MGS3100_03.ppt/Feb 11, 2016/Page 1 Georgia State University - Confidential MGS 3100 Business Analysis Time Series Forecasting Feb 11, 2016

MGS3100_03.ppt/Feb 11, 2016/Page 2 Georgia State University - Confidential Agenda Qualitative Forecasting Models Quantitative Forecasting Models Forecasting

MGS3100_03.ppt/Feb 11, 2016/Page 3 Georgia State University - Confidential Eight Steps to Forecasting Determine the use of the forecast  What objective are we trying to obtain? Select the items or quantities that are to be forecasted. Determine the time horizon of the forecast.  Short time horizon – 1 to 30 days  Medium time horizon – 1 to 12 months  Long time horizon – more than 1 year Select the forecasting model or models Gather the data to make the forecast. Validate the forecasting model Make the forecast Implement the results

MGS3100_03.ppt/Feb 11, 2016/Page 4 Georgia State University - Confidential Model Differences Qualitative (ex: Delphi) – incorporates judgmental & subjective factors into forecast. Quantitative (ex: Time-Series) – attempts to predict the future by using historical data. Causal – incorporates factors that may influence the quantity being forecasted into the model

MGS3100_03.ppt/Feb 11, 2016/Page 5 Georgia State University - Confidential Agenda Qualitative Forecasting Models Quantitative Forecasting Models Forecasting

MGS3100_03.ppt/Feb 11, 2016/Page 6 Georgia State University - Confidential Qualitative Forecasting Models Delphi method Iterative group process allows experts to make forecasts Participants:  decision makers: experts who make the forecast  staff personnel: assist by preparing, distributing, collecting, and summarizing a series of questionnaires and survey results  respondents: group with valued judgments who provide input to decision makers

MGS3100_03.ppt/Feb 11, 2016/Page 7 Georgia State University - Confidential Qualitative Forecasting Models Jury of executive opinion Opinions of a small group of high level managers, often in combination with statistical models. Result is a group estimate. Sales force composite Each salesperson estimates sales in his region. Forecasts are reviewed to ensure realistic. Combined at higher levels to reach an overall forecast. Consumer market survey Solicits input from customers and potential customers regarding future purchases. Used for forecasts and product design & planning

MGS3100_03.ppt/Feb 11, 2016/Page 8 Georgia State University - Confidential Agenda Qualitative Forecasting Models Quantitative Forecasting Models Forecasting

MGS3100_03.ppt/Feb 11, 2016/Page 9 Georgia State University - Confidential Time Series Forecasting Process Look at the data (Scatter Plot) Forecast using one or more techniques Evaluate the technique and pick the best one. Look  Forecast  Evaluate Look at data – Graph it! Forecast using appropriate method, based on best possible fit Evaluate using indicators (Bias, MAD, MAPE, MSE, Std Error, R2) Use indicators to evaluate model

MGS3100_03.ppt/Feb 11, 2016/Page 10 Georgia State University - Confidential Time Series Forecasting Process Observations from the scatter Plot Techniques to tryWays to evaluate 1.Data is reasonably stationary (no trend or seasonality) Heuristics - Averaging methods  Naive  Moving Averages  Simple Exponential Smoothing  MAD  MAPE  Standard Error  BIAS 1.Data shows a consistent trend  Simple Regression  Quadratic Regression  Log Y Regression  Other non-linear Regressions (not covered in this course)  MAD  MAPE  Standard Error  BIAS  R-Squared 1.Data shows both a trend and a seasonal pattern  Classical decomposition  Find Seasonal Index  Use one of the above regression analyses to find the trend component  MAD  MAPE  Standard Error  BIAS  R-Squared

MGS3100_03.ppt/Feb 11, 2016/Page 11 Georgia State University - Confidential Forecast Error Error - Difference between the actual value and the forecasted value. Also called the deviation Bias - The average of the errors MAD - Mean Absolute Deviation - Take the average of the absolute errors MAPE - Mean Absolute Percentage Error - Calculate the % of the error using the absolute error, then average the results MSE - Mean Square Error Standard Error - Take the square root of the MSE

MGS3100_03.ppt/Feb 11, 2016/Page 12 Georgia State University - Confidential Quantitative Forecasting Models - 1) Naïve Forecast Naïve Whatever happened recently will happen again this time (same time period) The model is simple and flexible Provides a baseline to measure other models Attempts to capture seasonal factors at the expense of ignoring trend The easiest possible method - use last periods number as your forecast

MGS3100_03.ppt/Feb 11, 2016/Page 13 Georgia State University - Confidential Qualitative Forecasting Models - 1) Naïve Forecast

MGS3100_03.ppt/Feb 11, 2016/Page 14 Georgia State University - Confidential Qualitative Forecasting Models - 1) Naïve Forecast

MGS3100_03.ppt/Feb 11, 2016/Page 15 Georgia State University - Confidential Qualitative Forecasting Models - 2) Moving Averages Moving Averages Assumes item forecasted will stay steady over time. Technique will smooth out short-term irregularities in the time series. Sliding scale for n time periods Σ Y i i=T-1 n YT=YT= ^ T-n

MGS3100_03.ppt/Feb 11, 2016/Page 16 Georgia State University - Confidential Qualitative Forecasting Models - 2) Moving Averages

MGS3100_03.ppt/Feb 11, 2016/Page 17 Georgia State University - Confidential Qualitative Forecasting Models - 2) Moving Averages

MGS3100_03.ppt/Feb 11, 2016/Page 18 Georgia State University - Confidential Qualitative Forecasting Models - 2) Moving Averages

MGS3100_03.ppt/Feb 11, 2016/Page 19 Georgia State University - Confidential Qualitative Forecasting Models - 3) Weighted Moving Averages Weighted Moving Averages Assumes data from some periods are more important than data from other periods (e.g. earlier periods). Use weights to place more emphasis on some periods and less on others.

MGS3100_03.ppt/Feb 11, 2016/Page 20 Georgia State University - Confidential Qualitative Forecasting Models - 3) Weighted Moving Averages

MGS3100_03.ppt/Feb 11, 2016/Page 21 Georgia State University - Confidential Qualitative Forecasting Models - 3) Weighted Moving Averages

MGS3100_03.ppt/Feb 11, 2016/Page 22 Georgia State University - Confidential Qualitative Forecasting Models - 4) Exponential Smoothing Moving average technique that requires little record keeping of past data. Uses a smoothing constant α with a value between 0 and 1. (Usual range 0.1 to 0.3) Applies alpha to most recent period, and applies one minus alpha distributed to previous values α = The weight assigned to the latest period Y T =α(Y T-1 ) + (1- α)(Y T-1 ) ^^

MGS3100_03.ppt/Feb 11, 2016/Page 23 Georgia State University - Confidential Qualitative Forecasting Models - 4) Exponential Smoothing

MGS3100_03.ppt/Feb 11, 2016/Page 24 Georgia State University - Confidential Qualitative Forecasting Models - 4) Exponential Smoothing

MGS3100_03.ppt/Feb 11, 2016/Page 25 Georgia State University - Confidential Qualitative Forecasting Models - 4) Exponential Smoothing

MGS3100_03.ppt/Feb 11, 2016/Page 26 Georgia State University - Confidential Qualitative Forecasting Models - 5) Trend Forecasting Trend analysis technique that fits a trend equation (or curve) to a series of historical data points. projects the curve into the future for medium and long term forecasts. Simple Regression Regression can be used to forecast trends Averages do not consider a trend Y=b 0 +b 1 *X ^ Intercept Slope = ΔY ΔX

MGS3100_03.ppt/Feb 11, 2016/Page 27 Georgia State University - Confidential Qualitative Forecasting Models - 5) Trend Forecasting Evaluation Method for Regression R 2 =SSR SST R 2 is the proportion of variability in Y that is explained by the regression model. Remaining is random. MAD = Sum Absolute Errors n-2 (Residual degrees of freedom) MAPE = Sum % Errors n-2 MSE = Sum Errors Squared n-2

MGS3100_03.ppt/Feb 11, 2016/Page 28 Georgia State University - Confidential Qualitative Forecasting Models - 5) Trend Forecasting Non-Linear Regression Examples i) Quadratic Regression Y = b 0 +b 1 +b 2 X 2 ^

MGS3100_03.ppt/Feb 11, 2016/Page 29 Georgia State University - Confidential Qualitative Forecasting Models - 5) Trend Forecasting Non-Linear Regression Examples ii) Exponential Logarithmic Regression ========== Therefore  Log =2 (To what power do we raise the base?)

MGS3100_03.ppt/Feb 11, 2016/Page 30 Georgia State University - Confidential Qualitative Forecasting Models - 5) Trend Forecasting Non-Linear Regression Examples iii) Classical Decomposition Y = (Trend x Cyclicality x Seasonality) + Error X Business / Economic Cycles too long Yd=Yd= Y SI To Deseasonalize:To Reseasonalize: Y=Y d (SI) ^

MGS3100_03.ppt/Feb 11, 2016/Page 31 Georgia State University - Confidential Qualitative Forecasting Models - 5) Linear Trend Analysis Midwestern Manufacturing Sales

MGS3100_03.ppt/Feb 11, 2016/Page 32 Georgia State University - Confidential Qualitative Forecasting Models - 5) Least Squares for Linear Regression Midwestern Manufacturing

MGS3100_03.ppt/Feb 11, 2016/Page 33 Georgia State University - Confidential Qualitative Forecasting Models - 5) Least Squares Method where = predicted value of the dependent variable (demand) X = value of the independent variable (time) a = Y-axis intercept b = slope of the regression line b =

MGS3100_03.ppt/Feb 11, 2016/Page 34 Georgia State University - Confidential Qualitative Forecasting Models - 5) Linear Trend Data & Error Analysis

MGS3100_03.ppt/Feb 11, 2016/Page 35 Georgia State University - Confidential Qualitative Forecasting Models - 5) Least Squares Graph

MGS3100_03.ppt/Feb 11, 2016/Page 36 Georgia State University - Confidential Qualitative Forecasting Models - 6) Seasonality Seasonality analysis adjustment to time series data due to variations at certain periods. adjust with seasonal index – ratio of average value of the item in a season to the overall annual average value. example: demand for coal & fuel oil in winter months.

MGS3100_03.ppt/Feb 11, 2016/Page 37 Georgia State University - Confidential Qualitative Forecasting Models - 6) Seasonality Analysis Seasonal Index – ratio of the average value of the item in a season to the overall average annual value. Example: average of year 1 January ratio to year 2 January ratio. ( )/2 = Ratio = demand / average demand If Year 3 average monthly demand is expected to be 100 units. Forecast demand Year 3 January: 100 X = 96 units Forecast demand Year 3 May: 100 X = 131 units

MGS3100_03.ppt/Feb 11, 2016/Page 38 Georgia State University - Confidential Qualitative Forecasting Models - 6) Deseasonalized Data Going back to the conceptual model, solve for trend: Trend = Y / Season (96 units/ = ) This eliminates seasonal variation and isolates the trend Now use the Least Squares method to compute the Trend Now that we have the Seasonal Indices and Trend, we can reseasonalize the data and generate the forecast Y = Trend x Seasonal Index