Tom Doan: Multivariate STAR Model using WinRats

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Multivariate STAR Model

by TomDoan » Tue Jun 17, 2014 1:21 pm

Attached is an example of a bivariate STAR model. The base model is a VAR on the GDP growth rate and an interest rate spread. The threshold variables are different lags of the growth rate: lag one in GDP equation and lag two in the spread equation. In this case, all four branches (two regimes x two equations) use the standard two lag VAR explanatory variables, though that isn't required.

As I've told a number of people who have asked about this, it's a straightforward extension of the STAR model to a multivariate setting. In fact, this uses the univariate regressions (done withNLLS) to get guess values for the multivariate regression (done with NLSYSTEM). The main reason there's a relatively thin literature with actual data is that it can be hard to get it to work properly. In this case, for instance, the spread equation fits better with a "sharp" rather than "smooth" transition, which means that the optimal value for the gamma (the scale in the logistic) is infinity and the center point can't be estimated well using non-linear least squares since the sum of squares isn't differentiable.

app19-9-2.rpfProgram file(1.71 KiB) Downloaded 74 times
g7_japan.datData file(2.93 KiB) Downloaded 53 times

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关键词：Multivariate multivariat Variate WinRATS winrat different equation interest standard example

农村固定观察点 发表于 2014-6-23 23:40
Multivariate STAR Modelby TomDoan » Tue Jun 17, 2014 1:21 pmAttached is an example  ...

转不了

1. *
   
2. * Martin, Hurn, Harris, "Econometric Modelling with Time Series"
   
3. * Application 19.9.2, from pp 745-748
   
4. * Bivariate Threshold Models
   
5. *
   
6. * Based upon Anderson, Anthansopoulos, and Vahid(2007), "Nonlinear
   
7. * autoregressive leading indicator models of output in G-7
   
8. * countries",Journal of Applied Econometrics, vol 22, 63–87.
   
9. *
   
10. open data "g7_japan.dat"
    
11. calendar(q) 1971:1
    
12. data(format=prn,nolabels,org=columns) 1971:01 1999:4 date growth spread
    
13. *
    
14. equation yeqn growth
    
15. # constant growth{1 2} spread{1 2}
    
16. equation seqn spread
    
17. # constant growth{1 2} spread{1 2}
    
18. *
    
19. frml(equation=yeqn,vector=bg1) fg1
    
20. frml(equation=yeqn,vector=bg2) fg2
    
21. frml(equation=seqn,vector=bs1) fs1
    
22. frml(equation=seqn,vector=bs2) fs2
    
23. *
    
24. set threshg = growth{2}
    
25. set threshs = growth{1}
    
26. *
    
27. stats threshg
    
28. nonlin(parmset=starg) gammag cg
    
29. compute gammag=2.0/sqrt(%variance),cg=%mean
    
30. stats threshs
    
31. nonlin(parmset=stars) gammas cs
    
32. compute gammas=2.0/sqrt(%variance),cs=%mean
    
33. *
    
34. nonlin(parmset=regg) bg1 bg2
    
35. nonlin(parmset=regs) bs1 bs2
    
36. *
    
37. frml glstarg = %logistic(gammag*(threshg-cg),1.0)
    
38. frml glstars = %logistic(gammas*(threshs-cs),1.0)
    
39. *
    
40. frml lstarg growth = g=glstarg,fg1+g*fg2
    
41. frml lstars spread = g=glstars,fs1+g*fs2
    
42. *
    
43. * Estimate growth equation separately
    
44. *
    
45. nlls(parmset=regg,frml=lstarg) growth
    
46. nlls(parmset=regg+starg,frml=lstarg) growth
    
47. *
    
48. * Estimate spread equation separately
    
49. *
    
50. nlls(parmset=regs,frml=lstars) spread
    
51. nlls(parmset=regs+stars,frml=lstars) spread
    
52. *
    
53. * Spread estimates what's effectively a sharp rather than smooth
    
54. * transition. For systems estimation purposes, we'll reset gammas to a
    
55. * finite number.
    
56. *
    
57. compute gammas=20.0
    
58. *
    
59. * Estimate the joint model. This again estimates a sharp transition for
    
60. * the spread equation.
    
61. *
    
62. nlsystem(parmset=regg+regs+starg+stars,iters=500) / lstarg lstars

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1. 1970.1        2.8653535        -1.34
   
2. 1970.2        0.85218774        -1.06
   
3. 1970.3        2.7600238        -1.29
   
4. 1970.4        -0.087854168        -0.74
   
5. 1971.1        0.40349162        0.03
   
6. 1971.2        1.5698773        0.82
   
7. 1971.3        1.6939963        1.27
   
8. 1971.4        0.97384889        1.78
   
9. 1972.1        2.7414848        1.85
   
10. 1972.2        2.000390        2.04
    
11. 1972.3        1.9493872        1.93
    
12. 1972.4        2.4649067        1.688
    
13. 1973.1        3.1298776        1.207
    
14. 1973.2        1.0335246        0.542
    
15. 1973.3        -0.02203533        -1.197
    
16. 1973.4        0.86308318        -1.691
    
17. 1974.1        -2.5521373        -3.28
    
18. 1974.2        0.86290798        -3.3
    
19. 1974.3        1.2202119        -3.47
    
20. 1974.4        -0.6257303        -3.862
    
21. 1975.1        -0.19899771        -3.57
    
22. 1975.2        2.4288561        -1.55
    
23. 1975.3        1.060049        -0.547
    
24. 1975.4        1.1123625        1.057
    
25. 1976.1        0.92575396        1.7
    
26. 1976.2        0.75111194        1.866
    
27. 1976.3        1.2462937        1.708
    
28. 1976.4        0.21873246        1.619
    
29. 1977.1        2.401667        1.718
    
30. 1977.2        0.75869245        1.834
    
31. 1977.3        0.60842583        1.881
    
32. 1977.4        1.4248766        1.256
    
33. 1978.1        1.6187592        1.41
    
34. 1978.2        0.76722453        1.954
    
35. 1978.3        1.3750835        1.94
    
36. 1978.4        1.2177584        1.533
    
37. 1979.1        0.87044509        2.311
    
38. 1979.2        1.7259966        2.7262
    
39. 1979.3        0.92863952        1.0502
    
40. 1979.4        0.86993798        0.5943
    
41. 1980.1        1.4647984        -0.73
    
42. 1980.2        -0.23876089        -4.033
    
43. 1980.3        0.88809499        -2.194
    
44. 1980.4        1.2162438        -0.0784
    
45. 1981.1        1.5577742        0.255
    
46. 1981.2        0.11375527        1.6622
    
47. 1981.3        0.99995247        1.7622
    
48. 1981.4        0.38833923        1.2286
    
49. 1982.1        0.93687825        0.9045
    
50. 1982.2        1.2753954        1.3425
    
51. 1982.3        0.38243548        1.423
    
52. 1982.4        0.90630802        0.5787
    
53. 1983.1        0.45208817        0.8577
    
54. 1983.2        0.27505216        1.2929
    
55. 1983.3        1.5118282        0.7474
    
56. 1983.4        0.33403826        0.4925
    
57. 1984.1        1.569055        0.1775
    
58. 1984.2        1.3476366        1.2125
    
59. 1984.3        0.61552627        0.4747
    
60. 1984.4        0.78283434        -0.1075
    
61. 1985.1        1.5364632        0.1833
    
62. 1985.2        1.8370137        0.1324
    
63. 1985.3        0.57253672        -0.5163
    
64. 1985.4        1.4975401        -2.2
    
65. 1986.1        -1.0225196        -0.8239
    
66. 1986.2        1.512838        0.5894
    
67. 1986.3        0.64926161        0.37
    
68. 1986.4        1.2952376        0.4275
    
69. 1987.1        0.4900279        -0.1342
    
70. 1987.2        0.49334769        0.7485
    
71. 1987.3        1.7711997        2.0908
    
72. 1987.4        2.1496419        0.4675
    
73. 1988.1        1.6486104        0.4366
    
74. 1988.2        0.68988429        1.0507
    
75. 1988.3        1.9921443        0.7622
    
76. 1988.4        1.2267913        0.12
    
77. 1989.1        1.2755196        0.7443
    
78. 1989.2        -0.13647397        0.3134
    
79. 1989.3        2.0117067        -0.155
    
80. 1989.4        1.2332191        -0.4172
    
81. 1990.1        0.37702198        0.7142
    
82. 1990.2        2.1358704        -0.1439
    
83. 1990.3        1.1565279        1.046
    
84. 1990.4        1.2190627        -1.0931
    
85. 1991.1        1.0639901        -1.3006
    
86. 1991.2        0.6255564        -0.8441
    
87. 1991.3        0.31595603        -0.8604
    
88. 1991.4        0.80395942        -0.717
    
89. 1992.1        0.59646885        -0.2161
    
90. 1992.2        -0.31155528        0.4511
    
91. 1992.3        -0.46916051        0.3916
    
92. 1992.4        0.018439978        0.5433
    
93. 1993.1        0.092148919        0.9282
    
94. 1993.2        0.34939351        0.8757
    
95. 1993.3        0.14674863        0.5022
    
96. 1993.4        -0.11921685        0.136
    
97. 1994.1        0.000000        1.21
    
98. 1994.2        0.51254002        1.6075
    
99. 1994.3        0.60978573        1.7309
    
100. 1994.4        -0.27257876        1.6169
     
101. 1995.1        -0.52910176        0.8211
     
102. 1995.2        1.5429604        0.8609
     
103. 1995.3        0.64637984        1.3765
     
104. 1995.4        0.73110169        1.711
     
105. 1996.1        2.6214625        1.8445
     
106. 1996.2        0.095143371        1.9285
     
107. 1996.3        -0.4071561        1.5821
     
108. 1996.4        1.0620486        1.444
     
109. 1997.1        1.9898616        1.24
     
110. 1997.2        -2.8004904        1.4243
     
111. 1997.3        0.77626748        1.042
     
112. 1997.4        -0.37013169        1.1357
     
113. 1998.1        0.1723247        0.8491
     
114. 1998.2        -0.72576783        0.7732
     
115. 1998.3        -0.28657047        0.3385
     
116. 1998.4        -0.8295904        1.109
     
117. 1999.1        1.9537807        1.1091
     
118. 1999.2        0.1031371        1.16
     
119. 
     
120. Date        Growth                Spread

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