TREND AND SEASONALITY 77-83
TECHNIQUES FOR TRENDS
- Need to look at historical data to discover if a trend exists
- If data shows a trend, need to develop an equation that reps the
trend in order to forecast
LINEAR TREND
- Linear regression fit a trend line to a series of historical data and use
regression to find the equation of the line (called the least squares lines)
- Minimizes the square of errors
- Use simple linear regression
- Equation: y = a+bx
- Slope: b = n(sum t*y) - sum(t)sum(y) / n(sum t^2) - (sum
t)^
- Y intercept: a = sum y - b(sum t) / n
- Linear trend line develops a line of best fit
- Amongst the actual observation data points
,
, NONLINEAR TREND
- Linear trends = easy to estimate because they are like a line
- Non linear = can take various shapes and thus difficult to estimate or
formulate in the form of a formula
TREND ADJUSTED EXPONENTIAL SMOOTHING
- Aka double exponential smoothing
- Has the ability to adjust to changes in trends
- Manager must decide if this benefit justifies the extra calculations
- Used when a time series exhibits a trend
- Forecast will lag behind the trend
w If data is increasing --> forecast will be too low
w Iff data is decreasing --> forecast will be too high
- Alpha a = smoothing constant for average
- Beta b = smoothing constant for trend
w Select values of a and b (usually through trial and error)
and make an estimate of starting smoothes series and
smoothed trend
- Use the most recent trend to estimate starting smoothing average
and trend
TECHNIQUES FOR TRENDS
- Need to look at historical data to discover if a trend exists
- If data shows a trend, need to develop an equation that reps the
trend in order to forecast
LINEAR TREND
- Linear regression fit a trend line to a series of historical data and use
regression to find the equation of the line (called the least squares lines)
- Minimizes the square of errors
- Use simple linear regression
- Equation: y = a+bx
- Slope: b = n(sum t*y) - sum(t)sum(y) / n(sum t^2) - (sum
t)^
- Y intercept: a = sum y - b(sum t) / n
- Linear trend line develops a line of best fit
- Amongst the actual observation data points
,
, NONLINEAR TREND
- Linear trends = easy to estimate because they are like a line
- Non linear = can take various shapes and thus difficult to estimate or
formulate in the form of a formula
TREND ADJUSTED EXPONENTIAL SMOOTHING
- Aka double exponential smoothing
- Has the ability to adjust to changes in trends
- Manager must decide if this benefit justifies the extra calculations
- Used when a time series exhibits a trend
- Forecast will lag behind the trend
w If data is increasing --> forecast will be too low
w Iff data is decreasing --> forecast will be too high
- Alpha a = smoothing constant for average
- Beta b = smoothing constant for trend
w Select values of a and b (usually through trial and error)
and make an estimate of starting smoothes series and
smoothed trend
- Use the most recent trend to estimate starting smoothing average
and trend
