Chapter 16 - Times series forecasting and index numbers. This chapter includes contents: Time series components and models, time series regression, multiplicative decomposition, simple exponential smoothing, Holt-Winter’s Models, the Box Jenkins methodology (optional advanced section), forecast error comparisons, index numbers. | Times Series Forecasting and Index Numbers Chapter 16 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Time Series Forecasting Time Series Components and Models Time Series Regression Multiplicative Decomposition Simple Exponential Smoothing Holt-Winter’s Models The Box Jenkins Methodology (Optional Advanced Section) Forecast Error Comparisons Index Numbers 16- Time Series Components and Models Trend Long-run growth or decline Cycle Long-run up and down fluctuation around the trend level Seasonal Regular periodic up and down movements that repeat within the calendar year Irregular Erratic very short-run movements that follow no regular pattern LO16-1: Identify the components of a times series. 16- Time Series Exhibiting Trend, Seasonal, and Cyclical Components LO16-1 Figure 16- Seasonality Some products have demand that varies a great deal by period Coats, bathing . | Times Series Forecasting and Index Numbers Chapter 16 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Time Series Forecasting Time Series Components and Models Time Series Regression Multiplicative Decomposition Simple Exponential Smoothing Holt-Winter’s Models The Box Jenkins Methodology (Optional Advanced Section) Forecast Error Comparisons Index Numbers 16- Time Series Components and Models Trend Long-run growth or decline Cycle Long-run up and down fluctuation around the trend level Seasonal Regular periodic up and down movements that repeat within the calendar year Irregular Erratic very short-run movements that follow no regular pattern LO16-1: Identify the components of a times series. 16- Time Series Exhibiting Trend, Seasonal, and Cyclical Components LO16-1 Figure 16- Seasonality Some products have demand that varies a great deal by period Coats, bathing suits, bicycles This periodic variation is called seasonality Constant seasonality: the magnitude of the swing does not depend on the level of the time series Increasing seasonality: the magnitude of the swing increases as the level of the time series increases Seasonality alters the linear relationship between time and demand LO16-1 16- Time Series Regression Within regression, seasonality can be modeled using dummy variables Consider the model: yt = b0 + b1t + bQ2Q2 + bQ3Q3 + bQ4Q4 + et For Quarter 1, Q2 = 0, Q3 = 0 and Q4 = 0 For Quarter 2, Q2 = 1, Q3 = 0 and Q4 = 0 For Quarter 3, Q2 = 0, Q3 = 1 and Q4 = 0 For Quarter 4, Q2 = 0, Q3 = 0 and Q4 = 1 The b coefficient will then give us the seasonal impact of that quarter relative to Quarter 1 Negative means lower sales, positive lower sales LO16-2: Use time series regression to forecast time series having linear, quadratic, and certain types of seasonal patterns. 16- Transformations Sometimes, transforming the sales
