Part 2 Error Statistics, Moving Average, and Exponential Smoothing

Time Series Forecasting: Part 2 Error Statistics, Moving Average, and Exponential Smoothing

Steven Coy Ph.D.

Professor of Management

Forecast Error

Forecast error formula

Some facts about forecast error:

Error is not really a bad thing

Error is inevitable

No forecasting model is always right!

Most forecasting models are always wrong!

Forecast Accuracy Metrics

Mean Absolute Deviation (MAD) or Mean Absolute Error (MAE) weights all errors evenly.

Mean Squared Error (MSE) weights errors according to their squared values.

Mean Absolute Percentage Error (MAPE_ weights errors according to relative error.

Bias measures the degree to which the forecast overstates or understates the actual value.

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Measures of Forecast Accuracy Gasoline Sales

Forecasting method is called the Naïve method.

Next forecast is last observed value:

From Business Analytics by Camm, Cochran, Fry, Ohlmann, Anderson, Sweeney, and Williams. 2015

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Measures of Forecast Accuracy Gasoline Sales

Compare the accuracy of the two forecasting methods by comparing the values of MAE, MSE, and MAPE for each method.

Which is the better technique for this data?

Material from Business Analytics by Camm, Cochran, Fry, Ohlmann, Anderson, Sweeney, and Williams. 2015

Naïve method Average of Past Values
MAE 3.73 2.69
MSE 16.27 8.10
MAPE 19.24% 12.85%
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Moving Average

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General Merchandise Sales Example: Moving Average

Note: The Retail Sales Data appear in column J of the spreadsheet.

This example is covered in the Time Series Forecasting Examples Videos.

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Line Plot of Actual and Moving Average Forecasts

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Enlarged View of MA Forecasts

Increasing number of periods in MA results in smoother forecasts. Green is MA(3) and red is MA(6).

Exponential Smoothing

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General Merchandise Sales Example: Exponential Smoothing

Note: The Retail Sales Data appear in column J, and the ES forecasts appear in column M.

This example is covered in the Time Series Forecasting Examples Videos.

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Line Plot of Actual and Exponential Smoothing Forecasts

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