Question 1

A

On its face, the scarcity of available data in this example would suggest the adoption of a model-based method. Certain data-driven methods may prove fruitful - for example seasonal naive (with the seasons being weeks).

B

The hospital admissions data may be useful to the clinic if there were a demonstrable relationship between the two facilities’ admissions. The other condition is that the hospital data must be available at the time of prediction in order to influence the forecast. For example, the clinic’s forecasting method cannot depend on hospital admissions data that would occur in the future.

C

The advantage of this approach (basically, this is seasonal naive) are several: 1. It’s simple, both easy to understand and to implement. 2. It would be easy to automate. 3. Since it’s seasonal naive, this method should be compared with any more complex approach. In other words, this method needs to be calculated anyway.

There are a few disadvantages to this method too:

  1. It does not account for week-to-week changes in level that might be predictable if a more complex method were attempted.
  2. It accounts for day-of-week seasonality, but wouldn’t consider more global changes to the series, for example, if there were consistently more visits in autumn versus spring due to flu season.

D

A semi-automated method would be ideal for this task. Running through key automation factors yields a mixed result:

  1. How many series need to be forecasted? The prompt only mentions one, though it is possible a real-world scenario may require more (e.g. staffing by department for the clinic). Automation level recommendation: Low (assuming one series).
  2. Is the forecasting an ongoing process? Yes, an ongoing process as it has to do with staffing requirements for anticipated patient demand. Automation level recommendation: High.
  3. Which data and software will be available? This is unknown. We know we have access to the most recent month of daily history. We may have access to the hospital’s admissions, and we may be able to gather more history for the clinic’s own admissions. It’s implied that the administrator doesn’t have specialized software in this scenario. Automation level recommendation: Low-ish, mostly due to limited data to process and unknown software support.
  4. What forecast expertise is available? While not specifically known, we can presume that the administrator is not a forecasting specialist. This suggests an approach with a higher level of automation.

Overall, something semi-automated might be a nice solution here. For example an excel-based forecasting approach that applies a model to determine each week’s forecast level, then a standard day-of-week percentage to take the weekly level to the day.

E

Option one: An equal-weight average the existing seasonal naive forecast with a linear regression forecast, which could help to capture trend while preserving the seasonal characteristics of each week.
Option two: An equal-weight average between a linear regression (model-based) and a data-driven method, like a smoothing method (assuming we have enough data to train the data-driven method).
In this example, we’d expect to gain some accuracy by using different methods applied to the same data (Armstrong argues even better results would be obtained in cases of data and method differences between the component forecasts).

Question 2

A

Persistence Method: AKA Naive, is data-driven.

Physical Approach: Model-based - the time series’ history is used to set parameters.

Statistical Approach: Data-driven, explicitly not based on a mathematical model. The reference to ease of use and low cost indicate that it is easy to automate - another hallmark of a data-driven method. Using its own forecast error to tune the next step ahead forecast makes it a two-level method.

Hybrid Approach: This is a combination approach, using the other three methods described above.

B

Persistence Method: Is an extrapolation method. It relies solely on its own history to make predictions.

Physical Approach: Appears to be a correlation modeling method (though we don’t have a lot to go on). The use of physical conditions of the atmosphere to predict wind power generation means this approach is using external data (i.e., not an extrapolation method). The description doesn’t mention an assumption of a causal relationship between atmospheric conditions and output, so we land on correlation by deduction.

Statistical Approach: An extrapolation method, since no outside data are referred to, and the forecast is referring only to its own history.

Hybrid Approach: A combination method combining two or more of the above to create an ensemble forecast.

C

The hybrid approach can realize the same advantages and disadvantages described for combination forecasts in general.
By combining two or more forecasts by a predetermined weighting, predictive performance is generally improved. Per Armstrong, forecast accuracy generally continues to improve as additional forecasts are added to the combination model (at least five forecasts were described as ideal, though he cautioned of diminishing returns at higher numbers).
The disadvantages of the hybrid approach are found in: * Increased costs / complexity of implementation * The requirement for analysts who are familiar with multiple methods * And pre-determining a rule for combining the forecasts to avoid weighting forecasts to match individual bias.