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TimeSeries.pdf

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Time Series and Forecasting

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A TIME SERIES is a collection of data recorded over a period of time (weekly, monthly, or quarterly), that can be used by management to compute forecasts as input to planning and decision making. It usually assumes past patterns will continue into the future.

Time Series and its Components

Components of a Time Series  Secular Trend – the smooth long term direction of a time series  Cyclical Variation – the rise and fall of a time series over periods longer than

one year  Seasonal Variation – Patterns of change in a time series within a year which

tends to repeat each year  Irregular Variation – residuals and exogenous shocks

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Secular Trend – Example

The number of employees at Home Depot from 1993 to 2012

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Cyclical Variation – Sample Chart

The annual unit sales of batteries sold by National Battery Retails Inc. from 1991 to 2010

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Seasonal Variation – Sample Chart

Quarterly sales of Hercher Sporting G Inc, a Chicago area sporting goods company specializes in selling baseball and softball equipment to high schools, colleges and youth leagues.

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Example: Sears Revenue Data

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Sears Quartly Revenue 1995-2013

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The Moving Average Method  Useful in smoothing time series to see its

trend.  Basic method used in measuring seasonal

fluctuation.  Applicable when a time series follows a

fairly linear trend.

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Moving Average Method - Example

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Example: Sears Revenue Data

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Sears Quartly Revenue 1995-2013

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Linear Trend  The long term trend of a time series may approximate

a straight line.

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Linear Trend – Using the Least Squares Method, Regression Analysis, and Excel

 Use the least squares method in Simple Linear Regression to find the best linear relationship between the times series and time.

 Code time (t) and use it as the independent variable. That is, let t be 1 for the first year, 2 for the second, and so on.

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Linear Trend Plot

y = 49.411x + 7514.9 R² = 0.1752

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Sears Quartly Revenue 1995-2013

Structural Break

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Seasonal Variation  One of the components of a time series.  Seasonal variations are fluctuations that coincide with certain

seasons and are repeated year after year.  Understanding seasonal fluctuations help plan for sufficient goods

and materials on hand to meet varying seasonal demand.  Analysis of seasonal fluctuations over a period of years help in

evaluating current sales.

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Seasonally Adjusted and Detrended Data

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Component Analysis for Revenue Multiplicative Model

Original Data

Seasonally Adjusted Data

Detrended Data

Seas. Adj. and Detr. Data

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Example: Sears Revenue Data

• The merger of Kmart and Sears closed on March 24, 2015. • The company expected consistent quarters of decline ever since. • The Sears CEO Eddie Lampert’s penny-pinching ways could have

been the major reason for the decline, according to some critics. • “In 2010, Lampert’s capital expenditure on store improvements

was roughly 1 percent of sales. Compare that to Macy’s, which is 2.5 percent, and Walmart’s 8.8 percent of sales.”

• “In February, he (Lampert) flummoxed the industry by hiring an IBM veteran with no retail experience to run Sears and Kmart.”

• Source: “Not so fast, Eddie” by Jamens Covert, New York post, May 22, 2015

  • Time Series and Forecasting
  • Time Series and its Components
  • Secular Trend – Example
  • Cyclical Variation – Sample Chart
  • Seasonal Variation – Sample Chart
  • Example: Sears Revenue Data
  • The Moving Average Method
  • Moving Average Method - Example
  • Example: Sears Revenue Data
  • Linear Trend
  • Linear Trend – Using the Least Squares Method, Regression Analysis, and Excel
  • Linear Trend Plot
  • Seasonal Variation
  • Seasonally Adjusted and Detrended Data
  • Example: Sears Revenue Data