1 Module 4. Forecasting MGS3100 Slide 2 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment Delphi Method Grassroots Slide 3 3 Casual Models: Causal Model Year 2000 Sales Price Population Advertising Time Series Models: Time Series Model Year 2000 Sales Sales 1999 Sales 1998 Sales 1997 -- Forecasting based on data and models Quantitative Forecasting Slide 4 4 Causal forecasting Regression Find a straight line that fits the data best. y = Intercept + slope * x (= b 0 + b 1 x) Slope = change in y / change in x Best line! Intercept Slide 5 5 Causal Forecasting Models Curve Fitting: Simple Linear Regression One Independent Variable (X) is used to predict one Dependent Variable (Y): Y = a + b X Given n observations (X i, Y i ), we can fit a line to the overall pattern of these data points. The Least Squares Method in statistics can give us the best a and b in the sense of minimizing (Y i - a - bX i ) 2 : Regression formula is an optional learning objective Slide 6 6 Curve Fitting: Simple Linear Regression Find the regression line with Excel Use Function: a = INTERCEPT(Y range; X range) b = SLOPE(Y range; X range) Use Solver Use Excels Tools | Data Analysis | Regression Curve Fitting: Multiple Regression Two or more independent variables are used to predict the dependent variable: Y = b 0 + b 1 X 1 + b 2 X 2 + + b p X p Use Excels Tools | Data Analysis | Regression Slide 7 7 Time Series Forecasting Process Look at the data (Scatter Plot) Forecast using one or more techniques Evaluate the technique and pick the best one. Observations from the scatter Plot Techniques to tryWays to evaluate Data is reasonably stationary (no trend or seasonality) Heuristics - Averaging methods Naive Moving Averages Simple Exponential Smoothing MAD MAPE Standard Error BIAS Data shows a consistent trend Regression Linear Non-linear Regressions (not covered in this course) MAD MAPE Standard Error BIAS R-Squared Data shows both a trend and a seasonal pattern Classical decomposition Find Seasonal Index Use regression analyses to find the trend component MAD MAPE Standard Error BIAS R-Squared Slide 8 8 BIAS - The arithmetic mean of the errors n is the number of forecast errors Excel: =AVERAGE(error range) Mean Absolute Deviation - MAD No direct Excel function to calculate MAD Evaluation of Forecasting Model Slide 9 9 Mean Square Error - MSE Excel: =SUMSQ(error range)/COUNT(error range) Standard error is square root of MSE Mean Absolute Percentage Error - MAPE R 2 - only for curve fitting model such as regression In general, the lower the error measure (BIAS, MAD, MSE) or the higher the R 2, the better the forecasting model Evaluation of Forecasting Model Slide 10 10 Stationary data forecasting Nave I sold 10 units yesterday, so I think I will sell 10 units today. n-period moving average For the past n days, I sold 12 units on average. Therefore, I think I will sell 12 units today. Exponential smoothing I predicted to sell 10 units at the beginning of yesterday; At the end of yesterday, I found out I sold in fact 8 units. So, I will adjust the forecast of 10 (yesterdays forecast) by adding adjusted error ( * error). This will compensate over (under) forecast of yesterday. Slide 11 11 Nave Model The simplest time series forecasting model Idea: what happened last time (last year, last month, yesterday) will happen again this time Nave Model: Algebraic: F t = Y t-1 Y t-1 : actual value in period t-1 F t : forecast for period t Spreadsheet: B3: = A2; Copy down Slide 12 12 Moving Average Model Simple n-Period Moving Average Issues of MA Model Nave model is a special case of MA with n = 1 Idea is to reduce random variation or smooth data All previous n observations are treated equally (equal weights) Suitable for relatively stable time series with no trend or seasonal pattern Slide 13 13 Smoothing Effect of MA Model Longer-period moving averages (larger n) react to actual changes more slowly Slide 14 14 Moving Average Model Weighted n-Period Moving Average Typically weights are decreasing: w 1 >w 2 >>w n Sum of the weights = w i = 1 Flexible weights reflect relative importance of each previous observation in forecasting Optimal weights can be found via Solver Slide 15 15 Weighted MA: An Illustration Month Weight Data August 17%130 September 33%110 October 50%90 November forecast: F Nov = (0.50)(90)+(0.33)(110)+(0.17)(130) = 103.4 Slide 16 16 Exponential Smoothing Concept is simple! Make a forecast, any forecast Compare it to the actual Next forecast is Previous forecast plus an adjustment Adjustment is fraction of previous forecast error Essentially Not really forecast as a function of time Instead, forecast as a function of previous actual and forecasted value Slide 17 17 Simple Exponential Smoothing A special type of weighted moving average Include all past observations Use a unique set of weights that weight recent observations much more heavily than very old observations: weight Decreasing weights given to older observations Today Slide 18 18 Simple ES: The Model New forecast = weighted sum of last period actual value and last period forecast : Smoothing constant F t :Forecast for period t F t-1 :Last period forecast Y t-1 :Last period actual value Slide 19 19 Simple Exponential Smoothing Properties of Simple Exponential Smoothing Widely used and successful model Requires very little data Larger, more responsive forecast; Smaller, smoother forecast (See Table 13.2) best can be found by Solver Suitable for relatively stable time series Slide 20 20 Time Series Components Trend persistent upward or downward pattern in a time series Seasonal Variation dependent on the time of year Each year shows same pattern Cyclical up & down movement repeating over long time frame Each year does not show same pattern Noise or random fluctuations follow no specific pattern short duration and non-repeating Slide 21 21 Time Series Components Time Trend Random movement Time Cycle Time Seasonal pattern Demand Time Trend with seasonal pattern Slide 22 22 Trend Model Curve fitting method used for time series data (also called time series regression model) Useful when the time series has a clear trend Can not capture seasonal patterns Linear Trend Model: Y t = a + bt t is time index for each period, t = 1, 2, 3, Slide 23 23 Pattern-based forecasting - Trend Regression Recall Independent Variable X, which is now time variable e.g., days, months, quarters, years etc. Find a straight line that fits the data best. y = Intercept + slope * x (= b 0 + b 1 x) Slope = change in y / change in x Best line! Intercept Slide 24 24 Pattern-based forecasting Seasonal Once data turn out to be seasonal, deseasonalize the data. The methods we have learned (Heuristic methods and Regression) is not suitable for data that has pronounced fluctuations. Make forecast based on the deseasonalized data Reseasonalize the forecast Good forecast should mimic reality. Therefore, it is needed to give seasonality back. Slide 25 25 Pattern-based forecasting Seasonal Deseasonalize Forecast Reseasonalize Actual dataDeseasonalized data Example (SI + Regression) Slide 26 26 Pattern-based forecasting Seasonal Deseasonalization Deseasonalized data = Actual / SI Reseasonalization Reseasonalized forecast = deseasonalized forecast * SI Slide 27 27 Seasonal Index Whats an index? Ratio SI = ratio between actual and average demand Suppose SI for quarter demand is 1.20 Whats that mean? Use it to forecast demand for next fall So, where did the 1.20 come from?! Slide 28 28 Calculating Seasonal Indices Quick and dirty method of calculating SI For each year, calculate average demand Divide each demand by its yearly average This creates a ratio and hence a raw index For each quarter, there will be as many raw indices as there are years Average the raw indices for each of the quarters The result will be four values, one SI per quarter Slide 29 29 Classical decomposition Start by calculating seasonal indices Then, deseasonalize the demand Divide actual demand values by their SI values y = y / SI Results in transformed data (new time series) Seasonal effect removed Forecast Regression if deseasonalized data is trendy Heuristics methods if deseasonalized data is stationary Reseasonalize with SI Slide 30 30 Causal or Time series? What are the difference? Which one to use? Slide 31 31 Can you describe general forecasting process? compare and contrast trend, seasonality and cyclicality? describe the forecasting method when data is stationary? describe the forecasting method when data shows trend? describe the forecasting method when data shows seasonality?
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