5

I'm in the process of becoming familiar with some on the version 10 new functionality. I have two data sets, datasetA and datasetC, of time series data that I would like to make forecasts on. Here is datasetA.

```
datasetA = {{0., 16.2}, {0.5, 20.}, {1., 19.}, {1.5, 28.5}, {2.,
17.8}, {2.5, 23.3}, {3., 19.9}, {3.5, 13.5}, {4., 20.1}, {4.5,
11.8}, {5., 29.8}, {5.5, 26.9}, {6., 32.3}, {6.5, 16.5}, {7.,
31.7}, {7.5, 24.2}, {8., 37.1}, {8.5, 25.9}, {9., 28.1}, {9.5,
35.6}, {10., 27.4}, {10.5, 30.4}, {11., 29.4}, {11.5, 29.3}, {12.,
29.4}, {12.5, 29.1}, {13., 31.4}, {13.5, 24.}, {14.,
30.9}, {14.5, 43.1}, {15., 28.7}, {15.5, 38.8}, {16.,
37.9}, {16.5, 34.8}, {17., 26.5}, {17.5, 44.4}, {18.,
39.2}, {18.5, 44.6}, {19., 26.9}, {19.5, 51.1}, {20., 34.}, {20.5,
42.6}, {21., 38.7}, {21.5, 45.1}, {22., 56.}, {22.5, 54.3}, {23.,
47.7}, {23.5, 48.6}, {24., 48.4}, {24.5, 47.1}, {25.,
45.4}, {25.5, 44.7}, {26., 35.7}, {26.5, 36.6}, {27.,
52.8}, {27.5, 56.6}, {28., 60.8}, {28.5, 58.4}, {29.,
52.7}, {29.5, 49.1}, {30., 44.8}};
```

And here is my attempt at modeling it with a SARIMA time series model, with the corresponding plot of the above data and a 30 day forecast.

```
tsmA = TimeSeriesModelFit[datasetA, {"SARIMA", Automatic}]
plot2 = ListLinePlot[{tsmA["TemporalData"],
TimeSeriesForecast[tsmA, {70}]}, Frame -> True,
FrameLabel -> {"Time (days)", "Output"},
PlotLabel -> "Plot 2 \nModel: tsmA with Forecast",
PlotLegends -> {"data", "forecast"}]
```

So far so good as this forecast looks reasonable.

Here is datasetC, my attempt at modeling it and its forecast.

```
datasetC = {{0., 25.2}, {0.5, 18.4}, {1., 22.1}, {1.5, 21.5}, {2.,
20.7}, {2.5, 33.}, {3., 15.3}, {3.5, 24.4}, {4., 33.7}, {4.5,
37.4}, {5., 31.8}, {5.5, 23.5}, {6., 30.2}, {6.5, 24.6}, {7.,
21.1}, {7.5, 27.7}, {8., 35.5}, {8.5, 29.3}, {9., 34.1}, {9.5,
30.1}, {10., 27.6}, {10.5, 34.4}, {11., 34.9}, {11.5, 37.9}, {12.,
40.5}, {12.5, 31.9}, {13., 37.5}, {13.5, 36.5}, {14.,
25.4}, {14.5, 28.}, {15., 41.2}, {15.5, 36.6}, {16., 33.5}, {16.5,
37.1}, {17., 22.7}, {17.5, 37.5}, {18., 48.8}, {18.5,
39.7}, {19., 47.5}, {19.5, 38.1}, {20., 30.9}, {20.5, 50.9}, {21.,
43.9}, {21.5, 39.4}, {22., 44.1}, {22.5, 45.7}, {23.,
38.6}, {23.5, 57.}, {24., 46.}, {24.5, 49.5}, {25., 38.}, {25.5,
49.}, {26., 46.1}, {26.5, 55.5}, {27., 47.7}, {27.5, 49.2}, {28.,
51.4}, {28.5, 50.2}, {29., 57.3}, {29.5, 53.}, {30., 46.2}};
tsmC = TimeSeriesModelFit[datasetC, {"SARIMA", Automatic}]
plot6 = ListLinePlot[{tsmC["TemporalData"],
TimeSeriesForecast[tsmC, {70}]}, Frame -> True,
FrameLabel -> {"Time (days)", "Output"},
PlotLabel -> "Plot 6 \nModel: tsmC with Forecast",
PlotLegends -> {"data", "forecast"}]
```

This forecast does not look reasonable. Can someone explain why this is and how I might produce a better forecast ? Eventually, I would like to produce a 90% prediction interval on the forecasts. Thanks.

1Why does the first looks "reasonable" to you and the second "unreasonable" ? – eldo – 2014-08-09T20:42:02.023

The forecast of Plot 2 seems to capture the positive and negative amplitudes around the dominant trend much better than that of Plot 6 where the amplitudes are much smaller than its associated data. – Steve – 2014-08-09T21:45:53.633

@Verbeia, thank you very much for your answer, you've given me a few things to think about. It very well could be that the model structure I'm assuming is not optimal for datasetC as I am learning time series methods at the same time with the implementation of those methods by Mathematica. If you can suggest a better approach to model datasetC that would be much appreciated. I take it that you are happy with the model of datasetA ? – Steve – 2014-08-10T13:20:00.120