FORECASTING

Types of ForecastsQualitative

Time Series

Causal Relationships

Simulation

Qualitative Forecasting Approaches

Historical AnalogyPanel ConsensusDelphiMarket Research

Quantitative Approaches

Naïve (time series)Moving Averages (time series)Exponential Smoothing (time

series)Trend Projection (time series)Linear Regression (causal)

Naïve Method

This period’s forecast = Last period’s observation

Crude but effectiveAugust sales = 1000; September sales

= ??1000!

Moving Averages

This period’s forecast = Average of past n period’s observations

Example: for n = 3: Sales for Jan through March were 100, 110, 150

April forecast = (100+110+150)/3 = 120

Example

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Year

Demand Demand

Naïve

3 Year Mvg Av

Evaluating Forecasts

Concept: Forecast worth function of how close forecasts are to observations

Mean Absolute Deviation (MAD)MAD = sum of absolute value of forecast

errors / number of forecasts (e.g. periods)MAD is the average of the absolute value of all of the

forecast errors.

Weighted Moving Averages

This period’s forecast = Weighted average of past n period’s observations

Example: for n = 3: Sales for Jan through March were 100, 110, 150

Suppose weights for last 3 periods are: .5 (March), .3 (Feb), and .2 (Jan)

April forecast =.5*150+.3*110+.2*100 = 128

Exponential Smoothing

New Forecast = Last period’s forecast + alpha * (Last period’s actual observation - last period’s forecast)

Mathematically: F(t) = F(t-1) + alpha * [A(t-1) - F(t-1)], where F is the forecast; A is the actual observation, and alpha is the smoothing constant -- between 0 and 1

Example: F(t-1) = 100; A(t-1) = 110; alpha = 0.4 -- Find F(t)

F(t) = 104

Can add parameters for trends and seasonality

Trend Projections

Use Linear regression

Model: yhat = a + b* x a = y-intercept: forecast at period 0

b = slope: rate of change in y for each period x

Example: Sales = 100 + 10 * t, where t is period

For t = 15, Find yhat --

yhat = 250

Can find and a and b via Method of Least Squares

Linear Regression

Model: yhat = a + b1 * x1 + b2 * x2 + … + bk * xk a = y-intercept bi = slope: rate of change in y for each increase in

xi, given that other xj’s are held constant Example: College GPA = 0.2 + 0.5 HS GPA +

0.001 HS SAT For a HS student with a 3.0 GPA and 1200 SAT -

what is the forecast? The forecast college GPA = 2.90 Can find a, b1, and b2 via Method of Least

Squares