[/C][C]0.0119[/C][C]0.0228[/C][C]0.0089[/C][C]0.0845[/C][C]0.2907[/C][/ROW]
[ROW][C]79[/C][C]0.0589[/C][C]0.1695[/C][C]0.0438[/C][C]1.7441[/C][C]0.3216[/C][C]0.5671[/C][/ROW]
[ROW][C]80[/C][C]0.0609[/C][C]0.0232[/C][C]0.0412[/C][C]0.0306[/C][C]0.2852[/C][C]0.5341[/C][/ROW]
[ROW][C]81[/C][C]0.061[/C][C]0.0215[/C][C]0.039[/C][C]0.026[/C][C]0.2564[/C][C]0.5064[/C][/ROW]
[ROW][C]82[/C][C]0.0548[/C][C]-0.043[/C][C]0.0394[/C][C]0.1299[/C][C]0.2438[/C][C]0.4937[/C][/ROW]
[ROW][C]83[/C][C]0.0569[/C][C]-0.0076[/C][C]0.0365[/C][C]0.0037[/C][C]0.2219[/C][C]0.4711[/C][/ROW]
[ROW][C]84[/C][C]0.0499[/C][C]-0.051[/C][C]0.0377[/C][C]0.2197[/C][C]0.2218[/C][C]0.4709[/C][/ROW]
[ROW][C]85[/C][C]0.0531[/C][C]-0.0365[/C][C]0.0376[/C][C]0.1295[/C][C]0.2147[/C][C]0.4633[/C][/ROW]
[ROW][C]86[/C][C]0.0584[/C][C]-0.0089[/C][C]0.0356[/C][C]0.0067[/C][C]0.1998[/C][C]0.447[/C][/ROW]
[ROW][C]87[/C][C]0.0532[/C][C]-0.1116[/C][C]0.0407[/C][C]1.2844[/C][C]0.2721[/C][C]0.5216[/C][/ROW]
[ROW][C]88[/C][C]0.064[/C][C]0.0035[/C][C]0.0383[/C][C]9e-04[/C][C]0.2552[/C][C]0.5051[/C][/ROW]
[ROW][C]89[/C][C]0.0642[/C][C]-0.0557[/C][C]0.0394[/C][C]0.2197[/C][C]0.2531[/C][C]0.5031[/C][/ROW]
[ROW][C]90[/C][C]0.0669[/C][C]-0.04[/C][C]0.0394[/C][C]0.1045[/C][C]0.2448[/C][C]0.4948[/C][/ROW]
[ROW][C]91[/C][C]0.0702[/C][C]0.0173[/C][C]0.0382[/C][C]0.0177[/C][C]0.2329[/C][C]0.4826[/C][/ROW]
[ROW][C]92[/C][C]0.0714[/C][C]0.003[/C][C]0.0365[/C][C]5e-04[/C][C]0.2213[/C][C]0.4704[/C][/ROW]
[ROW][C]93[/C][C]0.0716[/C][C]0.0126[/C][C]0.0353[/C][C]0.0091[/C][C]0.2112[/C][C]0.4595[/C][/ROW]
[ROW][C]94[/C][C]0.0652[/C][C]0.0021[/C][C]0.0338[/C][C]3e-04[/C][C]0.2016[/C][C]0.449[/C][/ROW]
[ROW][C]95[/C][C]0.0668[/C][C]0.0887[/C][C]0.0362[/C][C]0.5158[/C][C]0.2152[/C][C]0.4639[/C][/ROW]
[ROW][C]96[/C][C]0.0574[/C][C]-0.0848[/C][C]0.0382[/C][C]0.6396[/C][C]0.2329[/C][C]0.4826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151399&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151399&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
730.0394-0.049600.256100
740.0496-0.04950.04950.19960.22780.4773
750.0472-0.0210.040.04140.16570.407
760.05530.00380.0310.0010.12450.3529
770.05590.00120.0251e-040.09960.3156
780.05760.01190.02280.00890.08450.2907
790.05890.16950.04381.74410.32160.5671
800.06090.02320.04120.03060.28520.5341
810.0610.02150.0390.0260.25640.5064
820.0548-0.0430.03940.12990.24380.4937
830.0569-0.00760.03650.00370.22190.4711
840.0499-0.0510.03770.21970.22180.4709
850.0531-0.03650.03760.12950.21470.4633
860.0584-0.00890.03560.00670.19980.447
870.0532-0.11160.04071.28440.27210.5216
880.0640.00350.03839e-040.25520.5051
890.0642-0.05570.03940.21970.25310.5031
900.0669-0.040.03940.10450.24480.4948
910.07020.01730.03820.01770.23290.4826
920.07140.0030.03655e-040.22130.4704
930.07160.01260.03530.00910.21120.4595
940.06520.00210.03383e-040.20160.449
950.06680.08870.03620.51580.21520.4639
960.0574-0.08480.03820.63960.23290.4826


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; 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')