PROYECCIÓN DE TENDENCIA📈(SERIES DE TIEMPO🕑)|EJERCICIO RESUELTO

Summary

The video explains how to forecast future values in a time series using trend projection. This method fits a straight line to historical data and extends it to estimate future values.

The trend line is written as:

[ \hat{y}=a+bx ]

where:

• (\hat{y}) is the forecast value of the dependent variable.
• (a) is the y-intercept.
• (b) is the slope of the line.
• (x) is the independent variable, represented here by the time period.

Method Demonstrated

The example uses motorcycle sales from 2011 to 2020, measured in thousands of units.

1. Number the time periods: Assign period 1 to 2011, period 2 to 2012, and continue through period 10 for 2020.
2. Set up the variables: Use the period as (x) and sales as (y). Plot the periods on the horizontal axis and sales on the vertical axis to inspect the overall pattern.

3. Calculate the slope (b):

   • Add columns for (xy) and (x^2).
   • Calculate the required totals and means.

   • Apply the formula: [ b=\frac{\sum xy-n\bar{x}\bar{y}}{\sum x^2-n\bar{x}^2} ]

   • For the example, (b=1.1). Since sales are recorded in thousands, this represents an increase of about 1.1 thousand units per period. 4. Calculate the intercept (a): [ a=\bar{y}-b\bar{x} ] The example gives (a=20.4).

4. Write the trend equation: [ \hat{y}=20.4+1.1x ]

5. Forecast future periods:

   • For 2021, (x=11), giving a forecast of 32.5 thousand motorcycles (32,500 units).
   • For 2022, (x=12), giving a forecast of 33.6 thousand motorcycles (33,600 units).
6. Show the results on the graph: Plot the intercept and forecast points, then connect them to illustrate the fitted trend line and its upward direction.

The video cautions that forecasts several periods into the future may become less reliable because market conditions can change. It notes that some authors recommend limiting projections to about two periods.

Speakers and Sources Featured

• Professor Oscar Luis — the video’s instructor and narrator.
• The video also uses a table of motorcycle sales data and graphs as teaching materials. No other speakers are identified.