Let’s take a look at a dataset of quarterly visitor nights (in millions) from the 1st quarter of 1998 to the 4th quarter of 2011 for a certain region of Australia:
- Sydney – Sydney metropolitan area
- NSW – New South Wales other than Sydney
- Melbourne – Melbourne metropolitan area
- VIC – Victoria other than Melbourne
- BrisbaneGC – Brisbane and Gold Coast area
- QLD – Queensland other than Brisbane and the Gold Coast
- Capitals – the other 5 capital cities: Adelaide, Hobart, Perth, Darwin, & Canberra
- Other – all other areas of Australia
Stored as a .csv file, here is a snapshot of the top of the data….
….and the bottom of the data.
We can use the Browse upload functionality to get this data into ForecastGuru.
ForecastGuru instantly displays a bird’s eye graphical panel containing a time series plot for every instrument in your csv file. The white line represents the historical time series, whereas the blue line is the forecasts. The dark grey & light grey shaded regions around the forecasts represent the 80% & 95% confidence intervals respectively.
We can see the model chosen for each region in parentheses next to the graph title.
If the data is yearly, the model defaults to Holt’s Trend. With anything more granular, the default model is Holt-Winters Multiplicative. We see here forecasts for our regions 10 quarters out from the end of the data.
Directly below the figures is a data table containing your forecasts.
The application also gives the user the ability to manually change the forecasting model for each specific column.
We can also take a deeper dive into the profile of each instrument. See here a forecasting plot for Sydney supplemented with a forecast table, fit statistics, and accuracy measures.
Also, we have the ability to view the raw data via the Data tab.
Like the output so far and want to see how it works with your data? SIGN UP FOR THE APP NOW.
Finally, if you’re not sure which model is best for your data, you can allow the optimizer to choose for you by minimizing the MAPE (mean absolute square error), thus maximizing accuracy.
Sydney: Decomposition (STL + ETS(M,N,N))
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date |
2012 Q1 | 6153.85 | 5553.30 | 6754.39 | 5235.39 | 7072.30 | 2012 Q1 |
2012 Q2 | 4964.98 | 4295.53 | 5634.42 | 3941.15 | 5988.80 | 2012 Q2 |
2012 Q3 | 5063.54 | 4331.61 | 5795.46 | 3944.16 | 6182.92 | 2012 Q3 |
2012 Q4 | 5355.31 | 4565.80 | 6144.81 | 4147.86 | 6562.75 | 2012 Q4 |
2013 Q1 | 6153.85 | 5310.65 | 6997.04 | 4864.30 | 7443.40 | 2013 Q1 |
2013 Q2 | 4964.98 | 4071.29 | 5858.67 | 3598.20 | 6331.76 | 2013 Q2 |
2013 Q3 | 5063.54 | 4122.03 | 6005.05 | 3623.62 | 6503.45 | 2013 Q3 |
2013 Q4 | 5355.31 | 4368.26 | 6342.35 | 3845.76 | 6864.86 | 2013 Q4 |
2014 Q1 | 6153.85 | 5123.26 | 7184.44 | 4577.69 | 7730.00 | 2014 Q1 |
2014 Q2 | 4964.98 | 3892.58 | 6037.37 | 3324.89 | 6605.06 | 2014 Q2 |
alpha | l |
0.49 | 10808.12 |
Init l |
10808.12 |
sigma2 | loglik | aic | bic | aicc | mse | amse |
0.00 | -458.30 | 922.59 | 928.67 | 923.05 | 236263.28 | 305027.90 |
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
-47.36 | 486.07 | 384.08 | -0.65 | 3.88 | 0.66 | 0.07 |
——————————————————————————————————————————————————————–
NSW:
Time Series Regression (Linear regression model)
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date |
2012 Q1 | 19262.48 | 18017.56 | 20507.40 | 17337.55 | 21187.41 | 2012 Q1 |
2012 Q2 | 12951.91 | 11706.99 | 14196.82 | 11026.98 | 14876.83 | 2012 Q2 |
2012 Q3 | 12450.69 | 11205.78 | 13695.61 | 10525.77 | 14375.62 | 2012 Q3 |
2012 Q4 | 13584.77 | 12339.85 | 14829.68 | 11659.84 | 15509.69 | 2012 Q4 |
2013 Q1 | 19091.79 | 17837.25 | 20346.33 | 17151.99 | 21031.59 | 2013 Q1 |
2013 Q2 | 12781.22 | 11526.68 | 14035.76 | 10841.42 | 14721.02 | 2013 Q2 |
2013 Q3 | 12280.01 | 11025.47 | 13534.54 | 10340.20 | 14219.81 | 2013 Q3 |
2013 Q4 | 13414.08 | 12159.54 | 14668.61 | 11474.27 | 15353.88 | 2013 Q4 |
2014 Q1 | 18921.10 | 17655.83 | 20186.37 | 16964.70 | 20877.50 | 2014 Q1 |
2014 Q2 | 12610.53 | 11345.26 | 13875.80 | 10654.13 | 14566.93 | 2014 Q2 |
Parameter | Coefficient | |||||
(Intercept) | 33662.79 | |||||
trend | -42.67 | |||||
season2 | -6267.90 | |||||
season3 | -6726.44 | |||||
season4 | -5549.70 |
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
-0.00 | 859.55 | 690.81 | -0.10 | 2.52 | 0.70 | 0.12 |
———————————————————————————————————————————————–
Melbourne:
Decomposition (STL + ETS(M,N,N))
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date | |
2012 Q1 | 5033.83 | 4548.93 | 5518.73 | 4292.24 | 5775.42 | 2012 Q1 | |
2012 Q2 | 4460.56 | 3975.66 | 4945.46 | 3718.97 | 5202.15 | 2012 Q2 | |
2012 Q3 | 4655.92 | 4171.02 | 5140.82 | 3914.33 | 5397.51 | 2012 Q3 | |
2012 Q4 | 4735.06 | 4250.16 | 5219.96 | 3993.47 | 5476.65 | 2012 Q4 | |
2013 Q1 | 5033.83 | 4548.93 | 5518.73 | 4292.24 | 5775.42 | 2013 Q1 | |
2013 Q2 | 4460.56 | 3975.66 | 4945.46 | 3718.97 | 5202.15 | 2013 Q2 | |
2013 Q3 | 4655.92 | 4171.02 | 5140.82 | 3914.33 | 5397.51 | 2013 Q3 | |
2013 Q4 | 4735.06 | 4250.16 | 5219.96 | 3993.47 | 5476.65 | 2013 Q4 | |
2014 Q1 | 5033.83 | 4548.93 | 5518.73 | 4292.24 | 5775.42 | 2014 Q1 | |
2014 Q2 | 4460.56 | 3975.66 | 4945.46 | 3718.97 | 5202.15 | 2014 Q2 | |
alpha | l | ||||||
0.00 | 8545.72 | ||||||
Init l | |||||||
8545.72 | |||||||
sigma2 | loglik | aic | bic | aicc | mse | amse | |
0.00 | -444.10 | 894.20 | 900.28 | 894.66 | 138048.06 | 136574.06 | |
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
-0.17 | 371.55 | 300.58 | -0.20 | 3.53 | 0.70 | 0.05 |
———————————————————————————————————————————————–
VIC:
Time Series Regression (Linear regression model)
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date | |
2012 Q1 | 12360.75 | 11589.00 | 13132.50 | 11167.44 | 13554.05 | 2012 Q1 | |
2012 Q2 | 7174.96 | 6403.21 | 7946.71 | 5981.66 | 8368.26 | 2012 Q2 | |
2012 Q3 | 5917.60 | 5145.85 | 6689.35 | 4724.30 | 7110.91 | 2012 Q3 | |
2012 Q4 | 7029.17 | 6257.42 | 7800.92 | 5835.87 | 8222.48 | 2012 Q4 | |
2013 Q1 | 12297.39 | 11519.67 | 13075.10 | 11094.86 | 13499.91 | 2013 Q1 | |
2013 Q2 | 7111.60 | 6333.89 | 7889.32 | 5909.08 | 8314.13 | 2013 Q2 | |
2013 Q3 | 5854.25 | 5076.53 | 6631.96 | 4651.72 | 7056.77 | 2013 Q3 | |
2013 Q4 | 6965.82 | 6188.10 | 7743.53 | 5763.29 | 8168.34 | 2013 Q4 | |
2014 Q1 | 12234.03 | 11449.66 | 13018.40 | 11021.21 | 13446.85 | 2014 Q1 | |
2014 Q2 | 7048.24 | 6263.88 | 7832.61 | 5835.43 | 8261.06 | 2014 Q2 | |
Parameter | Coefficient | ||||||
(Intercept) | 19064.59 | ||||||
trend | -15.84 | ||||||
season2 | -5169.95 | ||||||
season3 | -6411.46 | ||||||
season4 | -5284.05 | ||||||
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
0.00 | 532.85 | 405.77 | -0.12 | 2.76 | 0.78 | 0.12 |
———————————————————————————————————————————————–
BrisbaneGC:
Decomposition (STL + ETS(A,N,N))
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date | |
2012 Q1 | 7837.33 | 7017.28 | 8657.37 | 6583.18 | 9091.48 | 2012 Q1 | |
2012 Q2 | 6597.90 | 5765.26 | 7430.55 | 5324.48 | 7871.33 | 2012 Q2 | |
2012 Q3 | 7361.57 | 6516.52 | 8206.63 | 6069.17 | 8653.98 | 2012 Q3 | |
2012 Q4 | 7492.90 | 6635.61 | 8350.19 | 6181.79 | 8804.02 | 2012 Q4 | |
2013 Q1 | 7837.33 | 6967.98 | 8706.68 | 6507.77 | 9166.89 | 2013 Q1 | |
2013 Q2 | 6597.90 | 5716.66 | 7479.15 | 5250.15 | 7945.66 | 2013 Q2 | |
2013 Q3 | 7361.57 | 6468.59 | 8254.56 | 5995.87 | 8727.28 | 2013 Q3 | |
2013 Q4 | 7492.90 | 6588.33 | 8397.47 | 6109.48 | 8876.33 | 2013 Q4 | |
2014 Q1 | 7837.33 | 6921.32 | 8753.34 | 6436.41 | 9238.25 | 2014 Q1 | |
2014 Q2 | 6597.90 | 5670.60 | 7525.21 | 5179.71 | 8016.10 | 2014 Q2 | |
alpha | l | ||||||
0.18 | 13304.12 | ||||||
Init l | ||||||
13304.12 | ||||||
sigma2 | loglik | aic | bic | aicc | mse | amse |
409451.59 | -473.52 | 953.05 | 959.12 | 953.51 | 394828.32 | 403591.45 |
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
-37.33 | 628.35 | 495.76 | -0.49 | 3.79 | 0.73 | -0.03 |
———————————————————————————————————————————————–
QLD:
Decomposition (STL + ETS(M,N,N))
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date | |
2012 Q1 | 9592.99 | 8376.26 | 10809.71 | 7732.17 | 11453.80 | 2012 Q1 | |
2012 Q2 | 9272.53 | 8055.80 | 10489.25 | 7411.71 | 11133.34 | 2012 Q2 | |
2012 Q3 | 13424.26 | 12207.54 | 14640.98 | 11563.44 | 15285.08 | 2012 Q3 | |
2012 Q4 | 10125.43 | 8908.71 | 11342.15 | 8264.61 | 11986.25 | 2012 Q4 | |
2013 Q1 | 9592.99 | 8376.26 | 10809.71 | 7732.17 | 11453.80 | 2013 Q1 | |
2013 Q2 | 9272.53 | 8055.80 | 10489.25 | 7411.71 | 11133.34 | 2013 Q2 | |
2013 Q3 | 13424.26 | 12207.54 | 14640.98 | 11563.44 | 15285.08 | 2013 Q3 | |
2013 Q4 | 10125.43 | 8908.71 | 11342.15 | 8264.61 | 11986.25 | 2013 Q4 | |
2014 Q1 | 9592.99 | 8376.26 | 10809.71 | 7732.17 | 11453.80 | 2014 Q1 | |
2014 Q2 | 9272.53 | 8055.80 | 10489.25 | 7411.71 | 11133.34 | 2014 Q2 | |
alpha | l | ||||||
0.00 | 16936.63 | ||||||
Init l | |||||||
16936.63 | |||||||
sigma2 | loglik | aic | bic | aicc | mse | amse | |
0.00 | -495.62 | 997.24 | 1003.31 | 997.70 | 869198.32 | 848178.63 | |
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
-0.01 | 932.31 | 680.09 | -0.34 | 4.06 | 0.62 | 0.02 |
———————————————————————————————————————————————–
Capitals: Time Series Regression (Linear regression model)
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date | |
2012 Q1 | 8440.52 | 7540.95 | 9340.08 | 7049.58 | 9831.45 | 2012 Q1 | |
2012 Q2 | 6977.09 | 6077.52 | 7876.65 | 5586.15 | 8368.03 | 2012 Q2 | |
2012 Q3 | 7131.87 | 6232.31 | 8031.44 | 5740.94 | 8522.81 | 2012 Q3 | |
2012 Q4 | 7114.59 | 6215.02 | 8014.15 | 5723.65 | 8505.53 | 2012 Q4 | |
2013 Q1 | 8402.80 | 7496.29 | 9309.32 | 7001.12 | 9804.49 | 2013 Q1 | |
2013 Q2 | 6939.38 | 6032.86 | 7845.89 | 5537.69 | 8341.06 | 2013 Q2 | |
2013 Q3 | 7094.16 | 6187.64 | 8000.68 | 5692.47 | 8495.85 | 2013 Q3 | |
2013 Q4 | 7076.88 | 6170.36 | 7983.39 | 5675.19 | 8478.56 | 2013 Q4 | |
2014 Q1 | 8365.09 | 7450.82 | 9279.37 | 6951.41 | 9778.77 | 2014 Q1 | |
2014 Q2 | 6901.66 | 5987.39 | 7815.94 | 5487.98 | 8315.35 | 2014 Q2 | |
Parameter | Coefficient | ||||||
(Intercept) | 15230.91 | ||||||
trend | -9.43 | ||||||
season2 | -1454.00 | ||||||
season3 | -1289.79 | ||||||
season4 | -1297.64 | ||||||
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
-0.00 | 621.10 | 497.96 | -0.19 | 3.54 | 0.66 | 0.04 |
———————————————————————————————————————————————–
Other: Decomposition
(STL + ETS(M,N,N))
ls.best$ModelForecast[, 1] | Point Forecast | Lo 80 | Hi 80 | Lo 95 | Hi 95 | Date | |
2012 Q1 | 9997.83 | 9055.13 | 10940.52 | 8556.10 | 11439.56 | 2012 Q1 | |
2012 Q2 | 8330.69 | 7318.35 | 9343.04 | 6782.45 | 9878.94 | 2012 Q2 | |
2012 Q3 | 10332.65 | 9255.13 | 11410.17 | 8684.73 | 11980.57 | 2012 Q3 | |
2012 Q4 | 8708.92 | 7569.93 | 9847.90 | 6966.99 | 10450.85 | 2012 Q4 | |
2013 Q1 | 9997.83 | 8800.51 | 11195.15 | 8166.68 | 11828.97 | 2013 Q1 | |
2013 Q2 | 8330.69 | 7077.74 | 9583.65 | 6414.46 | 10246.92 | 2013 Q2 | |
2013 Q3 | 10332.65 | 9026.41 | 11638.89 | 8334.93 | 12330.37 | 2013 Q3 | |
2013 Q4 | 8708.92 | 7351.47 | 10066.36 | 6632.88 | 10784.95 | 2013 Q4 | |
2014 Q1 | 9997.83 | 8591.02 | 11404.63 | 7846.30 | 12149.35 | 2014 Q1 | |
2014 Q2 | 8330.69 | 6876.19 | 9785.20 | 6106.22 | 10555.17 | 2014 Q2 | |
alpha | l | ||||||
0.39 | 18438.28 | ||||||
Init l | |||||||
18438.28 | |||||||
sigma2 | loglik | aic | bic | aicc | mse | amse | |
0.00 | -484.55 | 975.10 | 981.17 | 975.56 | 596384.90 | 671311.37 | |
ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
-68.99 | 772.26 | 643.77 | -0.56 | 3.60 | 0.70 | -0.13 |