Time series-ppts.ppt
- 1. © 2011 Pearson Education, Inc Time Series Time Based observations/values. OR Data generated by processes over time.
- 2. © 2011 Pearson Education, Inc Descriptive v. Inferential Analysis • Time Series Analysis – Picture of the behavior of the time series – By Exponential Smoothing & Holt’s method • Inferential Analysis (Prediction) – Goal: Forecasting future values By Least Square Regression Method
- 3. © 2011 Pearson Education, Inc Time Series Components Tt = secular trend (The general movements persisting over a long period of time represented by the diagonal line which is drawn through the irregular curve) St = seasonal variations (the fluctuations that recur/repeat during specific time periods usually every year) Ct = cyclical variations (Pronounced fluctuations moving up and down every few years throughout the length of chart. These are attributable to business and economic conditions. These usually last longer than a year and not regular in magnitude and length ) Rt = residual/error (what remains after other components have been removed. Because of irregularities)
- 4. © 2011 Pearson Education, Inc Time Series Components
- 5. © 2011 Pearson Education, Inc Time Series Models Additive Yt = Tt + Ct + St + Rt Multiplicative Yt = Tt + Ct + St + Rt
- 6. © 2011 Pearson Education, Inc Prediction: Fitting Trend Line • Free hand method/Graphic method • Method of Semi average • Moving Average (3 yrs or 5 yrs) • Least square Regression Method
- 7. © 2011 Pearson Education, Inc Prediction: Simple Linear Regression • Model: E(Yt) = β0 + β1t • Relates time series, Yt, to time, t • Cautions – Risky to extrapolate (forecast beyond observed data) – Does not account for cyclical effects
- 8. © 2011 Pearson Education, Inc Simple Linear Regression Example The data shows the average undergraduate tuition at all 4– year institutions for the years 1996–2004 (Source: U.S. Dept. of Education). Use least– squares regression to fit a linear model. Forecast the tuition for 2005 (t = 11) and compute a 95% prediction interval for the forecast.
- 9. © 2011 Pearson Education, Inc Simple Linear Regression Solution From Excel ˆ 7997.533 528.158 t Y t
- 10. © 2011 Pearson Education, Inc Simple Linear Regression Solution $8,000 $9,000 $10,000 $11,000 $12,000 $13,000 $14,000 $15,000 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Year Tuition ˆ 7997.533 528.158 t Y t