金融时间序列学习 copula basic

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基础 copula 的使用
================================




虽然很多年前也通过R 软件，绘制了不同的图。 过去了五六年，新的程序绘制的图和多年以前绘制的图非常的不一样，不过感觉使用更方便，更强大。


粘贴几张图。


======================================================
Markov Switching Model

       AIC     BIC    logLik
  637.0736 693.479 -312.5368

Coefficients:

Regime 1
---------
               Estimate Std. Error t value  Pr(>|t|)   
(Intercept)(S)   0.8417     0.3026  2.7816  0.005409 **
x(S)            -0.0533     0.1347 -0.3957  0.692326   
y_1(S)           0.9208     0.0306 30.0915 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5034675
Multiple R-squared: 0.8375

Standardized Residuals:
          Min            Q1           Med            Q3           Max
-1.5153667482 -0.0906543177  0.0001873641  0.1656717258  1.2020898976

Regime 2
---------
               Estimate Std. Error t value  Pr(>|t|)   
(Intercept)(S)   8.6393     0.7254 11.9097 < 2.2e-16 ***
x(S)             1.8771     0.3107  6.0415 1.527e-09 ***
y_1(S)          -0.0569     0.0798 -0.7130    0.4758   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9339683
Multiple R-squared: 0.2408

Standardized Residuals:
        Min          Q1         Med          Q3         Max
-2.31102193 -0.03317755  0.01034138  0.04509104  2.85245597

Transition probabilities:
           Regime 1   Regime 2
Regime 1 0.98499729 0.02290884
Regime 2 0.01500271 0.97709116


=======================================================

copula 对数似然函数图：






其他图：

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关键词：Copula 金融时间序列 opula Basic ASIC

1. ## Copyright (C) 2012 Marius Hofert, Ivan Kojadinovic, Martin Maechler, and Jun Yan
   
2. ##
   
3. ## This program is free software; you can redistribute it and/or modify it under
   
4. ## the terms of the GNU General Public License as published by the Free Software
   
5. ## Foundation; either version 3 of the License, or (at your option) any later
   
6. ## version.
   
7. ##
   
8. ## This program is distributed in the hope that it will be useful, but WITHOUT
   
9. ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
   
10. ## FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
    
11. ## details.
    
12. ##
    
13. ## You should have received a copy of the GNU General Public License along with
    
14. ## this program; if not, see <[url]http://www.gnu.org/licenses/[/url]>.
    
15. 
    
16. ##>>> NOTA BENE must contain exactly the \dontrun{} part of
    
17. ## ../man/gofCopula.Rd
    
18. ## ===================
    
19. 
    
20. ## A two-dimensional data example ----------------------------------
    
21. x <- rCopula(200, claytonCopula(3))
    
22. 
    
23. ## Does the Gumbel family seem to be a good choice (statistic "Sn")?
    
24. gofCopula(gumbelCopula(), x)
    
25. ## With "SnC", really s..l..o..w.. --- with "SnB", *EVEN* slower
    
26. gofCopula(gumbelCopula(), x, method = "SnC", trafo.method = "cCopula")
    
27. ## What about the Clayton family?
    
28. gofCopula(claytonCopula(), x)
    
29. 
    
30. ## Similar with a different estimation method
    
31. gofCopula(gumbelCopula (), x, estim.method="itau")
    
32. gofCopula(claytonCopula(), x, estim.method="itau")
    
33. 
    
34. 
    
35. ## A three-dimensional example  ------------------------------------
    
36. x <- rCopula(200, tCopula(c(0.5, 0.6, 0.7), dim = 3, dispstr = "un"))
    
37. 
    
38. ## Does the Gumbel family seem to be a good choice?
    
39. g.copula <- gumbelCopula(dim = 3)
    
40. gofCopula(g.copula, x)
    
41. ## What about the t copula?
    
42. t.copula <- tCopula(dim = 3, dispstr = "un", df.fixed = TRUE)
    
43. if(FALSE) ## this is *VERY* slow currently
    
44.   gofCopula(t.copula, x)
    
45. 
    
46. ## The same with a different estimation method
    
47. gofCopula(g.copula, x, estim.method="itau")
    
48. if(FALSE) # still really slow
    
49.   gofCopula(t.copula, x, estim.method="itau")
    
50. 
    
51. ## The same using the multiplier approach
    
52. gofCopula(g.copula, x, simulation="mult")
    
53. gofCopula(t.copula, x, simulation="mult")
    
54. if(FALSE) # no yet possible
    
55.     gofCopula(t.copula, x, simulation="mult", estim.method="itau")

复制代码

======================================

> ## Does the Gumbel family seem to be a good choice (statistic "Sn")?
> gofCopula(gumbelCopula(), x)
========Warning in fitCopula.ml(copula, u = data, method = method, start = start,  :
  possible convergence problem: optim() gave code=52
=====Warning in fitCopula.ml(copula, u = data, method = method, start = start,  :
  possible convergence problem: optim() gave code=52
======================Warning in fitCopula.ml(copula, u = data, method = method, start = start,  :
  possible convergence problem: optim() gave code=52
==============================================================

        Parametric bootstrap-based goodness-of-fit test of Gumbel copula, dim. d = 2, with
        'method'="Sn", 'estim.method'="mpl":

data:  x
statistic = 0.244, parameter = 2.09, p-value = 5e-04

> ## With "SnC", really s..l..o..w.. --- with "SnB", *EVEN* slower
> gofCopula(gumbelCopula(), x, method = "SnC", trafo.method = "cCopula")
==============================================================================================Warning in fitCopula.ml(copula, u = data, method = method, start = start,  :
  possible convergence problem: optim() gave code=52
===

        Parametric bootstrap-based goodness-of-fit test of Gumbel copula, dim. d = 2, with
        'method'="SnC", 'estim.method'="mpl", 'trafo.method'="cCopula":

data:  x
statistic = 0.565, parameter = 2.09, p-value = 5e-04

> ## What about the Clayton family?
> gofCopula(claytonCopula(), x)
=================================================================================================

        Parametric bootstrap-based goodness-of-fit test of Clayton copula, dim. d = 2, with
        'method'="Sn", 'estim.method'="mpl":

data:  x
statistic = 0.0163, parameter = 3.24, p-value = 0.44

>
> ## Similar with a different estimation method
> gofCopula(gumbelCopula (), x, estim.method="itau")
=================================================================================================

        Parametric bootstrap-based goodness-of-fit test of Gumbel copula, dim. d = 2, with
        'method'="Sn", 'estim.method'="itau":

data:  x
statistic = 0.163, parameter = 2.58, p-value = 5e-04

> gofCopula(claytonCopula(), x, estim.method="itau")
=================================================================================================

        Parametric bootstrap-based goodness-of-fit test of Clayton copula, dim. d = 2, with
        'method'="Sn", 'estim.method'="itau":

data:  x
statistic = 0.0169, parameter = 3.17, p-value = 0.31

>
>
> ## A three-dimensional example  ------------------------------------
> x <- rCopula(200, tCopula(c(0.5, 0.6, 0.7), dim = 3, dispstr = "un"))
>