2.1 Tecniche di Previsione.pdf

Forecasting  Forecasting
Forecast – An estimate of the future level of some variable.
Why Forecast?
Assess long-term capacity needs
Develop budgets, hiring plans, etc.
Plan production or order materials  Laws of Forecasting
Forecasts are almost always...

Forecasting  Forecasting
Forecast – An estimate of the future level of some variable.
Why Forecast?
Assess long-term capacity needs
Develop budgets, hiring plans, etc.
Plan production or order materials  Laws of Forecasting
Forecasts are almost always wrong by some amount (but they are still useful).
Forecasts for the near term tend to be more accurate.
Forecasts for groups of products or services tend to be more accurate.  Forecasting Methods
Qualitative forecasting techniques – Forecasting techniques based on intuition or informed opinion.
Used when data are scarce, not available, or irrelevant.
Quantitative forecasting models – Forecasting models that use measurable, historical data to generate forecasts.
Time series and causal models Selecting a Forecasting Method  Demand movement
Randomness – Unpredictable movement from one time period to the next.
Trend – Long-term movement up or down in a time series.
Seasonality – A repeated pattern of spikes or drops in a time series associated with certain times of the year. Time series with randomness  Time series with Trend and Seasonality  Last Period Model
Last Period Model - The simplest time series model that uses demand for the current period as a forecast for the next period. Ft+1 = Dt where Ft+1= forecast for the next period, t+1 and Dt = demand for the current period, t Last Period Model  Moving Average Model
Moving Average Model – A time series forecasting model that derives a forecast by taking an average of recent demand value. n ∑D t +1−i Ft +1 = i =1 n  Moving Average Model Period Demand 1 12 n 2 15 ∑ Dt +1−i 3 4 11 9 Ft +1 = i =1 5 10 n 6 8 7 14 3-period moving average 8 12 forecast for Period 8: = (14 + 8 + 10) / 3 = 10.67  Weighted Moving Average Model
Weighted Moving Average Model – A form of the moving average model that allows the actual weights applied to past observations to differ.  Weighted Moving Average Model Period Demand 1 12 2 15 3 11 4 9 5 10 6 8 7 14 3-period weighted moving 8 12 average forecast for Period 8= [(0.5 × 14) + (0.3 × 8) + (0.2 × 10)] / 1 = 11.4  Exponential Smoothing Model
Exponential Smoothing Model – A form of the moving average model in which the forecast for the next period is calculated as the weighted average of the current period’s actual value and forecast.  Exponential Smoothing Model α =.3 Period Demand Forecast 1 50 40 2 46.3 * 50 + (1-.3) * 40 = 43 3 52.3 * 46 + (1-.3) * 43 = 43.9 4 48.3 * 52 + (1-.3) * 43.9 = 46.33 5 47.3 * 48 + (1-.3) * 46.33 = 46.83 6.3 * 47 + (1-.3) * 46.83 = 46.88 α ??  Adjusted Exponential Smoothing
Adjusted Exponential Smoothing Model – An expanded version of the exponential smoothing model that includes a trend adjustment factor. AFt+1 = Ft+1 +Tt+1 where AFt+1 = adjusted forecast for the next period Ft+1 = unadjusted forecast for the next period = α Dt + (1 – α) Ft Tt+1 = trend factor for the next period = β (Ft+1 – Ft) + (1 – β)Tt Tt = trend factor for the current period β = smoothing constant for the trend adjustment factor Adjusted Exponential Smoothing - Example  Linear Regression
 Linear Regression
How to calculate the a and b Linear Regression – Example Linear Regression – Example 9.3 Linear Regression – Example The graph shows an upward trend of 7.33 sales per month.  Seasonal Adjustments
Seasonality – Repeated patterns or drops in a time series associated with certain times of the year.  Seasonal Adjustments
Four-step procedure:
For each of the demand values in the time series, calculate the corresponding forecast using the unadjusted forecast model.
For each demand value, calculate (Demand/Forecast).
If the time series covers multiple years, take the average (Demand/Forecast) for corresponding months or quarters to derive the seasonal index. Otherwise use (Demand/Forecast) calculated in Step 2 as the seasonal index.
Multiply the unadjusted forecast by the seasonal index to get the seasonally adjusted forecast value. Seasonality – Example Note that the regression forecast does not reflect the seasonality. Seasonality – Example  Seasonality – Example Calculate the (Demand/Forecast) for each of the time periods: January 2012: (Demand/Forecast) = 51/106.9 =.477 January 2013: (Demand/Forecast) = 112/205.6 =.545 Calculate the monthly seasonal indices: Monthly seasonal index, January = (.477 +.545)/2 =.511 Calculate the seasonally adjusted forecasts Seasonally adjusted forecast = unadjusted forecast x seasonal index January 2012: 106.9 x.511 = 54.63 January 2013: 205.6 x.511 = 105.06 Seasonality – Example 9.4 Note that the regression forecast now does reflect the seasonality.  Causal Forecasting Models
Linear Regression
Multiple Regression
Examples:  Multiple Regression
Multiple Regression – A generalized form of linear regression that allows for more than one independent variable.  Forecast Accuracy How do we know:
If a forecast model is “best”?
If a forecast model is still working?
What types of errors a particular forecasting model is prone to make? Need measures of forecast accuracy  Measures of Forecast Accuracy
Forecast error for period i FEi =
Mean forecast error (MFE) =
Mean absolute deviation (MAD) =  Measures of Forecast Accuracy
Mean absolute percentage error MAPE =
Tracking Signal TS= MFE, MAD, TS Forecast Accuracy – Example Forecast Accuracy – Example  Forecast Accuracy – Example
Model 2 has the lowest MFE so it is the least biased.
Model 2 also has the lowest MAD and MAPE values so it appears to be superior.
Calculate the tracking signal for the first 10 weeks. Forecast Accuracy – Example  Forecast Accuracy – Example
The tracking signal for Model 2 gets very low in week 5, however the model recovers.
You need to continue to update the tracking signal in the future.