Time Series Approaches to Forecasting Demand

• Average (base)
• Trend
• Seasonality
• Cyclical (we don't worry about this)
• Random (noise)

• Case I: No trend, no seasonality

Here we are interested in separating the base (average) from the random componet.
Two models for this case are moving averages and simple exponential smoothing
• Moving averages:

The model:
• A_t = (D_t + D _t-1 + D _t-2 ...)/n (The smoothing equation)
• F _t+1 = A_t (the forecasting equation)
where D _t is the actual demand in t, A_t is the smoothed (average) demand and F_t+1 is the forecast made in period t for period t+1.
• Exponential smoothing:

The model:
• A_t = a*D_t + (1- a)* A_t-1 (The smoothing equation)
• F _t+1 = A_t (The forecasting equation)
a ,the smoothing constant, is a parameter between 0 and 1.

Example

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• Case II: Trend, but no seasonality

The model for this case is Trend Adjusted Exponential Smoothing
If past data shows any positive or negative trend, the simple exponential model would not do well. The Trend adjusted method is an extension of the simple exponential model that incorporates an explicit trend component , T_t.
• Trend Adjusted Exponential Smoothing:

the Model:
• A_t = a*D_t + (1- a)* (A_t-1 + T _t-1) (The smoothing equation for the average)
• T_t = b(A_t - A_t-1) + (1- b)* T _t-1 ( The smoothing equation for the trend)
• F _t+1 = A_t +T _t (The forecasting equation)

a and b are smoothing constants between 0 and 1.

Example

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• Case III: Linear trend and seasonality

This is a simplified case in the sense that we are assuming that trend remains constant. The model used for this case is based on regression analysis
• First estimate the equation of a straight line in the form of A _t = a + b * t

where A _t is analogous to smoothed demand, A_t in the exponential models, a is the intercept (estimate of average demand)and b is the slope (estimate of the constant trend).
• then estimate seasonal indices from the D_t/A_t as in:

Example 

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