Quantitative Analyst Project

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Course Learning Outcomes for Unit VIII Upon completion of this unit, students should be able to:

7. Assess the differences between correlation and causation. 7.1 Develop a forecasting model. 7.2 Justify the selection of a forecasting model over other techniques in a given scenario.

Reading Assignment Chapter 5: Forecasting

Unit Lesson As noted in Unit VI, decision-making under certainty is still work, but work with a certain advantage of knowing. Often, it is just a matter of comparing more than one outcome’s alternative (e.g., comparing rates on bonds for purchase). Mostly, though, as noted in Chapter 5, leaders make decisions without knowing future events. This is why—as discussed throughout the course—determining causation and forecasting are such lucrative activities. Does weather forecasting look interesting to you? Quantitative analysis has made it better, as you will see in this unit and Chapter 5. Types of Forecasting Models Figure 5.1 on page 150 of the textbook shows you how to organize forecasting. Some of these approaches are now familiar to you. Qualitative Models: The Qualitative Models are, by their nature, subjective. Without using mathematics, finding and leveraging judgments based on experience counts toward getting close to the “future truth” that you may profit by. Qualitative models may be used in combination with the other categories of approaches. For example, these types listed—the Delphi Method, Jury of Executive Opinion, Sales Force Composite, and Consumer Market Survey—all treat the recipients of the questions as subject matter experts (or at least experienced, such as shoppers) and collect their opinions. These responses may be guided by presenting them quantitative analysis that were performed first. Perhaps this makes it easier to ask the panels the right questions in hopes of getting useful answers, but care should be taken not to add bias to the whole analysis effort, or the actual events could be nowhere near the qualitative models’ forecast. Causal Models: These consist of regression analyses or multiple regressions that forecast with collected data, which by definition occurred in the past. Because these models have dependent variables, which are influenced by independent variables in their equations, these models are considered to be casual—have determined that one change causes another. If you are reading this, you have probably completed Unit VII and already worked with these models. So, you will explore new models! Time-Series Models: These are quantitative models that also use past-occurring data, but add to them the values of their occurrence in time. Time matters in time-series models, whether the data shows trends, seasonal changes, cycles, or just random occurrences. Accordingly, time-series approaches have these possible phenomenon as components: a trend component ( = T), seasonal component ( = S), cyclical component ( = C), and random component ( = R), with two time-series model forms generally used:

The multiplicative model, where Demand = T x S x C X R, or

the additive model, where Demand = T + S + C + R

UNIT VIII STUDY GUIDE

Causation and Forecasting

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Measures of Forecast Accuracy As with regression analysis for correlation, you can use similar mathematics to assess how accurate forecasts are or how minimized the error is in them. Forecast error = actual value minus forecast value, as it does in the family budgets. Again, like similar equations, you can find the mean of the errors (mean absolute deviation [MAD]) if you have collected past data and time intervals, as shown with the Walker Distributors example in Table 5.1 on page 153 of the textbook. In this example, this equation was used to find the MAD of Walker’s sales forecast by dividing the sum of the absolute values of forecast errors by the numbers of errors n:

MAD = ∑ | Forecast error | n

The absolute value was taken for the same reason you would take squares in regression analyses: to prevent errors from cancelling each other out and distorting the data from trends, seasonal movements, or cycles. An effective way to understand how important the MAD can be to forecasts on behalf of society is to consider the hurricane landfall forecast example on page 154 of the textbook, and further peruse the National Hurricane Center information at noaa.gov. Hurricanes are a permanent part of North American geography and can have enough force to destroy and damage much of the area where it makes landfall and travels before dissipation. The storm’s effects can also injure or kill many people. Certainly, the ramifications of hurricane occurrence are of great interest to the countries of the Caribbean Sea (this includes the United States) where the left hook–shaped tracks of hurricanes traditionally are traced. The MADs regarding predicted and actual landfalls become a serious matter with so much at stake, and the U.S. government invests in a significant amount of resources in working on the task of forecasting, to include defining the problem (Step 1 of the Quantitative Analysis Approach, as you know) of the accurate forecasts that are needed. A point can be noted here about a “quick” way to forecast, and you do this all the time. The Naïve Model is taking the last measured value and forecasting that this value will be the next one that occurs. The Naïve Model obviously does not take into account time intervals; instead, the user more or less concedes, “well, it was this just the last time, so I say it will be this the next time.” The model is obviously well named! Even though there seems to be little science about the approach, there is quite a bit of reality to the answer. Indeed, whatever just happened (e.g., yesterday’s high temperature) tends to frequently happen again—and for a while—before shifting to a different value (such as the onset of winter temperatures). Moving-Averages Among the time-series models, you use moving-averages if variations are random, and the situation does not involve trend, seasonal, or cyclic variations. The moving-average model is one of the models that “smooths” the forecast so random variations do not influence the solution more than their values and occurrences make logical. As you can see on pages 156–7 of the textbook, calculating the moving-average forecast as the sum of numbers in previous periods t-1 divided by the number of periods n is taking just a certain number of recent values occurring in the past and calculating where the average may be moving. As you may see in Table 5.2 on page 157 of the textbook, values from a year ago may not be interesting; but what happened in the past three months, or four, or six, would be interesting as changes tend to gradually happen. Weighted Moving-Averages If you have a moving-average model and approach, you can also have a weighted moving-average model. This entails assigning weight, or multiplying wi to values, before summing them, and then dividing this by the sum of the weights. These weighted factors account for things with a higher probability occurring more than things with a lower probability. What could be the issue with any averages? Moving-average models are slow to pick up the first signs of significant change. It is possible, then, that a business depending too much on forecasts from averages may miss a shift in product popularity, changing trends, or outside changes.

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Exponential Smoothing Next in the time-series models is exponential smoothing, which is a type of moving-average approach but using little past data, as can be seen by its equation:

New Forecast = Last Period’s Forecast + α(Last Period’s Actual Demand – Last Period’s Forecast) with α as a weight, or smoothing constant, between 0 and 1. With exponential smoothing, you adjust the last forecast by the error determined from what actually happened. As can be seen in the example described on page 159 of the textbook, once a forecast is found to have an error in a certain direction, exponential smoothing will move the next forecast in the direction that the actual values seem to be moving. When actual values move in time intervals, you may see that they don’t seem random but are following a pattern. As can be seen on page 163 of the textbook, exponential smoothing can be accomplished while taking the trend into account by using an additional constant β. Another common approach is the trend projection method. This method is just a matter of taking the linear regression equation Ŷ = b0 + b1X to represent the data, using a least squares method for checking the fit and measuring significance (as was practiced in Unit VII), and projecting a continuance of the trend—often by extending the line of the linear equation. This projection may accurately forecast the trend for a while, but as you know, trends do not last forever. This signals practical limitations with believing too much in such a forecast. Seasonal Indices As the planet Earth has seasons, the societal change in dynamics aligned with these seasons is inevitable and shows in such phenomenon as sales, travel, agriculture, and other activities that include the weather and outdoors. Forecasting with taking into account seasonal cycles or other movements can be expected, as practical leaders acknowledge such expected tendencies. In terms of most seasonal adjustments for forecasting, an average season is assumed to have a value of 1, and a seasonal index is the comparison of a season of interest with that average season. The following variations can be performed to forecast things with seasonal indices:

 Deseasonalized data: Dividing the data by the seasonal index removes the seasonal effect; then, a

forecast using deseasonalized data is made and finally, the seasonal index is multiplied back in to the forecasts, restoring the effect of seasons in the forecasts.

 Decomposition: In decomposition, like converting to deseasonalized data, data is divided by the seasonal index to show a liner trend without seasonal effect, in the general form of Ŷ = b0 + b1X, as can be seen in the example of Figure 5.5 on page 171 of the textbook. Note in the table’s graph how rises and falls of the data were removed when the seasonal effect was divided out. A line Ŷ = b0 + b1X can be found for the deseasonalized data, which is then multiplied across all terms by the seasonal index to determine the equation for the seasonal forecast.

Below are two ways to find the seasonal index:

1. If the data has no trend present, you divide the average of a given season by the average of all the data from all seasons. You may recall that if the seasonal index is 1, then the time interval is having an “average” season, as a value divided by 1 remains the same value.

2. If the data includes the effect of a trend, the main challenge is that a data’s change could be due either to a trend or a seasonal change, or both or neither! So analysts compute a centered moving- average (CMA) to use in calculations so a trend is not mistaken for a season. This CMA is an average of just enough data to take seasons into account (e.g., four quarters if quarters are running seasonally). As noted on page 170 of the textbook, the steps for computing with a CMA include the following:

 Compute a CMA for each observation, except in cases where there is not enough data left to average.

 Find seasonal ratios. Each seasonal ratio = observation data / observation’s CMA.

 Average the seasonal ratios to get seasonal indices.

 If seasonal indices do not yet add up to equal the number of seasons, multiply each seasonal index by the value (number of seasons / sum of the indices).

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And, after eight units of quantitative analysis, you can see why skilled analysts draw high salaries! Having the practice and experience to be able to identify the problem, choose a fitting model, and calculate accurately are attributes that contribute to the decision process. You have the quantitative analysis approach steps and the ranks of equations to help you be effective in this role. And remember that a leader’s outlook toward challenges provides energy to efforts and is decisive toward successes.

Reference Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2015). Quantitative analysis for management (12th

ed.). Upper Saddle River, NJ: Pearson.

Suggested Reading The links below will direct you to a PowerPoint view of the Chapter 5 Presentation. This will summarize and reinforce the information from this chapter in your textbook. Click here to access a PowerPoint presentation for Chapter 5. Click here to access the PDF view of the presentation. For an overview of the chapter equations, read the “Key Equations” on page 178–179 of the textbook.

Learning Activities (Nongraded) Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit them. If you have questions, contact your instructor for further guidance and information. Complete Solved Problems 5-1 and 5-2 on pages 179–180; and Self-test problems 1-14 on pages 180–181 (use the key in the back of the book in Appendix H to check your answers). For the Solved Problems, the problem is presented first, followed by its solution. Challenge yourself to apply what you have learned, and see if you can work out the problems without first looking at the solution, only using the solution to check your own work.