FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 23 Dec 2016 11:43:21 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/23/t1482489858h7pzbr8jewm512f.htm/, Retrieved Thu, 03 Apr 2025 03:50:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302852, Retrieved Thu, 03 Apr 2025 03:50:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Forecasting] [ARIMA FORECAST] [2016-12-23 10:43:21] [1e1af2256d87dfd5401e4c69cd3b64ca] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2300
2140
2760
1900
3140
2160
2060
3480
3340
3180
2800
2780
4180
2820
3500
3860
4040
2900
4400
3680
2960
4020
3360
3480
4820
3100
3200
3400
4320
4040
3600
3880
3140
3340
3540
4800
5400
3680
5860
4000
4380
4080
4780
4180
4060
4620
4320
4800
4760
4780
6260

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302852&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302852&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






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[51])
395860-------
404000-------
414380-------
424080-------
434780-------
444180-------
454060-------
464620-------
474320-------
484800-------
494760-------
504780-------
516260-------
52NA3724.25892263.40675185.1111NA3e-040.35573e-04
53NA4820.08943280.21446359.9644NANA0.71230.0334
54NA4451.61462910.82075992.4085NANA0.68180.0107
55NA4730.1523026.21536434.0888NANA0.47710.0392
56NA4360.42492588.18036132.6694NANA0.57910.0178
57NA4313.68682536.28796091.0857NANA0.61020.0159
58NA4665.62412847.98826483.26NANA0.51960.0428
59NA4408.42072554.38416262.4572NANA0.53720.0252
60NA4955.64963094.50136816.7979NANA0.56510.0848
61NA4828.58412954.34286702.8255NANA0.52860.0672
62NA4836.4012945.78156727.0205NANA0.52330.07
63NA6353.18374456.67978249.6878NANA0.53840.5384
64NA3786.14051301.61846270.6626NANANA0.0255
65NA4862.56632294.24627430.8864NANANA0.1431
66NA4508.74991934.59157082.9084NANANA0.0912
67NA4777.63382073.27747481.9901NANANA0.1413
68NA4393.68191624.47737162.8864NANANA0.0933
69NA4350.41081572.06597128.7557NANANA0.089
70NA4699.63531884.43857514.832NANANA0.1387
71NA4434.00251584.80667283.1985NANANA0.1045
72NA4980.39522122.13957838.6509NANANA0.1901
73NA4852.29491980.84697723.7429NANANA0.1683
74NA4855.52361968.56867742.4785NANANA0.1702
75NA6370.42713476.87879263.9754NANANA0.5298

\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[51]) \tabularnewline
39 & 5860 & - & - & - & - & - & - & - \tabularnewline
40 & 4000 & - & - & - & - & - & - & - \tabularnewline
41 & 4380 & - & - & - & - & - & - & - \tabularnewline
42 & 4080 & - & - & - & - & - & - & - \tabularnewline
43 & 4780 & - & - & - & - & - & - & - \tabularnewline
44 & 4180 & - & - & - & - & - & - & - \tabularnewline
45 & 4060 & - & - & - & - & - & - & - \tabularnewline
46 & 4620 & - & - & - & - & - & - & - \tabularnewline
47 & 4320 & - & - & - & - & - & - & - \tabularnewline
48 & 4800 & - & - & - & - & - & - & - \tabularnewline
49 & 4760 & - & - & - & - & - & - & - \tabularnewline
50 & 4780 & - & - & - & - & - & - & - \tabularnewline
51 & 6260 & - & - & - & - & - & - & - \tabularnewline
52 & NA & 3724.2589 & 2263.4067 & 5185.1111 & NA & 3e-04 & 0.3557 & 3e-04 \tabularnewline
53 & NA & 4820.0894 & 3280.2144 & 6359.9644 & NA & NA & 0.7123 & 0.0334 \tabularnewline
54 & NA & 4451.6146 & 2910.8207 & 5992.4085 & NA & NA & 0.6818 & 0.0107 \tabularnewline
55 & NA & 4730.152 & 3026.2153 & 6434.0888 & NA & NA & 0.4771 & 0.0392 \tabularnewline
56 & NA & 4360.4249 & 2588.1803 & 6132.6694 & NA & NA & 0.5791 & 0.0178 \tabularnewline
57 & NA & 4313.6868 & 2536.2879 & 6091.0857 & NA & NA & 0.6102 & 0.0159 \tabularnewline
58 & NA & 4665.6241 & 2847.9882 & 6483.26 & NA & NA & 0.5196 & 0.0428 \tabularnewline
59 & NA & 4408.4207 & 2554.3841 & 6262.4572 & NA & NA & 0.5372 & 0.0252 \tabularnewline
60 & NA & 4955.6496 & 3094.5013 & 6816.7979 & NA & NA & 0.5651 & 0.0848 \tabularnewline
61 & NA & 4828.5841 & 2954.3428 & 6702.8255 & NA & NA & 0.5286 & 0.0672 \tabularnewline
62 & NA & 4836.401 & 2945.7815 & 6727.0205 & NA & NA & 0.5233 & 0.07 \tabularnewline
63 & NA & 6353.1837 & 4456.6797 & 8249.6878 & NA & NA & 0.5384 & 0.5384 \tabularnewline
64 & NA & 3786.1405 & 1301.6184 & 6270.6626 & NA & NA & NA & 0.0255 \tabularnewline
65 & NA & 4862.5663 & 2294.2462 & 7430.8864 & NA & NA & NA & 0.1431 \tabularnewline
66 & NA & 4508.7499 & 1934.5915 & 7082.9084 & NA & NA & NA & 0.0912 \tabularnewline
67 & NA & 4777.6338 & 2073.2774 & 7481.9901 & NA & NA & NA & 0.1413 \tabularnewline
68 & NA & 4393.6819 & 1624.4773 & 7162.8864 & NA & NA & NA & 0.0933 \tabularnewline
69 & NA & 4350.4108 & 1572.0659 & 7128.7557 & NA & NA & NA & 0.089 \tabularnewline
70 & NA & 4699.6353 & 1884.4385 & 7514.832 & NA & NA & NA & 0.1387 \tabularnewline
71 & NA & 4434.0025 & 1584.8066 & 7283.1985 & NA & NA & NA & 0.1045 \tabularnewline
72 & NA & 4980.3952 & 2122.1395 & 7838.6509 & NA & NA & NA & 0.1901 \tabularnewline
73 & NA & 4852.2949 & 1980.8469 & 7723.7429 & NA & NA & NA & 0.1683 \tabularnewline
74 & NA & 4855.5236 & 1968.5686 & 7742.4785 & NA & NA & NA & 0.1702 \tabularnewline
75 & NA & 6370.4271 & 3476.8787 & 9263.9754 & NA & NA & NA & 0.5298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302852&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[51])[/C][/ROW]
[ROW][C]39[/C][C]5860[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]4000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]4380[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]4080[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]4780[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]4180[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]4060[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]4620[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]4320[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]4800[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]4760[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]4780[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]6260[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]NA[/C][C]3724.2589[/C][C]2263.4067[/C][C]5185.1111[/C][C]NA[/C][C]3e-04[/C][C]0.3557[/C][C]3e-04[/C][/ROW]
[ROW][C]53[/C][C]NA[/C][C]4820.0894[/C][C]3280.2144[/C][C]6359.9644[/C][C]NA[/C][C]NA[/C][C]0.7123[/C][C]0.0334[/C][/ROW]
[ROW][C]54[/C][C]NA[/C][C]4451.6146[/C][C]2910.8207[/C][C]5992.4085[/C][C]NA[/C][C]NA[/C][C]0.6818[/C][C]0.0107[/C][/ROW]
[ROW][C]55[/C][C]NA[/C][C]4730.152[/C][C]3026.2153[/C][C]6434.0888[/C][C]NA[/C][C]NA[/C][C]0.4771[/C][C]0.0392[/C][/ROW]
[ROW][C]56[/C][C]NA[/C][C]4360.4249[/C][C]2588.1803[/C][C]6132.6694[/C][C]NA[/C][C]NA[/C][C]0.5791[/C][C]0.0178[/C][/ROW]
[ROW][C]57[/C][C]NA[/C][C]4313.6868[/C][C]2536.2879[/C][C]6091.0857[/C][C]NA[/C][C]NA[/C][C]0.6102[/C][C]0.0159[/C][/ROW]
[ROW][C]58[/C][C]NA[/C][C]4665.6241[/C][C]2847.9882[/C][C]6483.26[/C][C]NA[/C][C]NA[/C][C]0.5196[/C][C]0.0428[/C][/ROW]
[ROW][C]59[/C][C]NA[/C][C]4408.4207[/C][C]2554.3841[/C][C]6262.4572[/C][C]NA[/C][C]NA[/C][C]0.5372[/C][C]0.0252[/C][/ROW]
[ROW][C]60[/C][C]NA[/C][C]4955.6496[/C][C]3094.5013[/C][C]6816.7979[/C][C]NA[/C][C]NA[/C][C]0.5651[/C][C]0.0848[/C][/ROW]
[ROW][C]61[/C][C]NA[/C][C]4828.5841[/C][C]2954.3428[/C][C]6702.8255[/C][C]NA[/C][C]NA[/C][C]0.5286[/C][C]0.0672[/C][/ROW]
[ROW][C]62[/C][C]NA[/C][C]4836.401[/C][C]2945.7815[/C][C]6727.0205[/C][C]NA[/C][C]NA[/C][C]0.5233[/C][C]0.07[/C][/ROW]
[ROW][C]63[/C][C]NA[/C][C]6353.1837[/C][C]4456.6797[/C][C]8249.6878[/C][C]NA[/C][C]NA[/C][C]0.5384[/C][C]0.5384[/C][/ROW]
[ROW][C]64[/C][C]NA[/C][C]3786.1405[/C][C]1301.6184[/C][C]6270.6626[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.0255[/C][/ROW]
[ROW][C]65[/C][C]NA[/C][C]4862.5663[/C][C]2294.2462[/C][C]7430.8864[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.1431[/C][/ROW]
[ROW][C]66[/C][C]NA[/C][C]4508.7499[/C][C]1934.5915[/C][C]7082.9084[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.0912[/C][/ROW]
[ROW][C]67[/C][C]NA[/C][C]4777.6338[/C][C]2073.2774[/C][C]7481.9901[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.1413[/C][/ROW]
[ROW][C]68[/C][C]NA[/C][C]4393.6819[/C][C]1624.4773[/C][C]7162.8864[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.0933[/C][/ROW]
[ROW][C]69[/C][C]NA[/C][C]4350.4108[/C][C]1572.0659[/C][C]7128.7557[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.089[/C][/ROW]
[ROW][C]70[/C][C]NA[/C][C]4699.6353[/C][C]1884.4385[/C][C]7514.832[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.1387[/C][/ROW]
[ROW][C]71[/C][C]NA[/C][C]4434.0025[/C][C]1584.8066[/C][C]7283.1985[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.1045[/C][/ROW]
[ROW][C]72[/C][C]NA[/C][C]4980.3952[/C][C]2122.1395[/C][C]7838.6509[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.1901[/C][/ROW]
[ROW][C]73[/C][C]NA[/C][C]4852.2949[/C][C]1980.8469[/C][C]7723.7429[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.1683[/C][/ROW]
[ROW][C]74[/C][C]NA[/C][C]4855.5236[/C][C]1968.5686[/C][C]7742.4785[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.1702[/C][/ROW]
[ROW][C]75[/C][C]NA[/C][C]6370.4271[/C][C]3476.8787[/C][C]9263.9754[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0.5298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302852&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[51])
395860-------
404000-------
414380-------
424080-------
434780-------
444180-------
454060-------
464620-------
474320-------
484800-------
494760-------
504780-------
516260-------
52NA3724.25892263.40675185.1111NA3e-040.35573e-04
53NA4820.08943280.21446359.9644NANA0.71230.0334
54NA4451.61462910.82075992.4085NANA0.68180.0107
55NA4730.1523026.21536434.0888NANA0.47710.0392
56NA4360.42492588.18036132.6694NANA0.57910.0178
57NA4313.68682536.28796091.0857NANA0.61020.0159
58NA4665.62412847.98826483.26NANA0.51960.0428
59NA4408.42072554.38416262.4572NANA0.53720.0252
60NA4955.64963094.50136816.7979NANA0.56510.0848
61NA4828.58412954.34286702.8255NANA0.52860.0672
62NA4836.4012945.78156727.0205NANA0.52330.07
63NA6353.18374456.67978249.6878NANA0.53840.5384
64NA3786.14051301.61846270.6626NANANA0.0255
65NA4862.56632294.24627430.8864NANANA0.1431
66NA4508.74991934.59157082.9084NANANA0.0912
67NA4777.63382073.27747481.9901NANANA0.1413
68NA4393.68191624.47737162.8864NANANA0.0933
69NA4350.41081572.06597128.7557NANANA0.089
70NA4699.63531884.43857514.832NANANA0.1387
71NA4434.00251584.80667283.1985NANANA0.1045
72NA4980.39522122.13957838.6509NANANA0.1901
73NA4852.29491980.84697723.7429NANANA0.1683
74NA4855.52361968.56867742.4785NANANA0.1702
75NA6370.42713476.87879263.9754NANANA0.5298






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPEsMAPESq.EMSERMSEScaledEMASE
520.2001NANANANA00NANA
530.163NANANANANANANANA
540.1766NANANANANANANANA
550.1838NANANANANANANANA
560.2074NANANANANANANANA
570.2102NANANANANANANANA
580.1988NANANANANANANANA
590.2146NANANANANANANANA
600.1916NANANANANANANANA
610.198NANANANANANANANA
620.1994NANANANANANANANA
630.1523NANANANANANANANA
640.3348NANANANANANANANA
650.2695NANANANANANANANA
660.2913NANANANANANANANA
670.2888NANANANANANANANA
680.3216NANANANANANANANA
690.3258NANANANANANANANA
700.3056NANANANANANANANA
710.3278NANANANANANANANA
720.2928NANANANANANANANA
730.3019NANANANANANANANA
740.3034NANANANANANANANA
750.2317NANANANANANANANA

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & sMAPE & Sq.E & MSE & RMSE & ScaledE & MASE \tabularnewline
52 & 0.2001 & NA & NA & NA & NA & 0 & 0 & NA & NA \tabularnewline
53 & 0.163 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
54 & 0.1766 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
55 & 0.1838 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
56 & 0.2074 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
57 & 0.2102 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
58 & 0.1988 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
59 & 0.2146 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
60 & 0.1916 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
61 & 0.198 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
62 & 0.1994 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
63 & 0.1523 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
64 & 0.3348 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
65 & 0.2695 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
66 & 0.2913 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
67 & 0.2888 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
68 & 0.3216 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
69 & 0.3258 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
70 & 0.3056 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
71 & 0.3278 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
72 & 0.2928 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
73 & 0.3019 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
74 & 0.3034 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
75 & 0.2317 & NA & NA & NA & NA & NA & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302852&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]sMAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][C]ScaledE[/C][C]MASE[/C][/ROW]
[ROW][C]52[/C][C]0.2001[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]0[/C][C]0[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]53[/C][C]0.163[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]54[/C][C]0.1766[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]55[/C][C]0.1838[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]56[/C][C]0.2074[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]57[/C][C]0.2102[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]58[/C][C]0.1988[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]59[/C][C]0.2146[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]60[/C][C]0.1916[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]61[/C][C]0.198[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]62[/C][C]0.1994[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]63[/C][C]0.1523[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]64[/C][C]0.3348[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]65[/C][C]0.2695[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]66[/C][C]0.2913[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]67[/C][C]0.2888[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]68[/C][C]0.3216[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]69[/C][C]0.3258[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]70[/C][C]0.3056[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]71[/C][C]0.3278[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]72[/C][C]0.2928[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]73[/C][C]0.3019[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]74[/C][C]0.3034[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]75[/C][C]0.2317[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302852&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302852&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.PEMAPEsMAPESq.EMSERMSEScaledEMASE
520.2001NANANANA00NANA
530.163NANANANANANANANA
540.1766NANANANANANANANA
550.1838NANANANANANANANA
560.2074NANANANANANANANA
570.2102NANANANANANANANA
580.1988NANANANANANANANA
590.2146NANANANANANANANA
600.1916NANANANANANANANA
610.198NANANANANANANANA
620.1994NANANANANANANANA
630.1523NANANANANANANANA
640.3348NANANANANANANANA
650.2695NANANANANANANANA
660.2913NANANANANANANANA
670.2888NANANANANANANANA
680.3216NANANANANANANANA
690.3258NANANANANANANANA
700.3056NANANANANANANANA
710.3278NANANANANANANANA
720.2928NANANANANANANANA
730.3019NANANANANANANANA
740.3034NANANANANANANANA
750.2317NANANANANANANANA


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = pearson ;
Parameters (R input):
par1 = 0 ; 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*2
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,fx))
(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.spe <- array(0, dim=fx)
perf.scalederr <- array(0, dim=fx)
perf.mase <- array(0, dim=fx)
perf.mase1 <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.smape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.smape1 <- 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)
perf.scaleddenom <- 0
for (i in 2:fx) {
perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
}
perf.scaleddenom = perf.scaleddenom / (fx-1)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+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.smape[1] = abs(perf.spe[1])
perf.mape1[1] = perf.mape[1]
perf.smape1[1] = perf.smape[1]
perf.mse[1] = perf.se[1]
perf.mase[1] = abs(perf.scalederr[1])
perf.mase1[1] = perf.mase[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.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
perf.smape1[i] = perf.smape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
perf.mase1[i] = perf.mase[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',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)
a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))
a<-table.element(a,round(perf.mase1[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')