Time Series Lecture Notes

Introduction to Time Series Methods

• First Method: Free Hand Method
• Second Method: Method of Semi Averages
  • Important and easy to understand
  • Graphical method

Method of Semi Averages

• Objective: Fit a trend value using the method of semi-averages.
• Data Provided: Sales data from 1991 to 1996 (in thousands of units)

Steps to Calculate Semi Averages:

1. Divide the Data:
   • Split the 6 years data into two groups of 3 years each.
2. Calculate the Averages:
   • First Group (1991-1993):
     • Sales: 20, 24, 22
     • Total = 20 + 24 + 22 = 66
     • Average = 66 / 3 = 22
   • Second Group (1994-1996):
     • Sales: 30, 28, 32
     • Total = 30 + 28 + 32 = 90
     • Average = 90 / 3 = 30

Graphical Representation:

• X-axis: Years (1991, 1992, 1993, 1994, 1995, 1996)
• Y-axis: Sales (Class Interval of 10 - From 10 to 40)

Plotting the Actual and Trend Lines:

1. Plot Actual Sales Data:
   • 1991: 20
   • 1992: 24
   • 1993: 22
   • 1994: 30
   • 1995: 28
   • 1996: 30
2. Plot Semi-Averages:
   • Average for 1991-1993 (22) is plotted for the year 1992.
   • Average for 1994-1996 (30) is plotted for the year 1995.
3. Draw Trend Line:
   • Connect the two semi-averages on the graph.

Observations:

• The trend line should ideally go through the plotted points of actual sales data.
• Verify that the trend line is positioned correctly relative to actual sales.

Conclusion:

• Note:
  • 6 years of data were used. Average for the first three years is 22; for the last three years is 30.
  • This process is simple and effective for understanding trends in time series data.

Next Steps:

• Explore other methods of trend analysis.
• Review additional resources linked in the description for further study.

Additional Resources:

• Search for specific topics on YouTube (e.g., Break-even point) for more learning materials.