Understanding xtTime.t and Data Analysis Techniques

Explore slides on various data analysis techniques, including autoregressive models, time series visualization, and statistical analysis. Learn about xtTime.t, AR models, data transformation, and more for comprehensive data analysis insights.

• Data Analysis
• Time Series
• Autoregressive Models
• Statistical Techniques

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3. xt Time t

5. ?? ?? ? ?0 ?1 ? ? (?? ??)2= (?? ?0 ?1?? 1)2 ?=1 ?=1

6. 73, 67, 83, 53, 78, 88, 57, 1, 29, 14, 80, 77, 19, 14, 41, 55, 74, 98, 84, 88, 78, 15, 66, 99, 80, 75, 124, 103, 57, 49, 70, 112, 107, 123, 79, 92, 89, 116, 71, 68, 59, 84, 39, 33, 71, 83, 77, 37, 27, 30.

7. SSE = 32995.57

8. ? ? ? ?(?,?) ?? ?? ?,? ??+1??+2 ??

9. xt xt-k k t

10. xt

11. xt xt-1 et vs. 1. et t 140 120 100 xt 80 60 40 20 xt-1 0 20 40 60 80 100 120 140 0

12. 80 80 60 60 40 40 et e 20 20 0 0 0 0 20 40 60 80 100 120 -3 -2 -1 1 2 3 -20 -20 z -40 -40 80 -60 -60 60 -80 -80 40 et 20 t 0 10 20 30 40 50 0 -20 -40 -60 -80

13. xt ? AR(2): AR(3):

14. ??(?) ?

15. ?? a0a1 a2

16. t=3 n. n-2

18. {xt-1, ...,xt-p} xt xt

19. xt-k = xt k ? k t

20. ?(0,1/?) ? 1 ? ? ? z1 ? ? ? ? z1 ? ? ? z1 ? 2 , ? + ? z1 ? ? 2

21. ?2 k 0

22. ? ? 0 0 t f

23. 80 60 e 40 = 43702.08 20 0 0 -3 -2 -1 1 2 3 -20 z -40 -60 -80

24. t xt-a0

25. q ?q

26. a0 b1 a0 b1 a0 b1

27. a0 = 67.72, b1=0.4 e0=0, = 33542.65 a0 b1

28. b1=0.4, 0.5, 0.6

30. (k>1) 0 . k< q

31. q=8 Autocorrelation rk 0 Lag k rk

32. k p p ap: p ap p p p=8 rk PACF(k) 0 Lag k k

33. a0 (1-B)xt =xt-xt-1 1 I(1). x. (1-B)xt (1-B)xt . xt xt t t

34. I(2) xt t

35. ARMA(p, q) ARIMA(p,d,q)

36. I(12): 1 ?12??= ?0+ ??