Chapter 4 Problem 1

(a) If data is available only for the last month, how does this affect the choice of model-based vs data-driven methods?

Given there is only a month of data available, meaning around 30 days depending on the month, then that would mean a model-based method would be more useful since it is more advantageous to use with short series as opposed to data-driven models which excel with longer series.

(b) The clinic has access to the admissions data of a nearby hospital. Under what conditions will including the hospital information be potentially useful for forecasting the clinics daily visits?

For the hospital admissions data to be useful for forecasting clinic visits, first a correlation between the series must be determined. This can be done casually using assumptions derived from theoretical models, use a multivariate time series model, or heuristically if by a source that is deemed knowledgeable on the subject. Another condition to using the hospital admissions data is it must be available at the time of prediction, so we would most likely need the hospital’s estimates for admissions to use with the forecast of the clinic visits.

(c)Thus far, the clinic administrator takes a heuristic approach, using the visit numbers from the same day of the previous week as a forecast. What is the advantage of this approach? What is the disadvantage?

The advantage of this approach is if the data is seasonal with the period being a week, then it would mirror that seasonal trend of visits following a similar pattern week to week depending on the day. The disadvantage is any week to week fluctuations, such as a school vacation when people are available for visits, would not be captured by looking at the same day of the last week and not using the more recent data from the days prior.

(d) What level of automation appears to be required for this task? Explain.

Since this forecast will be used for daily staffing going forward, some automation will be needed. Given the small amount of data to start, a model-based method is preferred which is less easy to automate. Add on that the seasonality assumption from part c is heuristic, the forecast will need to be monitored often to see if that assumption holds true over time.

(e) Describe two approaches for improving the current heuristic (naïve) forecasting approach using ensembles.

The first approach to improve the forecast would be to do a non-seasonal naïve forecast to average with the heuristic one. This would account for recent data as well as incorporating the possible weekly seasonality that is assumed by the clinic administrator. A second approach is to use a different series of data collecting clinic visits. If the original set is collected electronically, a manual collection system could be implemented and used in a forecast that is then combined with the other forecasts.

Chapter 4 Problem 2

(a) For each of the four types of methods, describe whether it is model-based, data-driven, or a combination.

Persistence Method- this is model-based because it is using a mathematical function to forecast and not adjusting based on data. ####Physical Approach- this is data-driven since it uses parameterizations based on the atmosphere.

Statistical Approach- this is data-driven because it is not based on a predefined mathematical model and is based on patterns. It also tunes parameters based on recent data. ####Hybrid Approach- this is a comnination because it combines other methods with are model-based and data-driven.

(b) For each of the four types of methods, describe whether it is based on extrapolation, causal modeling, correlation modeling, or a combination.

Persistence Method- Extrapolation since it forecasts based on its own historical values like a naive forecast. ####Physical Approach- Correlation modeling because it uses information about the atmosphere to forecast the wind.

Statistical Approach- causal modeling because it is using the difference between expected and actual wind speeds to tune the parameters. ####Hybrid Approach- combination because it is combining methods that use the other modeling types to forecast.

(c)Describe the advantages and disadvantages of the hybrid approach.

The advantage of the hybrid approach are that is combines different approaches which has been found to be more accurate than a single method. Each different approach has strengths and weaknesses, so combining them can help offset and make a stronger forecast. This also leads to reducing variance in forecasting errors. The disadvantages of the hybrid approach are: it takes more effort, requires analysts who can perform different methods, and need to determine the rule for combining forecasts.