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Chapter 10 – Basic Regression Analysis with Time Series Data

Chapter 10 – Basic Regression Analysis with Time Series Data. What is Time Series Data and why is it Different?. There is a time ordering of the data The past can affect the future, but the future cannot affect the past. Example: National population from 1900 to 2006 (data set NATPOP).

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Chapter 10 – Basic Regression Analysis with Time Series Data

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  1. Chapter 10 – Basic Regression Analysis with Time Series Data

  2. What is Time Series Data and why is it Different? There is a time ordering of the data The past can affect the future, but the future cannot affect the past. Example: National population from 1900 to 2006 (data set NATPOP)

  3. What is Time Series Data and why is it Different? Random nature of times series data Formally, the process that generates time series data is called a stochastic or time series process

  4. What is Time Series Data and why is it Different? Random nature of times series data Random sample from a population vs. random sample of time series data

  5. Examples of Time Series Data: Uncorrelated data, constant process model

  6. Examples of Time Series Data: Autocorrelateddata

  7. Examples of Time Series Data: Trend

  8. Examples of Time Series Data: Cyclic or seasonal data

  9. Examples of Time Series Data: Nonstationarydata

  10. Examples of Time Series Data: A mixture of patterns

  11. Cyclic patterns of different magnitudes

  12. Atypical events

  13. Atypical events

  14. Famous Time Series Expert –Yogi Berra The future ain’t what it used to be.

  15. Famous Time Series Expert –Yogi Berra You can observe a lot just by watching. The basic graphical display for time series data is the time series plot which is just a graph of the observations vs. time periods.

  16. Time Series Plot Example Open TRAFFIC2 data set and make time series plot of year vs. statewide total accidents (totacc) In Minitab need to choose series and time stamp

  17. Time Series Plot Example

  18. Notice that the histograms look very similar even though the time series behavior is very different Time series plots

  19. Histogram of totacc

  20. When there are two or more variables of interest, scatter plots can be useful

  21. ForecastingIt is difficult to make predictions, especially about the future. – Neils Bohr

  22. Forecasting

  23. Forecasting is useful in many fields: Business and industry Economics Finance Environmental sciences Social sciences Political sciences

  24. Problem definition Data collection Data analysis Model selection and fitting Model validation Model deployment Monitoring forecasting model performance Data Analysis Process:

  25. gfr – number of children born to every 1,000 women of childbearing age from 1913 to 1984. Make a time series plot of gfr Time Series Example – Data Set FERTIL3

  26. Time Series Example – Data Set FERTIL3

  27. pe – average real dollar value of the personal tax exemption from 1913 to 1984. Make a time series plot of pe Time Series Example – Data Set FERTIL3

  28. Time Series Example – Data Set FERTIL3

  29. We want to predict gfr. Lets try this model: Time Series Example – Data Set FERTIL3

  30. We want to predict gfr. Notation for time series model slightly different: Time Series Example – Data Set FERTIL3

  31. The regression equation is gfr = 96.3 - 0.0071 pe Predictor CoefSE CoefT P Constant 96.344 4.305 22.38 0.000 pe -0.00710 0.03592 -0.20 0.844 S = 19.9400 R-Sq = 0.1% R-Sq(adj) = 0.0% Time Series Example – Data Set FERTIL3

  32. residual plots Time Series Example – Data Set FERTIL3

  33. residual plots Time Series Example – Data Set FERTIL3

  34. residual plots Time Series Example – Data Set FERTIL3

  35. residual plots Time Series Example – Data Set FERTIL3

  36. This model suffers from misspecification. Time Series Example – Data Set FERTIL3

  37. Scatter plot of gfr vs. pe Time Series Example – Data Set FERTIL3

  38. What could affect general fertility rate in the U.S.? Many things! • How about these two: • World War II • Availability of the birth control pill Time Series Example – Data Set FERTIL3

  39. ww2 is a dummy variable • 1 if year is 1941 through 1945 • 0 otherwise • pill is a dummy variable • 1 if year is 1963 or greater • 0 otherwise Time Series Example – Data Set FERTIL3

  40. Fit this model with two dummy variables. Time Series Example – Data Set FERTIL3

  41. gfr= 98.7 + 0.0825 pe - 24.2 ww2 - 31.6 pill Predictor CoefSE CoefT P Constant 98.682 3.208 30.76 0.000 pe 0.08254 0.02965 2.78 0.007 ww2 -24.238 7.458 -3.25 0.002 pill -31.594 4.081 -7.74 0.000 S = 14.6851 R-Sq = 47.3% R-Sq(adj) = 45.0% Time Series Example – Data Set FERTIL3

  42. Residual plots: Time Series Example – Data Set FERTIL3

  43. Residual plots: Time Series Example – Data Set FERTIL3

  44. Residual plots: Time Series Example – Data Set FERTIL3

  45. Residual plots: Time Series Example – Data Set FERTIL3

  46. Residual plots: Time Series Example – Data Set FERTIL3

  47. Residual plots: Time Series Example – Data Set FERTIL3

  48. Residual plots: Time Series Example – Data Set FERTIL3

  49. gfr = 98.7 + 0.0825 pe - 24.2 ww2 - 31.6 pill • ww2 is a dummy variable • 1 if year is 1941 through 1945 • 0 otherwise

  50. gfr = 98.7 + 0.0825 pe - 24.2 ww2 - 31.6 pill • pill is a dummy variable • 1 if year is 1963 or greater • 0 otherwise

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