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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, 03 Dec 2010 14:30:36 +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/03/t1291386567v1beq8pirt6whx8.htm/, Retrieved Tue, 07 May 2024 19:39:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104825, Retrieved Tue, 07 May 2024 19:39:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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] [] [2010-12-03 14:30:36] [df17410ebb98883e83037e1662207ccb] [Current]
- RMPD          [ARIMA Backward Selection] [] [2010-12-14 13:02:35] [9b13650c94c5192ca5135ec8a1fa39f7]
-   PD          [ARIMA Forecasting] [] [2010-12-14 13:04:06] [9b13650c94c5192ca5135ec8a1fa39f7]
- RMPD          [ARIMA Backward Selection] [] [2010-12-17 09:15:50] [8a9a6f7c332640af31ddca253a8ded58]
-   PD          [ARIMA Forecasting] [] [2010-12-17 09:23:13] [8a9a6f7c332640af31ddca253a8ded58]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,76
102,37
102,38
102,86
102,87
102,92
102,95
103,02
104,08
104,16
104,24
104,33
104,73
104,86
105,03
105,62
105,63
105,63
105,94
106,61
107,69
107,78
107,93
108,48
108,14
108,48
108,48
108,89
108,93
109,21
109,47
109,80
111,73
111,85
112,12
112,15
112,17
112,67
112,80
113,44
113,53
114,53
114,51
115,05
116,67
117,07
116,92
117,00
117,02
117,35
117,36
117,82
117,88
118,24
118,50
118,80
119,76
120,09

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104825&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]3 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=104825&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104825&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 time3 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])
34111.85-------
35112.12-------
36112.15-------
37112.17-------
38112.67-------
39112.8-------
40113.44-------
41113.53-------
42114.53-------
43114.51-------
44115.05-------
45116.67-------
46117.07-------
47116.92117.3186116.7516117.88560.08410.804910.8049
48117117.6293116.9171118.34140.04170.974510.9381
49117.02117.7054116.8411118.56970.060.945210.9252
50117.35118.2363117.2381119.23460.04090.991510.989
51117.36118.4393117.313119.56570.03020.97110.9914
52117.82119.1107117.8621120.35930.02140.99710.9993
53117.88119.2816117.9145120.64870.02220.981910.9992
54118.24119.9817118.499121.46430.01070.997310.9999
55118.5120.1967118.6008121.79260.01860.991910.9999
56118.8120.7696119.0623122.4770.01190.995411
57119.76122.4554120.638124.27270.0018111
58120.09122.8228120.8967124.7490.00270.999111

\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 & 111.85 & - & - & - & - & - & - & - \tabularnewline
35 & 112.12 & - & - & - & - & - & - & - \tabularnewline
36 & 112.15 & - & - & - & - & - & - & - \tabularnewline
37 & 112.17 & - & - & - & - & - & - & - \tabularnewline
38 & 112.67 & - & - & - & - & - & - & - \tabularnewline
39 & 112.8 & - & - & - & - & - & - & - \tabularnewline
40 & 113.44 & - & - & - & - & - & - & - \tabularnewline
41 & 113.53 & - & - & - & - & - & - & - \tabularnewline
42 & 114.53 & - & - & - & - & - & - & - \tabularnewline
43 & 114.51 & - & - & - & - & - & - & - \tabularnewline
44 & 115.05 & - & - & - & - & - & - & - \tabularnewline
45 & 116.67 & - & - & - & - & - & - & - \tabularnewline
46 & 117.07 & - & - & - & - & - & - & - \tabularnewline
47 & 116.92 & 117.3186 & 116.7516 & 117.8856 & 0.0841 & 0.8049 & 1 & 0.8049 \tabularnewline
48 & 117 & 117.6293 & 116.9171 & 118.3414 & 0.0417 & 0.9745 & 1 & 0.9381 \tabularnewline
49 & 117.02 & 117.7054 & 116.8411 & 118.5697 & 0.06 & 0.9452 & 1 & 0.9252 \tabularnewline
50 & 117.35 & 118.2363 & 117.2381 & 119.2346 & 0.0409 & 0.9915 & 1 & 0.989 \tabularnewline
51 & 117.36 & 118.4393 & 117.313 & 119.5657 & 0.0302 & 0.971 & 1 & 0.9914 \tabularnewline
52 & 117.82 & 119.1107 & 117.8621 & 120.3593 & 0.0214 & 0.997 & 1 & 0.9993 \tabularnewline
53 & 117.88 & 119.2816 & 117.9145 & 120.6487 & 0.0222 & 0.9819 & 1 & 0.9992 \tabularnewline
54 & 118.24 & 119.9817 & 118.499 & 121.4643 & 0.0107 & 0.9973 & 1 & 0.9999 \tabularnewline
55 & 118.5 & 120.1967 & 118.6008 & 121.7926 & 0.0186 & 0.9919 & 1 & 0.9999 \tabularnewline
56 & 118.8 & 120.7696 & 119.0623 & 122.477 & 0.0119 & 0.9954 & 1 & 1 \tabularnewline
57 & 119.76 & 122.4554 & 120.638 & 124.2727 & 0.0018 & 1 & 1 & 1 \tabularnewline
58 & 120.09 & 122.8228 & 120.8967 & 124.749 & 0.0027 & 0.9991 & 1 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104825&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]111.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]35[/C][C]112.12[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]112.15[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]112.17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]112.67[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]112.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]113.44[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]113.53[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]114.53[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]114.51[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]115.05[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]116.67[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]117.07[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]116.92[/C][C]117.3186[/C][C]116.7516[/C][C]117.8856[/C][C]0.0841[/C][C]0.8049[/C][C]1[/C][C]0.8049[/C][/ROW]
[ROW][C]48[/C][C]117[/C][C]117.6293[/C][C]116.9171[/C][C]118.3414[/C][C]0.0417[/C][C]0.9745[/C][C]1[/C][C]0.9381[/C][/ROW]
[ROW][C]49[/C][C]117.02[/C][C]117.7054[/C][C]116.8411[/C][C]118.5697[/C][C]0.06[/C][C]0.9452[/C][C]1[/C][C]0.9252[/C][/ROW]
[ROW][C]50[/C][C]117.35[/C][C]118.2363[/C][C]117.2381[/C][C]119.2346[/C][C]0.0409[/C][C]0.9915[/C][C]1[/C][C]0.989[/C][/ROW]
[ROW][C]51[/C][C]117.36[/C][C]118.4393[/C][C]117.313[/C][C]119.5657[/C][C]0.0302[/C][C]0.971[/C][C]1[/C][C]0.9914[/C][/ROW]
[ROW][C]52[/C][C]117.82[/C][C]119.1107[/C][C]117.8621[/C][C]120.3593[/C][C]0.0214[/C][C]0.997[/C][C]1[/C][C]0.9993[/C][/ROW]
[ROW][C]53[/C][C]117.88[/C][C]119.2816[/C][C]117.9145[/C][C]120.6487[/C][C]0.0222[/C][C]0.9819[/C][C]1[/C][C]0.9992[/C][/ROW]
[ROW][C]54[/C][C]118.24[/C][C]119.9817[/C][C]118.499[/C][C]121.4643[/C][C]0.0107[/C][C]0.9973[/C][C]1[/C][C]0.9999[/C][/ROW]
[ROW][C]55[/C][C]118.5[/C][C]120.1967[/C][C]118.6008[/C][C]121.7926[/C][C]0.0186[/C][C]0.9919[/C][C]1[/C][C]0.9999[/C][/ROW]
[ROW][C]56[/C][C]118.8[/C][C]120.7696[/C][C]119.0623[/C][C]122.477[/C][C]0.0119[/C][C]0.9954[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]57[/C][C]119.76[/C][C]122.4554[/C][C]120.638[/C][C]124.2727[/C][C]0.0018[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]58[/C][C]120.09[/C][C]122.8228[/C][C]120.8967[/C][C]124.749[/C][C]0.0027[/C][C]0.9991[/C][C]1[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104825&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104825&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])
34111.85-------
35112.12-------
36112.15-------
37112.17-------
38112.67-------
39112.8-------
40113.44-------
41113.53-------
42114.53-------
43114.51-------
44115.05-------
45116.67-------
46117.07-------
47116.92117.3186116.7516117.88560.08410.804910.8049
48117117.6293116.9171118.34140.04170.974510.9381
49117.02117.7054116.8411118.56970.060.945210.9252
50117.35118.2363117.2381119.23460.04090.991510.989
51117.36118.4393117.313119.56570.03020.97110.9914
52117.82119.1107117.8621120.35930.02140.99710.9993
53117.88119.2816117.9145120.64870.02220.981910.9992
54118.24119.9817118.499121.46430.01070.997310.9999
55118.5120.1967118.6008121.79260.01860.991910.9999
56118.8120.7696119.0623122.4770.01190.995411
57119.76122.4554120.638124.27270.0018111
58120.09122.8228120.8967124.7490.00270.999111






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
470.0025-0.003400.158900
480.0031-0.00530.00440.3960.27740.5267
490.0037-0.00580.00490.46980.34160.5844
500.0043-0.00750.00550.78560.45260.6727
510.0049-0.00910.00621.1650.5950.7714
520.0053-0.01080.0071.6660.77350.8795
530.0058-0.01180.00771.96450.94370.9714
540.0063-0.01450.00853.03341.20491.0977
550.0068-0.01410.00922.87881.39091.1794
560.0072-0.01630.00993.87951.63971.2805
570.0076-0.0220.0117.2652.15111.4667
580.008-0.02230.01197.46832.59421.6107

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
47 & 0.0025 & -0.0034 & 0 & 0.1589 & 0 & 0 \tabularnewline
48 & 0.0031 & -0.0053 & 0.0044 & 0.396 & 0.2774 & 0.5267 \tabularnewline
49 & 0.0037 & -0.0058 & 0.0049 & 0.4698 & 0.3416 & 0.5844 \tabularnewline
50 & 0.0043 & -0.0075 & 0.0055 & 0.7856 & 0.4526 & 0.6727 \tabularnewline
51 & 0.0049 & -0.0091 & 0.0062 & 1.165 & 0.595 & 0.7714 \tabularnewline
52 & 0.0053 & -0.0108 & 0.007 & 1.666 & 0.7735 & 0.8795 \tabularnewline
53 & 0.0058 & -0.0118 & 0.0077 & 1.9645 & 0.9437 & 0.9714 \tabularnewline
54 & 0.0063 & -0.0145 & 0.0085 & 3.0334 & 1.2049 & 1.0977 \tabularnewline
55 & 0.0068 & -0.0141 & 0.0092 & 2.8788 & 1.3909 & 1.1794 \tabularnewline
56 & 0.0072 & -0.0163 & 0.0099 & 3.8795 & 1.6397 & 1.2805 \tabularnewline
57 & 0.0076 & -0.022 & 0.011 & 7.265 & 2.1511 & 1.4667 \tabularnewline
58 & 0.008 & -0.0223 & 0.0119 & 7.4683 & 2.5942 & 1.6107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104825&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]0.0025[/C][C]-0.0034[/C][C]0[/C][C]0.1589[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]0.0031[/C][C]-0.0053[/C][C]0.0044[/C][C]0.396[/C][C]0.2774[/C][C]0.5267[/C][/ROW]
[ROW][C]49[/C][C]0.0037[/C][C]-0.0058[/C][C]0.0049[/C][C]0.4698[/C][C]0.3416[/C][C]0.5844[/C][/ROW]
[ROW][C]50[/C][C]0.0043[/C][C]-0.0075[/C][C]0.0055[/C][C]0.7856[/C][C]0.4526[/C][C]0.6727[/C][/ROW]
[ROW][C]51[/C][C]0.0049[/C][C]-0.0091[/C][C]0.0062[/C][C]1.165[/C][C]0.595[/C][C]0.7714[/C][/ROW]
[ROW][C]52[/C][C]0.0053[/C][C]-0.0108[/C][C]0.007[/C][C]1.666[/C][C]0.7735[/C][C]0.8795[/C][/ROW]
[ROW][C]53[/C][C]0.0058[/C][C]-0.0118[/C][C]0.0077[/C][C]1.9645[/C][C]0.9437[/C][C]0.9714[/C][/ROW]
[ROW][C]54[/C][C]0.0063[/C][C]-0.0145[/C][C]0.0085[/C][C]3.0334[/C][C]1.2049[/C][C]1.0977[/C][/ROW]
[ROW][C]55[/C][C]0.0068[/C][C]-0.0141[/C][C]0.0092[/C][C]2.8788[/C][C]1.3909[/C][C]1.1794[/C][/ROW]
[ROW][C]56[/C][C]0.0072[/C][C]-0.0163[/C][C]0.0099[/C][C]3.8795[/C][C]1.6397[/C][C]1.2805[/C][/ROW]
[ROW][C]57[/C][C]0.0076[/C][C]-0.022[/C][C]0.011[/C][C]7.265[/C][C]2.1511[/C][C]1.4667[/C][/ROW]
[ROW][C]58[/C][C]0.008[/C][C]-0.0223[/C][C]0.0119[/C][C]7.4683[/C][C]2.5942[/C][C]1.6107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104825&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104825&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
470.0025-0.003400.158900
480.0031-0.00530.00440.3960.27740.5267
490.0037-0.00580.00490.46980.34160.5844
500.0043-0.00750.00550.78560.45260.6727
510.0049-0.00910.00621.1650.5950.7714
520.0053-0.01080.0071.6660.77350.8795
530.0058-0.01180.00771.96450.94370.9714
540.0063-0.01450.00853.03341.20491.0977
550.0068-0.01410.00922.87881.39091.1794
560.0072-0.01630.00993.87951.63971.2805
570.0076-0.0220.0117.2652.15111.4667
580.008-0.02230.01197.46832.59421.6107


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; 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')