Six Sigma Black Belt Training

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Six Sigma Black Belt Training
Time Series Forecasting
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Time Series Forecasting
Time Series Data can be seen across two
dimensions the presence or absence of a trend,
and the presence or absence of seasonality, thus
creating four basic patterns for analysis. Shown
here are the techniques that are used to analyze
each of the four basic patterns.
Techniques for analyzing time series data
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Stationary Data No trend or Seasonality
For stationary data, averaging techniques are the
way to forecast. An n-period moving average is
used. The key question is what n should be, and
whether or not the average is weighted and if
so, what weighting scheme makes most sense. Here
is some sales data, in millions of dollars.
Period Sales 1 60 2 67 3 50 4 58 5 62
6 60 7 55 8 62 9 71 10 65
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Stationary Data The Naive Forecast - Minitab
The naïve forecast is the simplest form of a
moving average the average of 1 period!
Essentially, the actual value for a period is the
forecast for the subsequent one. Can be used as a
baseline for comparison. On occasion, may turn
out to be quite an effective forecast.
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The Naive Forecast Computational Details
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Stationary Data A 3-period Moving Average
Forecast
An 3 period moving average forecast on the same
data is shown here.
How does the forecast compare with the Naïve
forecast? Interpret MAD, MAPE, and MSD. Is there
a bias in the forecast?
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The 3-period MA Forecast Computational Details
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Stationary Data A Simple Exponential Smoothing
Forecast
A simple exponential smoothing forecast is a
weighted average of all historical data, with
weights getting exponentially smaller, the
further back in history one goes. It is generally
appropriate for a non-stationary, slowly
meandering mean value. Here it is applied to the
same stationary data as with the previous two
techniques.
How does the forecast here compare? What if alpha
were changed from 0.3 to some other value?
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Exponential Smoothing Computational Details
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Data with Trend Linear Model
For stationary data, regression analysis, or
fitting a trend line is not useful, since the
line will be horizontal, and essentially an
average. Similarly, for data with trend, a
moving average is not the best approach. Can you
see why not?
Period Sales 1 60 2 88 3 50 4 111
5 135 6 90 7 150 8 149 9 200 10 190
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Data with Trend and Seasonality Classical
Decomposition Model
Consider the sales data shown here for 4 years.
The graph at top left shows the trend and
seasonal components in the original data vividly.
Quarter Sales 1 25 2 28 3 35 4
50 5 39 6 44 7 55 8 70 9
52 10 60 11 77 12 100 13 85 14 100 15 111 16
140
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Data with Trend and Seasonality Classical
Decomposition Model
The green line shows the underlying trend, while
the red shows the fitted values. The blue line
shows the forecasts for the next four quarters,
adjusted for seasonality. Without adjustment, the
forecasts would be on the extended green line.
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Stationary data with Seasonality
What technique would you use for the following
data?
Period Sales 1 60 2 67 3 61 4 68 5 58
6 65 7 59 8 70 9 61 10 65