Question

Observations of any variable recorded over a sequential period of time are considered time-series. Forecasting models, used to estimate values for some future period, are generally classified as either qualitative or quantitative.

Use the internet to research the differences between a qualitative forecasting model and a quantitative forecasting model.

Assume you are an executive of a large transportation company, and your firm's profit is highly sensitive to fuel cost. The price of gasoline and diesel changes daily, however, your customers expect to be quoted a price for delivery services days, weeks, and sometimes, MONTHS in advance. Therefore, your firm relies heavily on forecasting the price of fuel. Which method of forecasting might you use, qualitative or quantitative? And finally, what are the limitations to business forecasting.

Answer 1

Observations of any variable recorded over time in sequential order are considered a time series. The measurements may be taken every hour, day, week, month, or year, or at any other regular interval. The time interval over which data are collected is called periodicity. There are two common approaches to forecasting:

1) Qualitative Forecasting method: When historical data are unavailable or not relevant to future. Forecasts generated subjectively by the forecaster. For example – a manager may use qualitative forecasts when he/she attempts to project sales for a brand-new product. Although qualitative forecasting method is attractive in certain scenarios, it’s often criticized as it’s prone to optimism and overconfidence.

2) Quantitative Forecasting method: When historical data on variables of interest are available. Methods are based on an analysis of historical data concerning the time-series of the specific variable of interest. Forecasts are generated through mathematical modelling. Quantitative forecasting methods are subdivided into two types:

• Time Series Forecasting methods: forecast of future values based on the past and present values of the variable being forecasted. These are also known as non-casual forecasting methods, they are purely time series models and do not present any explanation of the mechanism generating the variable of interest and simply provide a method for projecting historical data.
• Casual Forecasting methods: It attempts to find casual variables to account for changes (for the variable to be forecasted) in a time series. It forecasts the future values by examining the cause and effect relationships. Casual forecasting methods are based on a regression framework, where the variable of interest is related to a single or multiple independent variables. Here, forecasts are caused by the known values of the independent variables.

Let’s take an example of Gasoline sales (in 1000s of Gallons) over a period of time:

Year	1	2	3	4	5	6	7	8	9	10	11	12
Sales (Yi)	17	21	19	23	18	16	20	18	22	20	15	22

We drew a scattered diagram using the above-mentioned data. In figure 4, our visual impression of the long-term trend in the series is obscured by the amount of variation from year to year. It becomes difficult to judge whether any long term upward or downward trend exists in the series. To get a better overall impression of the pattern of movement in the data over time, we smooth the data.

One of the ways is using the Moving Averages method: here the mean of the time series data is taken from several consecutive periods. The term moving is used because it’s continually recomputed as new data becomes available, it progresses by dropping the earliest value and adding the latest value. To calculate moving averages, we need to know the length of periods chosen to be included in the moving average. Moving Averages are represented by MA(L ) where L denotes the length of periods chosen. A Weighted Moving Average (WMA) is prepared as It helps to smooth the price curve for better trend identification. It places even greater importance on recent data.

Using the above example, we prepare a table to show the Weighted Moving Averages:

we can observe that the 5 year moving averages smooth the series more than the 3 year moving averages because the period is longer. So, as L increases, it smoothens the variations better but the number of moving averages that we can calculate becomes fewer, this is because too many moving averages will be missing at the beginning and end of the series.

To calculate an exponentially smoothed value in time period ‘i’, we use the following understanding: -

E1 = Y1      Ei = WYi + (1-W)Ei-1,

where,

Ei is the value of the exponentially smoothed series being calculated in the time period ‘i’

Ei-1 is the value of the exponentially smoothed series already calculated in the time period ‘i-1’

Yi is the observed value of the time series in period ‘i’

W is subjectively assigned weight or smoothing coefficient (where, 0 < W < 1)

Let us use the same example of Gasoline sales (in 1000s of Gallons) over a period of time:

(Assume W = 0.5)

we can observe how exponentially smoothening the series with lesser variations. Now comes the point where we take a decision to choose the smoothing coefficient. When we use a small W (such as W = 0.05) then there’s heavy smoothing, as there’s more emphasis on the previous time period (Yi-1), therefore, slow adoption to recent data. If there’s moderate smoothing (such as W = 0.2) then there’s moderate smoothing or moderate adaptation to recent data. And if we choose a high value for W (such as W = 0.8) then there’s little smoothing and quick adaptation to the recent data.

Therefore, the selection has to be somewhat subjective. So, if our goal is to only smooth a series by eliminating unwanted cyclical and irregular variations, we should select a small value for W (thus less responsive to recent changes). If our goal is forecasting, then we should choose a large value for W