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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 computationMon, 13 Dec 2010 10:48:48 +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/13/t1292237272f9yj56gbmp68prg.htm/, Retrieved Mon, 06 May 2024 23:33:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108820, Retrieved Mon, 06 May 2024 23:33:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2010-12-13 08:35:23] [21eff0c210342db4afbdafe426a7c254]
-   PD  [(Partial) Autocorrelation Function] [] [2010-12-13 09:29:04] [21eff0c210342db4afbdafe426a7c254]
-    D    [(Partial) Autocorrelation Function] [] [2010-12-13 10:05:17] [21eff0c210342db4afbdafe426a7c254]
- RM D        [ARIMA Forecasting] [] [2010-12-13 10:48:48] [81d69fb83507cea26168920232cdff1b] [Current]
-   P           [ARIMA Forecasting] [] [2010-12-13 20:48:40] [21eff0c210342db4afbdafe426a7c254]
- RMPD          [Univariate Data Series] [] [2010-12-13 20:53:52] [21eff0c210342db4afbdafe426a7c254]
- RMPD            [Histogram] [] [2010-12-14 14:33:39] [21eff0c210342db4afbdafe426a7c254]
- RMPD              [Univariate Explorative Data Analysis] [] [2010-12-16 14:06:01] [21eff0c210342db4afbdafe426a7c254]
- RMPD              [Univariate Data Series] [] [2010-12-16 14:19:11] [de4adef75375d243bafd27c3fb0ddf4c]
-   PD              [Histogram] [] [2010-12-16 14:23:25] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD              [Univariate Explorative Data Analysis] [] [2010-12-16 14:27:05] [de4adef75375d243bafd27c3fb0ddf4c]
-    D                [Univariate Explorative Data Analysis] [] [2010-12-20 18:48:19] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [(Partial) Autocorrelation Function] [] [2010-12-20 19:31:04] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [(Partial) Autocorrelation Function] [] [2010-12-20 19:46:13] [de4adef75375d243bafd27c3fb0ddf4c]
-   P                   [(Partial) Autocorrelation Function] [] [2010-12-21 15:20:18] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [Variance Reduction Matrix] [] [2010-12-20 20:00:09] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [Standard Deviation-Mean Plot] [] [2010-12-20 20:07:24] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [Spectral Analysis] [] [2010-12-20 20:14:04] [de4adef75375d243bafd27c3fb0ddf4c]
-   P                   [Spectral Analysis] [] [2010-12-21 16:58:39] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [Univariate Data Series] [] [2010-12-20 20:24:23] [de4adef75375d243bafd27c3fb0ddf4c]
-   PD                [Univariate Explorative Data Analysis] [] [2010-12-20 20:29:24] [de4adef75375d243bafd27c3fb0ddf4c]
-   P                   [Univariate Explorative Data Analysis] [] [2010-12-21 15:07:46] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [ARIMA Backward Selection] [] [2010-12-20 20:35:32] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [ARIMA Forecasting] [] [2010-12-20 20:44:58] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD              [Variance Reduction Matrix] [] [2010-12-16 14:36:01] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD          [Univariate Data Series] [] [2010-12-13 21:02:07] [21eff0c210342db4afbdafe426a7c254]
-   PD            [Univariate Data Series] [] [2010-12-20 19:00:31] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD            [Variance Reduction Matrix] [] [2010-12-20 19:12:17] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD          [Central Tendency] [] [2010-12-13 21:04:38] [21eff0c210342db4afbdafe426a7c254]
- RMPD          [Central Tendency] [] [2010-12-13 21:08:56] [21eff0c210342db4afbdafe426a7c254]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
113
95.4
86.2
111.7
97.5
99.7
111.5
91.8
86.3
88.7
95.1
105.1
104.5
89.1
82.6
102.7
91.8
94.1
103.1
93.2
91
94.3
99.4
115.7
116.8
99.8
96
115.9
109.1
117.3
109.8
112.8
110.7
100
113.3
122.4
112.5
104.2
92.5
117.2
109.3
106.1
118.8
105.3
106
102
112.9
116.5
114.8
100.5
85.4
114.6
109.9
100.7
115.5
100.7
99
102.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 7 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108820&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108820&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108820&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 time7 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






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[46])
34100-------
35113.3-------
36122.4-------
37112.5-------
38104.2-------
3992.5-------
40117.2-------
41109.3-------
42106.1-------
43118.8-------
44105.3-------
45106-------
46102-------
47112.9109.7559101.9707117.5410.21430.97460.18610.9746
48116.5123.6956115.2694132.12190.04710.9940.61841
49114.8116.4475106.9297125.96530.36720.49570.79190.9985
50100.5105.986694.0195117.95360.18440.07440.61510.7431
5185.498.885786.2721111.49920.01810.4010.83950.3142
52114.6118.4577104.3718132.54360.295710.56950.989
53109.9111.75396.1345127.37150.40810.36040.62090.8895
54100.7111.398294.8976127.89880.10190.57060.73540.8679
55115.5119.5596101.6042137.51510.32880.98020.5330.9724
56100.7112.955993.8391132.07270.10450.39710.78380.8693
5799112.905892.7507133.06080.08810.88240.74910.8556
58102.3111.439390.0486132.82990.20120.87280.80650.8065

\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[46]) \tabularnewline
34 & 100 & - & - & - & - & - & - & - \tabularnewline
35 & 113.3 & - & - & - & - & - & - & - \tabularnewline
36 & 122.4 & - & - & - & - & - & - & - \tabularnewline
37 & 112.5 & - & - & - & - & - & - & - \tabularnewline
38 & 104.2 & - & - & - & - & - & - & - \tabularnewline
39 & 92.5 & - & - & - & - & - & - & - \tabularnewline
40 & 117.2 & - & - & - & - & - & - & - \tabularnewline
41 & 109.3 & - & - & - & - & - & - & - \tabularnewline
42 & 106.1 & - & - & - & - & - & - & - \tabularnewline
43 & 118.8 & - & - & - & - & - & - & - \tabularnewline
44 & 105.3 & - & - & - & - & - & - & - \tabularnewline
45 & 106 & - & - & - & - & - & - & - \tabularnewline
46 & 102 & - & - & - & - & - & - & - \tabularnewline
47 & 112.9 & 109.7559 & 101.9707 & 117.541 & 0.2143 & 0.9746 & 0.1861 & 0.9746 \tabularnewline
48 & 116.5 & 123.6956 & 115.2694 & 132.1219 & 0.0471 & 0.994 & 0.6184 & 1 \tabularnewline
49 & 114.8 & 116.4475 & 106.9297 & 125.9653 & 0.3672 & 0.4957 & 0.7919 & 0.9985 \tabularnewline
50 & 100.5 & 105.9866 & 94.0195 & 117.9536 & 0.1844 & 0.0744 & 0.6151 & 0.7431 \tabularnewline
51 & 85.4 & 98.8857 & 86.2721 & 111.4992 & 0.0181 & 0.401 & 0.8395 & 0.3142 \tabularnewline
52 & 114.6 & 118.4577 & 104.3718 & 132.5436 & 0.2957 & 1 & 0.5695 & 0.989 \tabularnewline
53 & 109.9 & 111.753 & 96.1345 & 127.3715 & 0.4081 & 0.3604 & 0.6209 & 0.8895 \tabularnewline
54 & 100.7 & 111.3982 & 94.8976 & 127.8988 & 0.1019 & 0.5706 & 0.7354 & 0.8679 \tabularnewline
55 & 115.5 & 119.5596 & 101.6042 & 137.5151 & 0.3288 & 0.9802 & 0.533 & 0.9724 \tabularnewline
56 & 100.7 & 112.9559 & 93.8391 & 132.0727 & 0.1045 & 0.3971 & 0.7838 & 0.8693 \tabularnewline
57 & 99 & 112.9058 & 92.7507 & 133.0608 & 0.0881 & 0.8824 & 0.7491 & 0.8556 \tabularnewline
58 & 102.3 & 111.4393 & 90.0486 & 132.8299 & 0.2012 & 0.8728 & 0.8065 & 0.8065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108820&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[46])[/C][/ROW]
[ROW][C]34[/C][C]100[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]35[/C][C]113.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]122.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]112.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]104.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]92.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]117.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]109.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]106.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]118.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]105.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]106[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]102[/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]109.7559[/C][C]101.9707[/C][C]117.541[/C][C]0.2143[/C][C]0.9746[/C][C]0.1861[/C][C]0.9746[/C][/ROW]
[ROW][C]48[/C][C]116.5[/C][C]123.6956[/C][C]115.2694[/C][C]132.1219[/C][C]0.0471[/C][C]0.994[/C][C]0.6184[/C][C]1[/C][/ROW]
[ROW][C]49[/C][C]114.8[/C][C]116.4475[/C][C]106.9297[/C][C]125.9653[/C][C]0.3672[/C][C]0.4957[/C][C]0.7919[/C][C]0.9985[/C][/ROW]
[ROW][C]50[/C][C]100.5[/C][C]105.9866[/C][C]94.0195[/C][C]117.9536[/C][C]0.1844[/C][C]0.0744[/C][C]0.6151[/C][C]0.7431[/C][/ROW]
[ROW][C]51[/C][C]85.4[/C][C]98.8857[/C][C]86.2721[/C][C]111.4992[/C][C]0.0181[/C][C]0.401[/C][C]0.8395[/C][C]0.3142[/C][/ROW]
[ROW][C]52[/C][C]114.6[/C][C]118.4577[/C][C]104.3718[/C][C]132.5436[/C][C]0.2957[/C][C]1[/C][C]0.5695[/C][C]0.989[/C][/ROW]
[ROW][C]53[/C][C]109.9[/C][C]111.753[/C][C]96.1345[/C][C]127.3715[/C][C]0.4081[/C][C]0.3604[/C][C]0.6209[/C][C]0.8895[/C][/ROW]
[ROW][C]54[/C][C]100.7[/C][C]111.3982[/C][C]94.8976[/C][C]127.8988[/C][C]0.1019[/C][C]0.5706[/C][C]0.7354[/C][C]0.8679[/C][/ROW]
[ROW][C]55[/C][C]115.5[/C][C]119.5596[/C][C]101.6042[/C][C]137.5151[/C][C]0.3288[/C][C]0.9802[/C][C]0.533[/C][C]0.9724[/C][/ROW]
[ROW][C]56[/C][C]100.7[/C][C]112.9559[/C][C]93.8391[/C][C]132.0727[/C][C]0.1045[/C][C]0.3971[/C][C]0.7838[/C][C]0.8693[/C][/ROW]
[ROW][C]57[/C][C]99[/C][C]112.9058[/C][C]92.7507[/C][C]133.0608[/C][C]0.0881[/C][C]0.8824[/C][C]0.7491[/C][C]0.8556[/C][/ROW]
[ROW][C]58[/C][C]102.3[/C][C]111.4393[/C][C]90.0486[/C][C]132.8299[/C][C]0.2012[/C][C]0.8728[/C][C]0.8065[/C][C]0.8065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108820&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108820&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[46])
34100-------
35113.3-------
36122.4-------
37112.5-------
38104.2-------
3992.5-------
40117.2-------
41109.3-------
42106.1-------
43118.8-------
44105.3-------
45106-------
46102-------
47112.9109.7559101.9707117.5410.21430.97460.18610.9746
48116.5123.6956115.2694132.12190.04710.9940.61841
49114.8116.4475106.9297125.96530.36720.49570.79190.9985
50100.5105.986694.0195117.95360.18440.07440.61510.7431
5185.498.885786.2721111.49920.01810.4010.83950.3142
52114.6118.4577104.3718132.54360.295710.56950.989
53109.9111.75396.1345127.37150.40810.36040.62090.8895
54100.7111.398294.8976127.89880.10190.57060.73540.8679
55115.5119.5596101.6042137.51510.32880.98020.5330.9724
56100.7112.955993.8391132.07270.10450.39710.78380.8693
5799112.905892.7507133.06080.08810.88240.74910.8556
58102.3111.439390.0486132.82990.20120.87280.80650.8065






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
470.03620.028609.885600
480.0348-0.05820.043451.777230.83145.5526
490.0417-0.01410.03372.714221.4594.6324
500.0576-0.05180.038230.102423.61994.86
510.0651-0.13640.0578181.863555.26867.4343
520.0607-0.03260.053614.882148.53756.9669
530.0713-0.01660.04833.433642.09416.488
540.0756-0.0960.0543114.451351.13877.1511
550.0766-0.0340.05216.480847.28796.8766
560.0863-0.10850.0577150.206657.57977.5881
570.0911-0.12320.0636193.370169.92438.3621
580.0979-0.0820.065283.526471.05788.4296

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
47 & 0.0362 & 0.0286 & 0 & 9.8856 & 0 & 0 \tabularnewline
48 & 0.0348 & -0.0582 & 0.0434 & 51.7772 & 30.8314 & 5.5526 \tabularnewline
49 & 0.0417 & -0.0141 & 0.0337 & 2.7142 & 21.459 & 4.6324 \tabularnewline
50 & 0.0576 & -0.0518 & 0.0382 & 30.1024 & 23.6199 & 4.86 \tabularnewline
51 & 0.0651 & -0.1364 & 0.0578 & 181.8635 & 55.2686 & 7.4343 \tabularnewline
52 & 0.0607 & -0.0326 & 0.0536 & 14.8821 & 48.5375 & 6.9669 \tabularnewline
53 & 0.0713 & -0.0166 & 0.0483 & 3.4336 & 42.0941 & 6.488 \tabularnewline
54 & 0.0756 & -0.096 & 0.0543 & 114.4513 & 51.1387 & 7.1511 \tabularnewline
55 & 0.0766 & -0.034 & 0.052 & 16.4808 & 47.2879 & 6.8766 \tabularnewline
56 & 0.0863 & -0.1085 & 0.0577 & 150.2066 & 57.5797 & 7.5881 \tabularnewline
57 & 0.0911 & -0.1232 & 0.0636 & 193.3701 & 69.9243 & 8.3621 \tabularnewline
58 & 0.0979 & -0.082 & 0.0652 & 83.5264 & 71.0578 & 8.4296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108820&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]47[/C][C]0.0362[/C][C]0.0286[/C][C]0[/C][C]9.8856[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]0.0348[/C][C]-0.0582[/C][C]0.0434[/C][C]51.7772[/C][C]30.8314[/C][C]5.5526[/C][/ROW]
[ROW][C]49[/C][C]0.0417[/C][C]-0.0141[/C][C]0.0337[/C][C]2.7142[/C][C]21.459[/C][C]4.6324[/C][/ROW]
[ROW][C]50[/C][C]0.0576[/C][C]-0.0518[/C][C]0.0382[/C][C]30.1024[/C][C]23.6199[/C][C]4.86[/C][/ROW]
[ROW][C]51[/C][C]0.0651[/C][C]-0.1364[/C][C]0.0578[/C][C]181.8635[/C][C]55.2686[/C][C]7.4343[/C][/ROW]
[ROW][C]52[/C][C]0.0607[/C][C]-0.0326[/C][C]0.0536[/C][C]14.8821[/C][C]48.5375[/C][C]6.9669[/C][/ROW]
[ROW][C]53[/C][C]0.0713[/C][C]-0.0166[/C][C]0.0483[/C][C]3.4336[/C][C]42.0941[/C][C]6.488[/C][/ROW]
[ROW][C]54[/C][C]0.0756[/C][C]-0.096[/C][C]0.0543[/C][C]114.4513[/C][C]51.1387[/C][C]7.1511[/C][/ROW]
[ROW][C]55[/C][C]0.0766[/C][C]-0.034[/C][C]0.052[/C][C]16.4808[/C][C]47.2879[/C][C]6.8766[/C][/ROW]
[ROW][C]56[/C][C]0.0863[/C][C]-0.1085[/C][C]0.0577[/C][C]150.2066[/C][C]57.5797[/C][C]7.5881[/C][/ROW]
[ROW][C]57[/C][C]0.0911[/C][C]-0.1232[/C][C]0.0636[/C][C]193.3701[/C][C]69.9243[/C][C]8.3621[/C][/ROW]
[ROW][C]58[/C][C]0.0979[/C][C]-0.082[/C][C]0.0652[/C][C]83.5264[/C][C]71.0578[/C][C]8.4296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108820&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108820&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
470.03620.028609.885600
480.0348-0.05820.043451.777230.83145.5526
490.0417-0.01410.03372.714221.4594.6324
500.0576-0.05180.038230.102423.61994.86
510.0651-0.13640.0578181.863555.26867.4343
520.0607-0.03260.053614.882148.53756.9669
530.0713-0.01660.04833.433642.09416.488
540.0756-0.0960.0543114.451351.13877.1511
550.0766-0.0340.05216.480847.28796.8766
560.0863-0.10850.0577150.206657.57977.5881
570.0911-0.12320.0636193.370169.92438.3621
580.0979-0.0820.065283.526471.05788.4296


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; 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')