Time-Series Forecasting Overview Moving Averages Exponential Smoothing Seasonality.

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Time-Series Forecasting •Overview •Moving Averages •Exponential Smoothing •Seasonality

Transcript of Time-Series Forecasting Overview Moving Averages Exponential Smoothing Seasonality.

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Time-Series Forecasting•Overview•Moving Averages•Exponential Smoothing•Seasonality

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Time Series ForecastingTime Series Forecasting

Time series data is simply a set of values of some variable measured at regular intervals over time.

One data set (variable) over time.

Based on historical data. The more data the better.

Assumption: Past behavior helps us predict future behavior.

Time series data can have one or more of the following components / factors / variations.TrendSeasonalCyclicalRandom

Moving AveragesExponential SmoothingSeasonal Methods

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Moving AveragesMoving Averages

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Moving AveragesMoving Averages

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Moving AveragesMoving Averages

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Moving AveragesMoving Averages

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Exponential SmoothingExponential Smoothing

Ft1 Ft (Dt Ft )

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Multiplicative MethodMultiplicative Method

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Multiplicative MethodMultiplicative Method

1. For each year, calculate the average demand for each season by dividing annual demand by the number of seasons per year

2. For each year, divide the actual demand for each season by the average demand per season, resulting in a seasonal index for each season

3. Calculate the average seasonal index for each season using the results from Step 2

4. Calculate each season’s forecast for next year

Multiplicative seasonal method, whereby seasonal factors are multiplied by an estimate of the average demand to arrive at a seasonal forecast

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Multiplicative MethodMultiplicative Method

Year1 Year2 Year3 Year4 Yr5ForecastQ1 45 70 100 100 132.82Q2 335 370 585 725 843.62Q3 520 590 830 1160 1300.03Q4 100 170 285 215 323.52           Totals 1000 1200 1800 2200 2600Average 250 300 450 550 650                        SFYr1 SFYr2 SFYr3 SFYr4 AvgSFQ1 0.18 0.23 0.22 0.18 0.20Q2 1.34 1.23 1.30 1.32 1.30Q3 2.08 1.97 1.84 2.11 2.00Q4 0.40 0.57 0.63 0.39 0.50

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Homework (#7)

b. Use exponential smoothing with a smoothing constant of 0.10 to forecast sales for the months May through December. Start with a January forecast of 20.

c. Use exponential smoothing with a smoothing constant of 0.90 to forecast sales for the months May through December. Start with a January forecast of 20.

d. Compute the errors for each forecasting period for each method. Use absolute values so that all errors are positive. Next average the errors (for the periods May through December) for each of the three forecasting methods. Which method gives the smallest mean error, i.e. is best?

Applying Time Series TechniquesMoving AveragesExponential smoothing alpha=0.10Exponential smoothing alpha=0.90

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Homework (#7)Applying Time Series TechniquesMultiplicative Seasonal Method for handling data with seasonal trends.