Week 04 Discussion - Averaging and Smoothing Methods: This week you are introduced to a class of forecasting techniquesknown collectively as "smoothing" methods. Compare and contrast these smoothing...

Week 04 Discussion - Averaging and Smoothing Methods:


This week you are introduced to a class of forecasting techniquesknown collectively as "smoothing" methods. Compare and contrast these smoothing methods with decomposition. How are they similar? How are they different? Which do you think would be more readily accepted in practice? Explain.


Answer all of the above questions in the discussion and make the discussion detailed 1.5 pages long!




Week 04 Discussion - Averaging and Smoothing Methods: This week you are introduced to a class of forecasting techniques known collectively as "smoothing" methods.  Compare and contrast these smoothing methods with decomposition.  How are they similar?  How are they different?  Which do you think would be more readily accepted in practice?  Explain. Answer all of the above questions in the discussion and make the discussion detailed 1.5 pages long! TIME SERIES SMOOTHING METHODS TIME SERIES SMOOTHING METHODS empirically-based assumes past fluctuations represent randomness that need to be smoothed determines the smooth curve to be extrapolated into the future very well accepted among practitioners useful for short-range forecasting for a large number of items, e.g., inventories for hundreds of products TWO CATEGORIES I. AVERAGING METHODS typically assigns equal weights to past observatons II. EXPONENTIAL SMOOTHING METHODS assigns decreasing weights to older observations weights decay exponentially from newest to oldest observations (hence the name!) SPECIFIC METHODS I. AVERAGING METHODS The Mean Moving Averages II. EXPONENTIAL SMOOTHING METHODS Single Exponential Smoothing (SES) Holt’s Linear Method Winter’s Trend and Seasonality Method (multiplicative or additive seasonality) STEPS IN FORECASTING Select a forecasting method based on the pattern of data. Divide data into two parts: an initialization part and a test part. Use the selected forecasting method to develop fitted values for the initialization part of the data. Use the method to forecast the test part of the data and evaluate the forecast error. Decide on adequacy of the forecasting method. ERRORS ARE NOT ALL SAME! Use the initialization set to evaluate the fit of various models by comparing “fitted” accuracy measures. These are based on the residuals (errors) calculated on the same set of data used to fit the model. These generally appear as part of the standard output provided by Minitab. Use the selected model to forecast the values in the test set. This is a true “holdout” sample as these observations were not used to fit the model. The residuals (errors) obtained from this set of data are used in computing forecast accuracy measures. THE MEAN compute the mean of the initialization part of the data to forecast the next period each successive forecast involves the addition of one more data point Advantages: easy to understand and use Disadvantages: appropriate only when data are stationary (has no noticeable trend or seasonality) ALTERNATE EXPRESSION FOR THE MEAN This shows how using the average of all past values as a forecast can be computed with only the previous forecast (multiplying it by t gives the total of the observations to that point) and the newly observed actual value. The forecast for period t+2 only requires knowledge of the previous forecast for the current period (t+1) and the observed value for the current period. MOVING AVERAGES involves computing a mean of the k most recent observations to forecast the next period each successive forecast is computed by dropping the oldest value and including the newest observation the mean “moves” through the data period by period moving average of order 1 is the naïve method increasing k results in a greater smoothing effect MOVING AVERAGES Advantages: mimics data better than the mean when data are not stationary number of data points in each average is constant Disadvantages: does not deal with trend or seasonality (forecast lags behind actual data) ALTERNATE EXPRESSION FOR A MOVING AVERAGE OF ORDER k This shows how each new forecast is simply an adjustment of the immediately preceding forecast. If k is a big number then this adjustment is small (conversely if k is a small number then this adjustment is large). It is useful to think of forecasts as adjusted previous forecasts (the adjustment being based on actual observed values). SINGLE EXPONENTIAL SMOOTHING the forecast is simply the previous forecast plus an adjustment for the error an alpha (α) value close to 1 includes a substantial adjustment for any error in the previous forecast (little smoothing) an alpha (α) value close to 0 produces a forecast that is very similar to the previous forecast (greater smoothing and less adjustment) need to determine the optimal value for alpha and an initial forecast (initialization) Advantages: requires few computations easy to use and understand attractive when a large number of items need to be forecasted Disadvantages: no ability to deal with trend or seasonality SINGLE EXPONENTIAL SMOOTHING HOLT’s LINEAR METHOD (or DOUBLE EXPONENTIAL SMOOTHING) an extension of Single Exponential Smoothing to accommodate trend involves three aspects: (1) the use of a single exponentially smoothed value, (2) an adjustment which is the difference between the single and double exponentially smoothed value, and (3) an adjustment for trend need to determine the optimal parameter value(s) need to determine the initial values for the smoothed series need to determine an initial trend estimate does not handle seasonality HOLT’s LINEAR METHOD WINTER’s TREND AND SEASONALITY METHOD (or TRIPLE EXPONENTIAL SMOOTHING) an extension of Simple Exponential Smoothing to accommodate trend and seasonality similar to Holt’s Linear Method with an additional equation used to estimate a seasonal index can handle additive or multiplicative seasonality involves three smoothing equations and the estimation of three smoothing parameters: alpha, beta and gamma need to find optimal values for three parameters need to determine an initial value for the seasonal estimate (in addition to the initial smoothed value and initial trend estimate) WINTER’s MULTIPLICATIVE MODEL WINTER’s ADDITIVE MODEL FITTING EXPONENTIAL SMOOTHING MODELS We will rely on Minitab to fit exponential smoothing models, so we won’t be doing calculations using the smoothing equations. Nonetheless, there are issues that need to be understood in fitting exponential smoothing models and using them to forecast. These are initialization, optimization and prediction intervals. IMPLEMENTATION ISSUES – INITIALIZATION Initialization Initial values are required to get the method started There are different ways to get initial values Initial values play a role in all subsequent forecasts Problem is somewhat academic because eventually their effects diminish significantly as we progress further into the future For example, if we are using Winter’s model we need initial values for Lt (initial smoothed value),Tt (initial value for trend) and St (initial seasonal index values). Minitab has its own default methods for initializing. IMPLEMENTATION ISSUES – OPTIMIZATION Optimization Need to find optimal values for the smoothing constants (up to three in Winter’s model: alpha, beta and gamma). Optimization must be based on some criteria (most forecasting packages give optimal parameter values by minimizing MSE). Minitab will optimize for alpha and beta but not gamma (it sets default values for gamma). IMPLEMENTATION ISSUES – PREDICTION INTERVALS Prediction Intervals Smoothing methods are empirical, not statistical. Although software packages may provide prediction intervals for forecasts generated by smoothing models, these are not true intervals (because these are not derived from statistical models). Be cautious when interpreting them. FINAL THOUGHTS Exponential smoothing is a procedure for continually revising a forecast in light of more-recent experience (actual values of the variable as they become realized). The ability to implement a tracking signal helps to automate these procedures (when the cumulative error goes outside some specified limit, the forecaster is alerted). Don’t forget that the adequacy of these models should be evaluated. 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