1. Introduction to Time Series Regression and Forecasting
Chapter 14
Introduction to Time Series Regression and Forecasting

2. Introduction to Time Series Regression and Forecasting (SW Chapter 14)

3. Example #1 of time series data: US rate of price inflation, as measured by the quarterly percentage change in the Consumer Price Index (CPI), at an annual rate

4. Example #2: US rate of unemployment

5. Why use time series data?

6. Time series data raises new technical issues

7. Using Regression Models for Forecasting (SW Section 14.1)

8. Introduction to Time Series Data and Serial Correlation (SW Section 14

9. We will transform time series variables using lags, first differences, logarithms, & growth rates

10. Example: Quarterly rate of inflation at an annual rate (U.S.)

11. Example: US CPI inflation – its first lag and its change

12. Autocorrelation

14. Sample autocorrelations

15. Example:

17. Other economic time series:

18. Other economic time series, ctd:

19. Stationarity: a key requirement for external validity of time series regression

20. Autoregressions (SW Section 14.3)

21. The First Order Autoregressive (AR(1)) Model

22. Example: AR(1) model of the change in inflation

23. Example: AR(1) model of inflation – STATA

24. Example: AR(1) model of inflation – STATA, ctd.

25. Example: AR(1) model of inflation – STATA, ctd

26. Forecasts: terminology and notation

27. Forecast errors

28. Example: forecasting inflation using an AR(1)

29. The AR(p) model: using multiple lags for forecasting

30. Example: AR(4) model of inflation

31. Example: AR(4) model of inflation – STATA

32. Example: AR(4) model of inflation – STATA, ctd.

33. Digression: we used Inf, not Inf, in the AR’s. Why?

34. So why use Inft, not Inft?

35. Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag (ADL) Model (SW Section 14.4)

36. Example: inflation and unemployment

37. The empirical U.S. “Phillips Curve,” 1962 – 2004 (annual)

38. The empirical (backwards-looking) Phillips Curve, ctd.

39. Example: dinf and unem – STATA

40. Example: ADL(4,4) model of inflation – STATA, ctd.

41. The test of the joint hypothesis that none of the X’s is a useful predictor, above and beyond lagged values of Y, is called a Granger causality test

42. Forecast uncertainty and forecast intervals

43. The mean squared forecast error (MSFE) is,

44. The root mean squared forecast error (RMSFE)

45. Three ways to estimate the RMSFE

46. The method of pseudo out-of-sample forecasting

47. Using the RMSFE to construct forecast intervals

48. Example #1: the Bank of England “Fan Chart”, 11/05

49. Example #2: Monthly Bulletin of the European Central Bank, Dec
Example #2: Monthly Bulletin of the European Central Bank, Dec. 2005, Staff macroeconomic projections

50. Example #3: Fed, Semiannual Report to Congress, 7/04

51. Lag Length Selection Using Information Criteria (SW Section 14.5)

52. The Bayes Information Criterion (BIC)

53. Another information criterion: Akaike Information Criterion (AIC)

54. Example: AR model of inflation, lags 0–6:

55. Generalization of BIC to multivariate (ADL) models

56. Nonstationarity I: Trends (SW Section 14.6)

57. Outline of discussion of trends in time series data:

58. 1. What is a trend?

61. What is a trend, ctd.

62. Deterministic and stochastic trends

63. Deterministic and stochastic trends, ctd.

64. Deterministic and stochastic trends, ctd.

65. Deterministic and stochastic trends, ctd.

66. Stochastic trends and unit autoregressive roots

67. Unit roots in an AR(2)

68. Unit roots in an AR(2), ctd.

69. Unit roots in the AR(p) model

70. Unit roots in the AR(p) model, ctd.

71. 2. What problems are caused by trends?

72. Log Japan gdp (smooth line) and US inflation (both rescaled), 1965-1981

73. Log Japan gdp (smooth line) and US inflation (both rescaled), 1982-1999

74. 3. How do you detect trends?

75. DF test in AR(1), ctd.

76. Table of DF critical values

77. The Dickey-Fuller test in an AR(p)

78. When should you include a time trend in the DF test?

79. Example: Does U.S. inflation have a unit root?

80. Example: Does U.S. inflation have a unit root? ctd

81. DF t-statstic = –2.69 (intercept-only):

82. 4. How to address and mitigate problems raised by trends

83. Summary: detecting and addressing stochastic trends

84. Nonstationarity II: Breaks and Model Stability (SW Section 14.7)

85. A. Tests for a break (change) in regression coefficients

87. Case II: The break date is unknown

88. The Quandt Likelihod Ratio (QLR) Statistic (also called the “sup-Wald” statistic)

89. The QLR test, ctd.

92. Has the postwar U.S. Phillips Curve been stable?

93. QLR tests of the stability of the U.S. Phillips curve.

95. B. Assessing Model Stability using Pseudo Out-of-Sample Forecasts

96. Application to the U.S. Phillips Curve:

97. POOS forecasts of Inf using ADL(4,4) model with Unemp

98. poos forecasts using the Phillips curve, ctd.

99. Summary: Time Series Forecasting Models (SW Section 14.8)

100. Summary, ctd.