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Comparison of the models. Concentration data Its ACF.

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Presentation on theme: "Comparison of the models. Concentration data Its ACF."— Presentation transcript:

1 Comparison of the models

2 Concentration data

3 Its ACF

4 Its PACF. AR(2)?

5 AR(1)? m = 17.06, p-value a 1 = , p-value Portmanteau test 47.44, p-value 0.003

6 AR(2)? m = 17.06, p-value a 1 = , p-value a 2 = , p-value Portmanteau test 26.97, p-value

7 AR(3)? m = 17.06, p-value a 1 = , p-value a 2 = , p-value a 3 = , p-value Portmanteau test 26.14, p-value

8 Increments of the data

9 ACF of the increments

10 PACF of the increments

11 MA(1)? b 1 = 0.701, p-value Portmanteau test 29.14, p-value

12 MA(2)? b 1 = , p-value b 2 = , p-value Portmanteau test 24.77, p-value

13 AR(4)? a 1 = , p-value a 2 = , p-value a 3 = , p-value a 4 = , p-value Portmanteau test 25.5, p-value

14 AR(5)? a 1 = , p-value a 2 = , p-value a 3 = , p-value a 4 = , p-value a 5 = , p-value Portmanteau test 25.4, p-value

15 AR(6)? a 1 = , p-value a 2 = , p-value a 3 = , p-value a 4 = , p-value a 5 = , p-value a 6 = , p-value Portmanteau test 14.81, p-value

16 AR(7)? a 1 = , p-value a 2 = , p-value a 3 = , p-value a 4 = , p-value a 5 = , p-value a 6 = , p-value a 7 = , p-value Portmanteau test 14.83, p-value

17 Coal Production data

18 Its ACF

19 Its PACF. AR(2)?

20 AR(1)? m = 3.772, p-value a 1 = , p-value Portmanteau test 21.44, p-value

21 AR(2)? m = 3.802, p-value a 1 = , p-value a 2 = , p-value Portmanteau test 12.03, p-value 0.97

22 AR(3)? m = 3.809, p-value a 1 = , p-value a 2 = , p-value a 3 = , p-value Portmanteau test 10.61, p-value

23 Profit Margin data

24 Its ACF

25 Its PACF. AR(1)?

26 AR(1)? m = 4.699, p-value a 1 = 0.876, p-value Portmanteau test 22.34, p-value Still, ρ(4) is out of range

27 AR(2)? m = 4.716, p-value a 1 = 1.026, p-value a 2 = , p-value Portmanteau test 21.98, p-value

28 ARMA(1,1)? m = 4.714, p-value a 1 = , p-value b 1 = , p-value Portmanteau test 19.06, p-value

29 Parts Availability data

30 Its increments

31 ACF for the increments. MA(1)?

32 PACF for the increments. AR(2)?

33 AR(1)? a 1 = , p-value Portmanteau test 22.4, p-value ρ(2) is way out of range though

34 AR(2)? a 1 = , p-value a 2 = , p-value Portmanteau test 14.5, p-value

35 AR(3)? a 1 = , p-value a 2 = , p-value a 3 = , p-value Portmanteau test 12.24, p-value

36 MA(1)? b 1 = , p-value Portmanteau test 12.23, p-value

37 Treasury Bonds Yield data

38 Its increments

39 ACF for the increments. MA(1)??

40 PACF for the increments. AR(1)?

41 AR(1)? a 1 = , p-value Portmanteau test 29.02, p-value

42 AR(2)? a 1 = , p-value a 2 = , p-value Portmanteau test 28.96, p-value

43 MA(1)? b 1 = , p-value Portmanteau test 36.57, p-value

44 MA(2)? b 1 = , p-value b 2 = , p-value Portmanteau test 30.89, p-value

45 ARMA(1,1)? a 1 = , p-value b 1 = , p-value Portmanteau test 28.94, p-value

46 Crops Prices data

47 Take the Logarithm

48 Take the difference

49 Its ACF

50 MA(3) might work?

51 MA(3)? b 1 = , p-value b 2 = , p-value b 3 = , p-value Portmanteau test 27.11, p-value

52 Residual ACF for MA(3) model. Looks good, but the estimate for b(3) has a big p-value 0.157

53 MA(2)? b 1 = , p-value b 2 = , p-value Portmanteau test 54.11, p-value

54 Residual ACF for MA(2) model, Portmanteau test has p-value

55 Switch to AR models. Here is PACF of the data.

56 AR(8)? Or AR(4)? 8 th value is almost 4 standard deviations

57 AR(4)? a 1 = , p-value a 2 = , p-value a 3 = , p-value a 4 = , p-value Portmanteau test 39.62, p-value

58 Residual ACF for AR(4). Portmanteau test is a No (p-value 0.008)

59 AR(8)? a 1 = , p-value a 2 = , p-value a 3 = , p-value a 4 = , p-value a 5 = , p-value a 6 = , p-value a 7 = , p-value a 8 = , p-value Portmanteau test 21.27, p-value

60 Residual ACF for AR(8). Portmanteau test is a Yes (p-value 0.215). Finally?

61 Since 8 is sort of too many, let’s try mixed models

62 ARMA(2,1)? a 1 = , p-value a 2 = , p-value b 1 = , p-value Portmanteau test 28.44, p-value

63 Residuals for ARMA(2,1). Portmanteau test is a Yes (p-value 0.161)

64 Best AIC score = ARMA(8,1) a 1 = , p-value a 2 = , p-value a 3 = , p-value a 4 = , p-value a 5 = , p-value a 6 = , p-value a 7 = , p-value a 8 = , p-value b 1 = , p-value Portmanteau test 12.1, p-value

65 Residual ACF for ARMA(8,1). Note that the first 5 values are practically zeroes, one of the symptoms of over- parametrization


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