1 / 19

Standard Trend Models

Standard Trend Models. Trend Curves. Purposes of a Trend Curve: 1. Forecasting the long run 2. Estimating the growth rate. Standard Trend Curves. Key Properties: have a simple form have good track records software for fitting is widely available. Types of Standard Trend Curves.

ethel
Download Presentation

Standard Trend Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Standard Trend Models

  2. Trend Curves • Purposes of a Trend Curve: 1. Forecasting the long run 2. Estimating the growth rate

  3. Standard Trend Curves • Key Properties: • have a simple form • have good track records • software for fitting is widely available

  4. Types of Standard Trend Curves • For unbounded data: • linear • quadratic • exponential • For bounded (S shaped) data: • logistic • Gompertz

  5. Unbounded Trend • Linear: Yt = b0 + b1 t + e • Quadratic: Yt = b0 + b1 t + b2 t2 + e • Log-linear:ln(Yt)= b0 + b1 t + e

  6. Two Standard S Curves 1. Logistic Curve 2. Gompertz Curve

  7. S – Curves (Life Cycle Theory) 4 Stages of New Technology Life Cycle 1. Slow growth at the beginning stage 2. Rapid growth 3. Slow growth during the mature stage 4. Decline during the final stage

  8. S - Curves Point of Inflection Y second derivative = 0 Y(ln(a) /b) = g/2 for L Y(ln(a) /b) = g /e for G Concave Up Concave down ln(a)/b Time

  9. Model Selection Process Linear / Quadratic Exponential (linear in log) (standard regression) 1. Timeplot 2. Take a log? No Yes 3. Bounded? No Yes Logistic / Gompertz/ (nonlinear regression)

  10. Nonlinear Least Squares • SPSS is one of the few statistics packages that provide routines for fitting nonlinear regression models. • You have to provide initial estimates for parameters.

  11. Getting Initial Parameter Values- Logistic Curve Estimate g from data, and compute Regress the variable on t.

  12. Getting Initial Parameter Values- Gompertz Curve Estimate g from data, and compute Regress the variable on t.

  13. Durbin-Watson Test

  14. White Noise Residuals • WN (white noise) – uncorrelated • Ex. et~ WN(0, s) (weak WN) • iid – independent and identically distributed • Ex. et ~ iid N(0, s) (strong WN)

  15. Spurious Trend Downward Bias: SE of Coefficient SER Positive Auto- Correlated Residual

  16. Trend Model With Correlated Residual

  17. Durbin Watson Statistic

  18. Some Key Values of DW Stat • E(DW) = 2 if H0 • Table available for DW if H0

  19. DW Test • The Null and Alternative Hypotheses • H0 : r = 0 • H1 : r > 0 -> positive autocorrelated residual

More Related