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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, 21 Dec 2010 16:44:16 +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/21/t1292949730he89f9p72z1ehcn.htm/, Retrieved Tue, 14 May 2024 16:44:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113745, Retrieved Tue, 14 May 2024 16:44:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129

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] [WS9 - ARIMA Forec...] [2010-12-04 16:25:58] [8ef49741e164ec6343c90c7935194465]
-   P         [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-04 16:58:46] [8ef49741e164ec6343c90c7935194465]
- R  D          [ARIMA Forecasting] [WS 9 - Forecasting] [2010-12-06 21:55:40] [18fa53e8b37a5effc0c5f8a5122cdd2d]
-   PD              [ARIMA Forecasting] [Paper - C&S ARIMA ] [2010-12-21 16:44:16] [89d441ae0711e9b79b5d358f420c1317] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.31
105.63
106.02
105.85
106.57
106.48
106.60
106.75
106.69
106.69
106.93
107.21
107.88
108.84
108.96
109.52
108.45
108.67
108.96
108.76
107.85
108.78
107.51
108.83
111.54
111.74
112.04
111.74
111.81
111.86
114.23
114.80
115.17
115.11
114.43
114.66
115.11
117.74
118.18
118.56
117.63
117.71
117.46
117.37
117.34
117.09
116.65
116.71
116.82
117.33
117.95
123.53
124.91
125.99
126.29
125.68
125.52

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'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113745&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113745&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'George Udny Yule' @ 72.249.76.132






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[45])
33115.17-------
34115.11-------
35114.43-------
36114.66-------
37115.11-------
38117.74-------
39118.18-------
40118.56-------
41117.63-------
42117.71-------
43117.46-------
44117.37-------
45117.34-------
46117.09117.3359115.6906118.98120.38480.49810.9960.4981
47116.65117.3353114.8446119.82610.29480.57650.98890.4985
48116.71117.3353114.2021120.46840.34780.66590.95290.4988
49116.82117.3353113.6685121.0020.39150.63090.88290.499
50117.33117.3353113.2029121.46760.4990.59650.42390.4991
51117.95117.3353112.7847121.88580.39560.50090.3580.4992
52123.53117.3353112.4019122.26860.00690.40350.31330.4992
53124.91117.3353112.0466122.62390.00250.01080.45650.4993
54125.99117.3353111.7138122.95670.00130.00410.4480.4993
55126.29117.3353111.3996123.27090.00160.00210.48360.4994
56125.68117.3353111.1013123.56930.00430.00240.49560.4994
57125.52117.3353110.8165123.8540.00690.00610.49940.4994

\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[45]) \tabularnewline
33 & 115.17 & - & - & - & - & - & - & - \tabularnewline
34 & 115.11 & - & - & - & - & - & - & - \tabularnewline
35 & 114.43 & - & - & - & - & - & - & - \tabularnewline
36 & 114.66 & - & - & - & - & - & - & - \tabularnewline
37 & 115.11 & - & - & - & - & - & - & - \tabularnewline
38 & 117.74 & - & - & - & - & - & - & - \tabularnewline
39 & 118.18 & - & - & - & - & - & - & - \tabularnewline
40 & 118.56 & - & - & - & - & - & - & - \tabularnewline
41 & 117.63 & - & - & - & - & - & - & - \tabularnewline
42 & 117.71 & - & - & - & - & - & - & - \tabularnewline
43 & 117.46 & - & - & - & - & - & - & - \tabularnewline
44 & 117.37 & - & - & - & - & - & - & - \tabularnewline
45 & 117.34 & - & - & - & - & - & - & - \tabularnewline
46 & 117.09 & 117.3359 & 115.6906 & 118.9812 & 0.3848 & 0.4981 & 0.996 & 0.4981 \tabularnewline
47 & 116.65 & 117.3353 & 114.8446 & 119.8261 & 0.2948 & 0.5765 & 0.9889 & 0.4985 \tabularnewline
48 & 116.71 & 117.3353 & 114.2021 & 120.4684 & 0.3478 & 0.6659 & 0.9529 & 0.4988 \tabularnewline
49 & 116.82 & 117.3353 & 113.6685 & 121.002 & 0.3915 & 0.6309 & 0.8829 & 0.499 \tabularnewline
50 & 117.33 & 117.3353 & 113.2029 & 121.4676 & 0.499 & 0.5965 & 0.4239 & 0.4991 \tabularnewline
51 & 117.95 & 117.3353 & 112.7847 & 121.8858 & 0.3956 & 0.5009 & 0.358 & 0.4992 \tabularnewline
52 & 123.53 & 117.3353 & 112.4019 & 122.2686 & 0.0069 & 0.4035 & 0.3133 & 0.4992 \tabularnewline
53 & 124.91 & 117.3353 & 112.0466 & 122.6239 & 0.0025 & 0.0108 & 0.4565 & 0.4993 \tabularnewline
54 & 125.99 & 117.3353 & 111.7138 & 122.9567 & 0.0013 & 0.0041 & 0.448 & 0.4993 \tabularnewline
55 & 126.29 & 117.3353 & 111.3996 & 123.2709 & 0.0016 & 0.0021 & 0.4836 & 0.4994 \tabularnewline
56 & 125.68 & 117.3353 & 111.1013 & 123.5693 & 0.0043 & 0.0024 & 0.4956 & 0.4994 \tabularnewline
57 & 125.52 & 117.3353 & 110.8165 & 123.854 & 0.0069 & 0.0061 & 0.4994 & 0.4994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113745&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[45])[/C][/ROW]
[ROW][C]33[/C][C]115.17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]34[/C][C]115.11[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]35[/C][C]114.43[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]114.66[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]115.11[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]117.74[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]118.18[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]118.56[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]117.63[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]117.71[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]117.46[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]117.37[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]117.34[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]117.09[/C][C]117.3359[/C][C]115.6906[/C][C]118.9812[/C][C]0.3848[/C][C]0.4981[/C][C]0.996[/C][C]0.4981[/C][/ROW]
[ROW][C]47[/C][C]116.65[/C][C]117.3353[/C][C]114.8446[/C][C]119.8261[/C][C]0.2948[/C][C]0.5765[/C][C]0.9889[/C][C]0.4985[/C][/ROW]
[ROW][C]48[/C][C]116.71[/C][C]117.3353[/C][C]114.2021[/C][C]120.4684[/C][C]0.3478[/C][C]0.6659[/C][C]0.9529[/C][C]0.4988[/C][/ROW]
[ROW][C]49[/C][C]116.82[/C][C]117.3353[/C][C]113.6685[/C][C]121.002[/C][C]0.3915[/C][C]0.6309[/C][C]0.8829[/C][C]0.499[/C][/ROW]
[ROW][C]50[/C][C]117.33[/C][C]117.3353[/C][C]113.2029[/C][C]121.4676[/C][C]0.499[/C][C]0.5965[/C][C]0.4239[/C][C]0.4991[/C][/ROW]
[ROW][C]51[/C][C]117.95[/C][C]117.3353[/C][C]112.7847[/C][C]121.8858[/C][C]0.3956[/C][C]0.5009[/C][C]0.358[/C][C]0.4992[/C][/ROW]
[ROW][C]52[/C][C]123.53[/C][C]117.3353[/C][C]112.4019[/C][C]122.2686[/C][C]0.0069[/C][C]0.4035[/C][C]0.3133[/C][C]0.4992[/C][/ROW]
[ROW][C]53[/C][C]124.91[/C][C]117.3353[/C][C]112.0466[/C][C]122.6239[/C][C]0.0025[/C][C]0.0108[/C][C]0.4565[/C][C]0.4993[/C][/ROW]
[ROW][C]54[/C][C]125.99[/C][C]117.3353[/C][C]111.7138[/C][C]122.9567[/C][C]0.0013[/C][C]0.0041[/C][C]0.448[/C][C]0.4993[/C][/ROW]
[ROW][C]55[/C][C]126.29[/C][C]117.3353[/C][C]111.3996[/C][C]123.2709[/C][C]0.0016[/C][C]0.0021[/C][C]0.4836[/C][C]0.4994[/C][/ROW]
[ROW][C]56[/C][C]125.68[/C][C]117.3353[/C][C]111.1013[/C][C]123.5693[/C][C]0.0043[/C][C]0.0024[/C][C]0.4956[/C][C]0.4994[/C][/ROW]
[ROW][C]57[/C][C]125.52[/C][C]117.3353[/C][C]110.8165[/C][C]123.854[/C][C]0.0069[/C][C]0.0061[/C][C]0.4994[/C][C]0.4994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113745&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[45])
33115.17-------
34115.11-------
35114.43-------
36114.66-------
37115.11-------
38117.74-------
39118.18-------
40118.56-------
41117.63-------
42117.71-------
43117.46-------
44117.37-------
45117.34-------
46117.09117.3359115.6906118.98120.38480.49810.9960.4981
47116.65117.3353114.8446119.82610.29480.57650.98890.4985
48116.71117.3353114.2021120.46840.34780.66590.95290.4988
49116.82117.3353113.6685121.0020.39150.63090.88290.499
50117.33117.3353113.2029121.46760.4990.59650.42390.4991
51117.95117.3353112.7847121.88580.39560.50090.3580.4992
52123.53117.3353112.4019122.26860.00690.40350.31330.4992
53124.91117.3353112.0466122.62390.00250.01080.45650.4993
54125.99117.3353111.7138122.95670.00130.00410.4480.4993
55126.29117.3353111.3996123.27090.00160.00210.48360.4994
56125.68117.3353111.1013123.56930.00430.00240.49560.4994
57125.52117.3353110.8165123.8540.00690.00610.49940.4994






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
460.0072-0.002100.060500
470.0108-0.00580.0040.46970.26510.5149
480.0136-0.00530.00440.3910.3070.5541
490.0159-0.00440.00440.26550.29670.5447
500.01800.003500.23730.4872
510.01980.00520.00380.37790.26080.5106
520.02150.05280.010838.37495.70562.3886
530.0230.06460.017557.376812.16453.4878
540.02440.07380.023874.904619.13564.3744
550.02580.07630.02980.187525.24085.024
560.02710.07110.032969.634829.27665.4108
570.02830.06980.035966.990132.41945.6938

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
46 & 0.0072 & -0.0021 & 0 & 0.0605 & 0 & 0 \tabularnewline
47 & 0.0108 & -0.0058 & 0.004 & 0.4697 & 0.2651 & 0.5149 \tabularnewline
48 & 0.0136 & -0.0053 & 0.0044 & 0.391 & 0.307 & 0.5541 \tabularnewline
49 & 0.0159 & -0.0044 & 0.0044 & 0.2655 & 0.2967 & 0.5447 \tabularnewline
50 & 0.018 & 0 & 0.0035 & 0 & 0.2373 & 0.4872 \tabularnewline
51 & 0.0198 & 0.0052 & 0.0038 & 0.3779 & 0.2608 & 0.5106 \tabularnewline
52 & 0.0215 & 0.0528 & 0.0108 & 38.3749 & 5.7056 & 2.3886 \tabularnewline
53 & 0.023 & 0.0646 & 0.0175 & 57.3768 & 12.1645 & 3.4878 \tabularnewline
54 & 0.0244 & 0.0738 & 0.0238 & 74.9046 & 19.1356 & 4.3744 \tabularnewline
55 & 0.0258 & 0.0763 & 0.029 & 80.1875 & 25.2408 & 5.024 \tabularnewline
56 & 0.0271 & 0.0711 & 0.0329 & 69.6348 & 29.2766 & 5.4108 \tabularnewline
57 & 0.0283 & 0.0698 & 0.0359 & 66.9901 & 32.4194 & 5.6938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113745&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]46[/C][C]0.0072[/C][C]-0.0021[/C][C]0[/C][C]0.0605[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]0.0108[/C][C]-0.0058[/C][C]0.004[/C][C]0.4697[/C][C]0.2651[/C][C]0.5149[/C][/ROW]
[ROW][C]48[/C][C]0.0136[/C][C]-0.0053[/C][C]0.0044[/C][C]0.391[/C][C]0.307[/C][C]0.5541[/C][/ROW]
[ROW][C]49[/C][C]0.0159[/C][C]-0.0044[/C][C]0.0044[/C][C]0.2655[/C][C]0.2967[/C][C]0.5447[/C][/ROW]
[ROW][C]50[/C][C]0.018[/C][C]0[/C][C]0.0035[/C][C]0[/C][C]0.2373[/C][C]0.4872[/C][/ROW]
[ROW][C]51[/C][C]0.0198[/C][C]0.0052[/C][C]0.0038[/C][C]0.3779[/C][C]0.2608[/C][C]0.5106[/C][/ROW]
[ROW][C]52[/C][C]0.0215[/C][C]0.0528[/C][C]0.0108[/C][C]38.3749[/C][C]5.7056[/C][C]2.3886[/C][/ROW]
[ROW][C]53[/C][C]0.023[/C][C]0.0646[/C][C]0.0175[/C][C]57.3768[/C][C]12.1645[/C][C]3.4878[/C][/ROW]
[ROW][C]54[/C][C]0.0244[/C][C]0.0738[/C][C]0.0238[/C][C]74.9046[/C][C]19.1356[/C][C]4.3744[/C][/ROW]
[ROW][C]55[/C][C]0.0258[/C][C]0.0763[/C][C]0.029[/C][C]80.1875[/C][C]25.2408[/C][C]5.024[/C][/ROW]
[ROW][C]56[/C][C]0.0271[/C][C]0.0711[/C][C]0.0329[/C][C]69.6348[/C][C]29.2766[/C][C]5.4108[/C][/ROW]
[ROW][C]57[/C][C]0.0283[/C][C]0.0698[/C][C]0.0359[/C][C]66.9901[/C][C]32.4194[/C][C]5.6938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113745&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113745&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
460.0072-0.002100.060500
470.0108-0.00580.0040.46970.26510.5149
480.0136-0.00530.00440.3910.3070.5541
490.0159-0.00440.00440.26550.29670.5447
500.01800.003500.23730.4872
510.01980.00520.00380.37790.26080.5106
520.02150.05280.010838.37495.70562.3886
530.0230.06460.017557.376812.16453.4878
540.02440.07380.023874.904619.13564.3744
550.02580.07630.02980.187525.24085.024
560.02710.07110.032969.634829.27665.4108
570.02830.06980.035966.990132.41945.6938


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,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')