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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 computationFri, 11 Dec 2009 04:25:10 -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/11/t12605307554y080rh3cctzxbx.htm/, Retrieved Mon, 29 Apr 2024 05:19:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65999, Retrieved Mon, 29 Apr 2024 05:19:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact231

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
-   PD        [Univariate Data Series] [Totaal Werkzoeken...] [2009-11-24 16:54:07] [ee7c2e7343f5b1451e62c5c16ec521f1]
-   P           [Univariate Data Series] [Totaal Werkzoeken...] [2009-11-24 17:23:40] [ee7c2e7343f5b1451e62c5c16ec521f1]
-   PD            [Univariate Data Series] [] [2009-12-04 16:45:53] [b7349fb284cae6f1172638396d27b11f]
-   PD              [Univariate Data Series] [] [2009-12-06 12:40:12] [f57b281e621ed7dff28b90886f5aa97c]
- RMP                   [ARIMA Forecasting] [] [2009-12-11 11:25:10] [4d89445a8ea4b299af2ee123046cffa6] [Current]
-                         [ARIMA Forecasting] [] [2009-12-11 11:37:19] [1eac2882020791f6c49a90a91c34285a]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.4
97
105.4
102.7
98.1
104.5
87.4
89.9
109.8
111.7
98.6
96.9
95.1
97
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3

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=65999&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=65999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65999&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[47])
35108.8-------
36102.3-------
3799-------
38100.7-------
39115.5-------
40100.7-------
41109.9-------
42114.6-------
4385.4-------
44100.5-------
45114.8-------
46116.5-------
47112.9-------
48102106.784798.4193115.150.13110.0760.85330.076
49106103.825795.46112.19140.30520.66560.87090.0168
50105.3103.637294.6886112.58580.35790.30240.740.0212
51118.8118.7052109.3996128.01070.4920.99760.75020.8893
52106.1103.292293.9151112.66930.27866e-040.7060.0223
53109.3112.0097102.4318121.58750.28960.88670.6670.4277
54117.2116.5653106.9104126.22030.44870.92990.6550.7716
5592.586.99277.275796.70830.133300.62590
56104.2101.8992.1159111.66410.32160.97010.60980.0136
57112.5116.0051106.1996125.81060.24180.99090.59520.7326
58122.4117.5136107.6805127.34670.1650.84120.58010.8211
59113.3113.7821103.9293123.63490.46180.04320.56960.5696

\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[47]) \tabularnewline
35 & 108.8 & - & - & - & - & - & - & - \tabularnewline
36 & 102.3 & - & - & - & - & - & - & - \tabularnewline
37 & 99 & - & - & - & - & - & - & - \tabularnewline
38 & 100.7 & - & - & - & - & - & - & - \tabularnewline
39 & 115.5 & - & - & - & - & - & - & - \tabularnewline
40 & 100.7 & - & - & - & - & - & - & - \tabularnewline
41 & 109.9 & - & - & - & - & - & - & - \tabularnewline
42 & 114.6 & - & - & - & - & - & - & - \tabularnewline
43 & 85.4 & - & - & - & - & - & - & - \tabularnewline
44 & 100.5 & - & - & - & - & - & - & - \tabularnewline
45 & 114.8 & - & - & - & - & - & - & - \tabularnewline
46 & 116.5 & - & - & - & - & - & - & - \tabularnewline
47 & 112.9 & - & - & - & - & - & - & - \tabularnewline
48 & 102 & 106.7847 & 98.4193 & 115.15 & 0.1311 & 0.076 & 0.8533 & 0.076 \tabularnewline
49 & 106 & 103.8257 & 95.46 & 112.1914 & 0.3052 & 0.6656 & 0.8709 & 0.0168 \tabularnewline
50 & 105.3 & 103.6372 & 94.6886 & 112.5858 & 0.3579 & 0.3024 & 0.74 & 0.0212 \tabularnewline
51 & 118.8 & 118.7052 & 109.3996 & 128.0107 & 0.492 & 0.9976 & 0.7502 & 0.8893 \tabularnewline
52 & 106.1 & 103.2922 & 93.9151 & 112.6693 & 0.2786 & 6e-04 & 0.706 & 0.0223 \tabularnewline
53 & 109.3 & 112.0097 & 102.4318 & 121.5875 & 0.2896 & 0.8867 & 0.667 & 0.4277 \tabularnewline
54 & 117.2 & 116.5653 & 106.9104 & 126.2203 & 0.4487 & 0.9299 & 0.655 & 0.7716 \tabularnewline
55 & 92.5 & 86.992 & 77.2757 & 96.7083 & 0.1333 & 0 & 0.6259 & 0 \tabularnewline
56 & 104.2 & 101.89 & 92.1159 & 111.6641 & 0.3216 & 0.9701 & 0.6098 & 0.0136 \tabularnewline
57 & 112.5 & 116.0051 & 106.1996 & 125.8106 & 0.2418 & 0.9909 & 0.5952 & 0.7326 \tabularnewline
58 & 122.4 & 117.5136 & 107.6805 & 127.3467 & 0.165 & 0.8412 & 0.5801 & 0.8211 \tabularnewline
59 & 113.3 & 113.7821 & 103.9293 & 123.6349 & 0.4618 & 0.0432 & 0.5696 & 0.5696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65999&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[47])[/C][/ROW]
[ROW][C]35[/C][C]108.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]102.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]99[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]100.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]115.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]100.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]109.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]114.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]85.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]100.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]114.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]116.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]112.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]106.7847[/C][C]98.4193[/C][C]115.15[/C][C]0.1311[/C][C]0.076[/C][C]0.8533[/C][C]0.076[/C][/ROW]
[ROW][C]49[/C][C]106[/C][C]103.8257[/C][C]95.46[/C][C]112.1914[/C][C]0.3052[/C][C]0.6656[/C][C]0.8709[/C][C]0.0168[/C][/ROW]
[ROW][C]50[/C][C]105.3[/C][C]103.6372[/C][C]94.6886[/C][C]112.5858[/C][C]0.3579[/C][C]0.3024[/C][C]0.74[/C][C]0.0212[/C][/ROW]
[ROW][C]51[/C][C]118.8[/C][C]118.7052[/C][C]109.3996[/C][C]128.0107[/C][C]0.492[/C][C]0.9976[/C][C]0.7502[/C][C]0.8893[/C][/ROW]
[ROW][C]52[/C][C]106.1[/C][C]103.2922[/C][C]93.9151[/C][C]112.6693[/C][C]0.2786[/C][C]6e-04[/C][C]0.706[/C][C]0.0223[/C][/ROW]
[ROW][C]53[/C][C]109.3[/C][C]112.0097[/C][C]102.4318[/C][C]121.5875[/C][C]0.2896[/C][C]0.8867[/C][C]0.667[/C][C]0.4277[/C][/ROW]
[ROW][C]54[/C][C]117.2[/C][C]116.5653[/C][C]106.9104[/C][C]126.2203[/C][C]0.4487[/C][C]0.9299[/C][C]0.655[/C][C]0.7716[/C][/ROW]
[ROW][C]55[/C][C]92.5[/C][C]86.992[/C][C]77.2757[/C][C]96.7083[/C][C]0.1333[/C][C]0[/C][C]0.6259[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]104.2[/C][C]101.89[/C][C]92.1159[/C][C]111.6641[/C][C]0.3216[/C][C]0.9701[/C][C]0.6098[/C][C]0.0136[/C][/ROW]
[ROW][C]57[/C][C]112.5[/C][C]116.0051[/C][C]106.1996[/C][C]125.8106[/C][C]0.2418[/C][C]0.9909[/C][C]0.5952[/C][C]0.7326[/C][/ROW]
[ROW][C]58[/C][C]122.4[/C][C]117.5136[/C][C]107.6805[/C][C]127.3467[/C][C]0.165[/C][C]0.8412[/C][C]0.5801[/C][C]0.8211[/C][/ROW]
[ROW][C]59[/C][C]113.3[/C][C]113.7821[/C][C]103.9293[/C][C]123.6349[/C][C]0.4618[/C][C]0.0432[/C][C]0.5696[/C][C]0.5696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65999&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[47])
35108.8-------
36102.3-------
3799-------
38100.7-------
39115.5-------
40100.7-------
41109.9-------
42114.6-------
4385.4-------
44100.5-------
45114.8-------
46116.5-------
47112.9-------
48102106.784798.4193115.150.13110.0760.85330.076
49106103.825795.46112.19140.30520.66560.87090.0168
50105.3103.637294.6886112.58580.35790.30240.740.0212
51118.8118.7052109.3996128.01070.4920.99760.75020.8893
52106.1103.292293.9151112.66930.27866e-040.7060.0223
53109.3112.0097102.4318121.58750.28960.88670.6670.4277
54117.2116.5653106.9104126.22030.44870.92990.6550.7716
5592.586.99277.275796.70830.133300.62590
56104.2101.8992.1159111.66410.32160.97010.60980.0136
57112.5116.0051106.1996125.81060.24180.99090.59520.7326
58122.4117.5136107.6805127.34670.1650.84120.58010.8211
59113.3113.7821103.9293123.63490.46180.04320.56960.5696






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
480.04-0.0448022.893200
490.04110.02090.03294.727513.81043.7162
500.04410.0160.02732.764910.12853.1825
510.048e-040.02060.0097.59872.7566
520.04630.02720.0227.8847.65572.7669
530.0436-0.02420.02237.34227.60352.7574
540.04230.00540.01990.40286.57482.5641
550.0570.06330.025330.33839.54523.0895
560.04890.02270.0255.3369.07753.0129
570.0431-0.03020.025612.28599.39843.0657
580.04270.04160.02723.877210.71463.2733
590.0442-0.00420.02510.23249.84113.1371

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
48 & 0.04 & -0.0448 & 0 & 22.8932 & 0 & 0 \tabularnewline
49 & 0.0411 & 0.0209 & 0.0329 & 4.7275 & 13.8104 & 3.7162 \tabularnewline
50 & 0.0441 & 0.016 & 0.0273 & 2.7649 & 10.1285 & 3.1825 \tabularnewline
51 & 0.04 & 8e-04 & 0.0206 & 0.009 & 7.5987 & 2.7566 \tabularnewline
52 & 0.0463 & 0.0272 & 0.022 & 7.884 & 7.6557 & 2.7669 \tabularnewline
53 & 0.0436 & -0.0242 & 0.0223 & 7.3422 & 7.6035 & 2.7574 \tabularnewline
54 & 0.0423 & 0.0054 & 0.0199 & 0.4028 & 6.5748 & 2.5641 \tabularnewline
55 & 0.057 & 0.0633 & 0.0253 & 30.3383 & 9.5452 & 3.0895 \tabularnewline
56 & 0.0489 & 0.0227 & 0.025 & 5.336 & 9.0775 & 3.0129 \tabularnewline
57 & 0.0431 & -0.0302 & 0.0256 & 12.2859 & 9.3984 & 3.0657 \tabularnewline
58 & 0.0427 & 0.0416 & 0.027 & 23.8772 & 10.7146 & 3.2733 \tabularnewline
59 & 0.0442 & -0.0042 & 0.0251 & 0.2324 & 9.8411 & 3.1371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65999&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]48[/C][C]0.04[/C][C]-0.0448[/C][C]0[/C][C]22.8932[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]0.0411[/C][C]0.0209[/C][C]0.0329[/C][C]4.7275[/C][C]13.8104[/C][C]3.7162[/C][/ROW]
[ROW][C]50[/C][C]0.0441[/C][C]0.016[/C][C]0.0273[/C][C]2.7649[/C][C]10.1285[/C][C]3.1825[/C][/ROW]
[ROW][C]51[/C][C]0.04[/C][C]8e-04[/C][C]0.0206[/C][C]0.009[/C][C]7.5987[/C][C]2.7566[/C][/ROW]
[ROW][C]52[/C][C]0.0463[/C][C]0.0272[/C][C]0.022[/C][C]7.884[/C][C]7.6557[/C][C]2.7669[/C][/ROW]
[ROW][C]53[/C][C]0.0436[/C][C]-0.0242[/C][C]0.0223[/C][C]7.3422[/C][C]7.6035[/C][C]2.7574[/C][/ROW]
[ROW][C]54[/C][C]0.0423[/C][C]0.0054[/C][C]0.0199[/C][C]0.4028[/C][C]6.5748[/C][C]2.5641[/C][/ROW]
[ROW][C]55[/C][C]0.057[/C][C]0.0633[/C][C]0.0253[/C][C]30.3383[/C][C]9.5452[/C][C]3.0895[/C][/ROW]
[ROW][C]56[/C][C]0.0489[/C][C]0.0227[/C][C]0.025[/C][C]5.336[/C][C]9.0775[/C][C]3.0129[/C][/ROW]
[ROW][C]57[/C][C]0.0431[/C][C]-0.0302[/C][C]0.0256[/C][C]12.2859[/C][C]9.3984[/C][C]3.0657[/C][/ROW]
[ROW][C]58[/C][C]0.0427[/C][C]0.0416[/C][C]0.027[/C][C]23.8772[/C][C]10.7146[/C][C]3.2733[/C][/ROW]
[ROW][C]59[/C][C]0.0442[/C][C]-0.0042[/C][C]0.0251[/C][C]0.2324[/C][C]9.8411[/C][C]3.1371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65999&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65999&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
480.04-0.0448022.893200
490.04110.02090.03294.727513.81043.7162
500.04410.0160.02732.764910.12853.1825
510.048e-040.02060.0097.59872.7566
520.04630.02720.0227.8847.65572.7669
530.0436-0.02420.02237.34227.60352.7574
540.04230.00540.01990.40286.57482.5641
550.0570.06330.025330.33839.54523.0895
560.04890.02270.0255.3369.07753.0129
570.0431-0.03020.025612.28599.39843.0657
580.04270.04160.02723.877210.71463.2733
590.0442-0.00420.02510.23249.84113.1371


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; 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')