Quantitative Methods

Quantitative forecasting techniques rely on historical data. They can be divided into two types:

  • Extrinsic
    • (Definition) Extrinsic Forecasting is a forecast method based on a correlated leading indicator, such as estimating furniture sales based on housing starts. Extrinsic forecasts tend to be more useful for large aggregations, such as total company sales, than for individual product sales.
    • Extrinsic techniques are known as casual techniques, because they analyze data on conditions thought to result in changes in demand for a particular item or group of items, such as forecasts of diaper demand based on the birth rate, i.e. the seek to find correlation or a cause-and-effect relationship between the indicator and overall market demand.
    • (Definition) Market Demand is the total demand that would exist within a defined customer group in a given geographical area during particular time period given a known marketing program.
  • Intrinsic
    • (Definition) Intrinsic Forecast is a forecast based on internal factors, such as an average of past sales.
    • Intrinsic techniques are known as time series models because they incorporate data collected during set intervals of time – hours, days, weeks, months.
    • Intrinsic techniques tend to be best for short-term forecasting.

The best practice for organizations is to do some form of both intrinsic and extrinsic forecasting and then modify these results with some type of qualitative method.

“Intrinsic” and “Extrinsic’ are simply referring to the source of the data.

Data Gathering and Formatting

Look at some rules to follow for gathering good data:

  • Record data in the terms needed for the forecast
    • Forecasts contain three dimensions:
      • Amount of demand
      • Time period
      • Items demanded
    • Track demand, not shipments. You want to know when customers actually wanted the items, not when the items were sent out.
    • Keep records for the same time periods to be used in scheduling – weeks, months, quarters.
    • Forecast demand for the items manufactured, including all product options, as well as total demand for the product. Demand forecasts for the product groups are more efficient when an overall forecast for a product group is coupled with a percentage breakdown for each subset of the group rather than producing multiple independent forecasts for each item.
  • Subtract returns and cancellations from the demand data
    • Be sure to record returns and cancellations and subtract them from the demand data for the period. They do not represent true demand.
  • Record events that may influence demand
    • Some events that may influence demand include sales promotions, strikes, and a competitor’s product introduction.
  • Keep separate demand records for each customer group
    • Your customer may typically buy in large or small lots, on different schedules, and so forth. Average overall demand will not necessarily be helpful in setting your schedules.

Quantitative Forecasting Techniques Based on Extrinsic Data

  • Extrinsic data is most commonly used in quantitative forecasting.
  • Some of the leading indicators that financial experts watch to predict coming trends include housing starts, construction contract award, automobile production, farm income, steel production, and gross national income. Unlike seasonal variations, these economic trends move in cycles that extend over a period of years. They are more likely to be helpful in predicting aggregate demand than demand for specific products or services.
  • Extrinsic data are more useful if they relate to very recent event s and trends. The more time that has passed since the time period the data refer to, the less useful the data become.
  • While it is important to verify that the extrinsic data used in forecasts are relatively fresh, the key challenge is to select an indicator that has true correlation to the demand being forecasted.

Example of Extrinsic Data in Chart Form (Source: www.calculatedriskblog.com)

Quantitative Forecasting Techniques Based on Intrinsic Data

  • Quantitative forecasting techniques using intrinsic data are also called time series models because they embody the notion that data distributed over time showing past performance can be used to predict performance in the future – almost always with some degree of error.
  • To be credible, time series forecasts should include an estimate of the degree of potential error.
  • A time series shows some combination of four types of variability: trend, seasonality, random variation and cycle.

  • Following are some basic techniques for developing forecasts from time series data, listed in ascending or descending order of sophistication:
    • Naïve Approach
    • Moving Averages
    • Weighted Moving Averages
    • Exponential smoothing

Naive Forecasting

  • Naïve forecasting assumes that demand in the next time period will be the same as demand in the last time period. For example, if a retailer sells 600 pairs of booths in February, the naïve forecast would be for demand of 600 pairs of boots in March.
  • This approach rules out all the types of fluctuation – trends, seasonality, random variation and cycles.
  • An alternative type of naïve forecast takes seasonality into account by assuming that demand for the month will be the same as demand for the same month in the prior year. This type of forecast can be useful if the trend tends to be flat and there is little random variation.

Moving Average Forecasting

  • Moving averages (or simple moving averages) represent a step up in sophistication from the naïve approach.
  • Instead of using the most recent period to forecast demand for the next period, a moving average uses the average demand from a series of preceding periods to forecast the next period’s demand.
  • It’s a “moving” average because it is recalculated for each new period.
  • A three month moving average, for instance, takes the average demand per month for the three preceding months and updates the calculation each month.

    3-Month Moving Average = (M1+M2+M3) / 3

  • Moving averages can be quiet useful – and many firms do use them – when demand is fairly constant from period to period.
  • The moving average mitigates the effects of random variations, so that orders do not vary in amount quiet so much from time to time as they would with a naïve forecast. This makes production more predictable, and that can be a money saver.
  • The naïve forecast methodology prevents an overreaction to any one month’s random variation.
  • The moving average method can be of limited usefulness for a product with wide seasonal variations in demand on top of random fluctuations.
  • Moving averages generally fail to recognize trends or seasonal effects.
  • On the plus side, the moving average method dies tend to correct for random variations. The more periods included in the average (say 6 months instead of three) the more it corrects for chance variations. However, the moving average method lags behind actual demand, and the more periods you include in the average, the more it lags.

The pluses and minuses of using the moving average method of forecasting can be summed up as follows:

  • The moving average smoothies out random variations, with longer periods removing more of the randomness. But longer periods also make the average less sensitive to real changes in the data.
  • Moving averages are not sensitive to trends or seasonal effects. The average of previous results by definition cannot predict movement to a higher or lower value than the period preceding the forecast.
  • As more periods are included in the average, calculations become more complex and you have to collect more data for every product/group.

Weighted Moving Average Forecasting

  • Weighted moving averages can provide somewhat more sophisticated basis for discerning data trends. To do this weighted average usually places more emphasis on recent periods and less on earlier periods, assuming that more recent periods have better predictive relevance.
  • Greater weight might alternatively be placed on earlier periods when a trend or seasonal effect is expected to change, for example, in the later stages of a product life cycle.
  • Weighing is done simply by multiplying recent demand numbers to make them larger before inserting them into the equation for calculating the average.

    3-Month Weighted Average = (W1 x M1) + (W2 X M2) + (W3 x M3) / (W1+W2+W3)

  • The challenging part of weighted averaging is selecting the weights. There is no formula to help you decide which weights will work best. You have to rely on guesswork or trial and error, which can be facilitated by the right software.

Exponential Smoothing

  • Exponential smoothing is more sophisticated version of the weighted moving average that is relatively easy to use and required very little record keeping.
  • The exponential smoothing equation requires only three basic terms:
    • The last period’s forecast.
    • The last period’s actual demand and
    • A smoothing constant (a number greater than 0 and less than 1 represented by (α), which is basically a percentage weighting where 1=100 percent).
  • There are two ways to present the same equation:
    • The first method helps call out how this forecast is built:

    New Forecast = Last Period’s Forecast + α (Last Period’s Demand – Last Period’s Forecast)

    • The second method is easier to calculate and is more commonly used:

    New Forecast = (α x Last Period’s Demand) + [(1-α) x Last Period’s Forecast]

  • Smoothing can make your forecasts somewhat more responsive to trends than simple moving averages. Like any weighted moving average, however, exponential smoothing lags behind changes in the data.
  • Generally speaking, firms use exponential smoothing constants that fall between 0.05 and 0.5. The higher the constant, the more weight your forecast gives to the actual demand data from the preceding period. A constant of 0.05 would give minimal weight to the preceding period. A constant of 1.0 would yield the same result as a naïve forecast, because it would include the entire last period’s demand (100%) and none of the last period’s forecast amount (0%).
  • Using best possible smoothing constant is crucial. The accuracy of your forecast depends upon it. Like the constants used in simple weighted averages, the exponential smoothing constant is not a given. It has to be determined and thus reflects the best judgement of experts, the series of previous forecast and demand numbers, or a combination of the two. Like the constants used in weighted averaging, the smoothing constant can be selected by trying various constants on the historical data to see which works best.

Modifying Quantitative Methods

  • Quantitative methods are usually modified to account for trends (including cycles) and seasonal effects.
  • As part of forecasting process, forecasters decompose data to remove trend and seasonality and then proceed with the forecast projection. Once the qualitative forecast of intrinsic data is completed, the forecasters recompose the forecast by applying any trend, cycle and seasonality adjustments to the forecasted data. Adjustments include modifying forecasts for internal trends (such as historical growth rate in demand of five percent for a product) or external trends (such as a recession suppressing demand to historically low levels).

Seasonal Index

  • Seasonal variations play havoc with forecasts, even those using weighted averages.
  • Since moving average always lags behind an upward or downward trend, forecasters have to develop other quantitative methods to take account of these seasonal movements.
  • “Seasonal” in this context can refer to any forecasting period, from actual seasons, to months, to days, or even to parts of days.


Computing seasonal index for home owner market segment for gas fireplaces requires the following calculations. We will use 3 years’ worth of monthly demand data:

  1. What is the seasonal average of monthly demand for each of the 12 months in the past 3 years?

    To determine this, divide the sum of the demand in the three January’s by 3, divide the sum of all February demand by 3, and so on till December.

  2. What is the deseasonalized average monthly demand during those 3 years?

    Calculate this by adding 12 monthly averages from the preceding step and divide the total by 12. (This monthly average is said to be “deseasonalized”, because it ignores the effect of seasonal variation. Note that using deseasonalized demand is an example of decomposing data prior to proceeding to the quantitative forecast computation).

  3. What is the seasonal (monthly) index?

    This is the average of particular month divided by the overall deseasonalized monthly average demand.

Seasonal Index = Average Demand for Period (e.g. Month) /
Deseasonalized Average Demand for all Periods (e.g. Year)


About Paresh Sharma


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