Scatterplot of y versus x Regression Line Superimposed

Transcription

1 Scatterplot of y versus x Regression Line Superimposed

2 Residual Plot Regression of y on x and z

3 1-Year Treasury Bond Rate

4 Change in 1-Year Treasury Bond Rate

5 Liquor Sales

6 Histogram and Descriptive Statistics Change in 1-Year Treasury Bond Rate

7 Scatterplot 1-Year versus 10-Year Treasury Bond Rate

8 Scatterplot Matrix 1-, 10-, 20-, and 30-Year Treasury Bond Rates

9 1. Modeling Trend Modeling and Forecasting Trend

10 Labor Force Participation Rate Females

11 Labor Force Participation Rate Males

12 Increasing and Decreasing Linear Trends

13 Linear Trend Female Labor Force Participation Rate

14 Linear Trend Male Labor Force Participation Rate

15 Volume on the New York Stock Exchange

16 Various Shapes of Quadratic Trends

17 Quadratic Trend Volume on the New York Stock Exchange

18 Log Volume on the New York Stock Exchange

19 Various Shapes of Exponential Trends

20 Linear Trend Log Volume on the New York Stock Exchange

21 Exponential Trend Volume on the New York Stock Exchange

22 Selecting Models

23

24 Consistency Efficiency

25 Degrees-of-Freedom Penalties Various Model Selection Criteria

26 Retail Sales

27 Retail Sales Linear Trend Regression Dependent Variable is RTRR Sample: 1955: :12 Included observations: 468 Variable Coefficient Std. Error T-Statistic Prob. C TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.17E+11 Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

28 Retail Sales Linear Trend Residual Plot

29 Retail Sales Quadratic Trend Regression Dependent Variable is RTRR Sample: 1955: :12 Included observations: 468 Variable Coefficient Std. Error T-Statistic Prob. C TIME TIME R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 3.46E+09 Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

30 Retail Sales Quadratic Trend Residual Plot

31 Retail Sales Log Linear Trend Regression Dependent Variable is LRTRR Sample: 1955: :12 Included observations: 468 Variable Coefficient Std. Error T-Statistic Prob. C TIME E R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

32 Retail Sales Log Linear Trend Residual Plot

33 Retail Sales Exponential Trend Regression Dependent Variable is RTRR Sample: 1955: :12 Included observations: 468 Convergence achieved after 1 iterations RTRR=C(1)*EXP(C(2)*TIME) Coefficient Std. Error T-Statistic Prob. C(1) C(2) E R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.30E+10 Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

34 Retail Sales Exponential Trend Residual Plot

35 Model Selection Criteria Linear, Quadratic and Exponential Trend Models Linear Trend Quadratic Trend Exponential Trend AIC SIC

36 3. Forecasting Trend

37 Retail Sales History, Quadratic Trend Forecast,

38 Retail Sales History, Quadratic Trend Forecast and Realization,

39 Retail Sales History, Linear Trend Forecast,

40 Retail Sales History, Linear Trend Forecast and Realization,

41 Modeling and Forecasting Seasonality 1. The Nature and Sources of Seasonality 2. Modeling Seasonality D 1 = (1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,...) D 2 = (0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,...) D 3 = (0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0,...) D 4 = (0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,...)

42

43 Gasoline Sales

44 Liquor Sales

45 Durable Goods Sales

46 Housing Starts,

47 Housing Starts,

48 Regression Results Seasonal Dummy Variable Model Housing Starts LS // Dependent Variable is STARTS Sample: 1946: :12 Included observations: 576 Variable Coefficient Std. Error t-statistic Prob. D D D D D D D D D D D D R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

49 Residual Plot

50 Estimated Seasonal Factors Housing Starts

51 3. Forecasting Seasonal Series

52 Housing Starts History, Forecast,

53 Housing Starts History, Forecast and Realization,