Mon 31 May 2010
Tracking signals measure how well predictions fit actual data.
Qualitative Analysis
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Mon 31 May 2010
Multiple Regression with Trend and Seasonal Components
Posted by Admin under Qualitative AnalysisNo Comments
Multiple regression can be used to develop an additive decomposition model.
One independent variable is time.
Seasons are represented by dummy independent variables.
Mon 31 May 2010
Decomposition Method with Trend and Seasonal Components
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Decomposition is the process of isolating linear trend and seasonal factors to develop more accurate forecasts.
There are five steps to decomposition:
1. Compute the seasonal index for each season.
2. Deseasonalize the data by dividing each number by its seasonal index.
3. Compute a trend line with the deseasonalized data.
4. Use the trend line to forecast.
5. Multiply the forecasts by the seasonal index.
Mon 31 May 2010
Centered Moving Average (CMA) is an approach that prevents a variation due to trend from being incorrectly interpreted as a variation due to the season.
Steps of Multiplicative Time-Series Model
1. Compute the CMA for each observation.
2.Compute seasonal ratio (observation/CMA).
3. Average seasonal ratios to get seasonal indices.
4. If seasonal indices do not add to the number of seasons, multiply each index by (number of seasons)/(sum of the indices).
Mon 31 May 2010
Seasonal indices can be used to make adjustments in the forecast for seasonality.
A seasonal index indicates how a particular season compares with an average season.
The seasonal index can be found by dividing the average value for a particular season by the average of all the data.
Mon 31 May 2010
where: Y = predicted value
b1 = slope of the trend line
b0 = intercept
X = time period (1,2,3…n)
Mon 31 May 2010
Trend projections are used to forecast time-series data that exhibit a linear trend.
Least squares may be used to determine a trend projection for future forecasts.
Least squares determines the trend line forecast by minimizing the mean squared error between the trend line forecasts and the actual observed values.
The independent variable is the time period and the dependent variable is the actual observed value in the time series.
Mon 31 May 2010
Simple exponential smoothing fails to respond to trends, so a more complex model is necessary with trend adjustment.
Simple exponential smoothing – first-order smoothing
Trend adjusted smoothing – second-order smoothing
Low b gives less weight to more recent trends, while high b gives higher weight to more recent trends.
Mon 31 May 2010
Exponential smoothing is a type of moving average technique that involves little record keeping of past data.
New forecast = previous forecast + a(previous actual –previous forecast)
Mon 31 May 2010
Weighted moving averages use weights to put more emphasis on recent periods.