CHAPTER 18 Models for time series and Forecastin to accompany Introduction to business statistics fourth edition, by Ronald m. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. stengel o The Wadsworth Group
CHAPTER 18 Models for Time Series and Forecasting to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group
l Chapter 18-Learning objectives Describe the trend, cyclical, seasonal, and irregular components of the time series model Fit a linear or quadratic trend equation to a time series Smooth a time series with the centered moving average and exponential smoothing techniques Determine seasonal indexes and use them to compensate for the seasonal effects in a time series Use the trend extrapolation and exponential smoothing forecast methods to estimate a future value Use mad and mse criteria to compare how well equations fit e Use index numbers to compare business or economic measures over time o 2002 The Wadsworth Group
Chapter 18 - Learning Objectives • Describe the trend, cyclical, seasonal, and irregular components of the time series model. • Fit a linear or quadratic trend equation to a time series. • Smooth a time series with the centered moving average and exponential smoothing techniques. • Determine seasonal indexes and use them to compensate for the seasonal effects in a time series. • Use the trend extrapolation and exponential smoothing forecast methods to estimate a future value. • Use MAD and MSE criteria to compare how well equations fit data. • Use index numbers to compare business or economic measures over time. © 2002 The Wadsworth Group
l Chapter 18-Key terms Time series Seasonal index Classical time series Ratio to moving model average method Trend value · Deseasonalizing Cyclical component MAD criterion Seasonal component mse criterion Irregular component Trend equation Constructing an index using the Cpi Moving average Shifting the base of an Exponential index smoothing g o 2002 The Wadsworth Group
Chapter 18 - Key Terms • Time series • Classical time series model – Trend value – Cyclical component – Seasonal component – Irregular component • Trend equation • Moving average • Exponential smoothing • Seasonal index • Ratio to moving average method • Deseasonalizing • MAD criterion • MSE criterion • Constructing an index using the CPI • Shifting the base of an index © 2002 The Wadsworth Group
l Classical Time Series model y=T°C·S° where y=observed value of the time series variable T= trend component, which reflects the general tendency of the time series without fluctuations C= cyclical component, which reflects systematic fluctuations that are not calendar-related, such as business cycles S=seasonal component, which reflects systematic fluctuations that are calendar-related, such as the day of the week or the month of the year I= irregular component, which reflects fluctuations that are not systematic o 2002 The Wadsworth Group
Classical Time Series Model y = T • C • S • I where y = observed value of the time series variable T = trend component, which reflects the general tendency of the time series without fluctuations C = cyclical component, which reflects systematic fluctuations that are not calendar-related, such as business cycles S = seasonal component, which reflects systematic fluctuations that are calendar-related, such as the day of the week or the month of the year I = irregular component, which reflects fluctuations that are not systematic © 2002 The Wadsworth Group
I Trend equations Linear: j=b0+ bix Quadratic: y=5o +61x+b2x2 j=the trend line estimate of y x= time period bo by and b2 are coefficients that are selected to minimize the deviations between the trend estimates j and the actual data values y for the past time periods. Regression methods are used to determine the best values for the coefficients o 2002 The Wadsworth Group
Trend Equations •Linear: = b0 + b1x •Quadratic: = b0 + b1x + b2x 2 = the trend line estimate of y x = time period b0 , b1 , and b2 are coefficients that are selected to minimize the deviations between the trend estimates and the actual data values y for the past time periods. Regression methods are used to determine the best values for the coefficients. y ? y ? y ? y ? © 2002 The Wadsworth Group