0
$\begingroup$

Does the plotted data look like a garch model? If it does, with which test, I can support this claim

http://i.stack.imgur.com/gEHr3.png

[1]   0.187415738   0.477868164   0.295777631   0.575167970   0.469157108
  [6]   0.328171826   1.292894322  -0.847711535   0.392077876   0.116540719
 [11]   0.314835442  -0.131731938   0.090753214   0.326724648  -0.504309863
 [16]   0.522419894  -0.458490815  -0.922188177   1.312544072  -0.124784861
 [21]  -0.440201131  -0.376074075   0.484759007  -0.544084907   0.184140601
 [26]   0.634605831  -1.015191304  -0.392407326   0.069140836   0.837570607
 [31]  -0.734046990   0.009650584  -0.297811017  -0.894844413   1.254269251
 [36]  -2.202675529   3.181080668   2.738269460  -1.531934991  -0.441972078
 [41]  -0.111205739   0.347052040   0.812613401   1.056684583  -0.498294836
 [46]  -0.318961547  -0.109851318  -0.118844912   0.404173405  -0.910582285
 [51]  -0.353860467  -0.750922999  -0.703591979  -0.637060347  -0.282754755
 [56]  -0.953784737   1.576556620   4.151024359  -5.425327217  -6.103292196
 [61]   7.943888186 -13.463531790   5.869748465 -14.205872960  -5.045698842
 [66]   6.001954472   4.930371803  -1.892510511   1.850741003  -0.954016972
 [71]  -0.077456198   0.040999835  -0.446823649   0.127273533   0.127966102
 [76]   0.216028033   0.626917525   0.282341328   0.328576480  -0.157644004
 [81]  -0.937382208   1.287429037   0.900623061  -0.677630409   0.427116916
 [86]   0.246673589   0.204713960  -0.177800003   0.290096733   0.758407267
 [91]  -0.328556185  -0.330455346  -0.526235619  -0.489013356   0.475158246
 [96]   0.430567333  -0.775044149   0.139062847   0.374927797  -0.528934679
[101]   0.217091044  -0.019686328   0.690038054  -0.450631659   0.530362959
[106]  -0.466588401   0.895308589   0.013337137  -0.257514294  -0.346425256
[111]   0.002790152   0.565433354  -1.038591166   1.439547986  -0.475994171
[116]  -0.573993908   0.844415185  -0.778530803  -0.743884821   1.258147231
[121]  -0.088087152   0.508910627  -0.071854449   0.410070978   0.471372207
[126]   0.094210278   1.334666193  -0.010790060  -0.305813138  -0.347626733
[131]  -0.467378439   0.372987762   0.481824018   0.415398181  -0.180618112
[136]   1.013615048  -0.156073342   0.356076568   0.169108466   0.275734683
[141]  -0.648042994   0.269037495   0.669168433  -0.239254253   0.796882449
[146]   1.336804388  -0.354919126  -0.525481668  -0.066679296  -0.645930518
[151]   0.415104329   1.070218821   2.305348685  -3.405189139  -3.799563891
[156]   0.721310801  -0.864861449  -1.169885359   0.052965774  -0.681096223
[161]  -0.227592654   0.538791441   0.123075072   0.471443863  -0.598493272
[166]  -0.575874729  -0.497991275  -1.149177081  -0.391882551  -0.724743988
[171]   0.151001413  -0.596898412   0.762378302  -1.740324011   0.255643898
[176]   0.417552215  -0.641130460  -0.775619616   0.968210920  -0.110971587
[181]  -0.143987039  -0.041898461   0.384757277   0.303919564   0.367943147
[186]  -0.123326308   0.506591242   0.631918157  -0.265859230   0.325193212
[191]   0.532946942   0.633710920   0.590115624   0.307122036   0.391484459
[196]  -0.036289366  -0.614109628  -0.638930907   0.881656376  -1.584292446




Call:
garch(x = data2, order = c(0, 1))

Model:
GARCH(0,1)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.57713 -0.68644  0.01396  0.79931  2.85119 

Coefficient(s):
    Estimate  Std. Error  t value Pr(>|t|)    
a0   0.21135     0.04085    5.174 2.30e-07 ***
a1   0.87577     0.16163    5.418 6.02e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Diagnostic Tests:
    Jarque Bera Test

data:  Residuals
X-squared = 1.4612, df = 2, p-value = 0.4816


    Box-Ljung test

data:  Squared.Residuals
X-squared = 0.0027, df = 1, p-value = 0.9584


Call:
garch(x = data2, order = c(1, 1))

Model:
GARCH(1,1)

Residuals:
      Min        1Q    Median        3Q       Max 
-2.257745 -0.252623  0.006404  0.248729  1.680547 

Coefficient(s):
    Estimate  Std. Error  t value Pr(>|t|)    
a0 3.497e+00   8.228e-01    4.251 2.13e-05 ***
a1 1.048e+00   8.054e-01    1.301    0.193    
b1 2.371e-14   1.779e-01    0.000    1.000    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Diagnostic Tests:
    Jarque Bera Test

data:  Residuals
X-squared = 143.2293, df = 2, p-value < 2.2e-16


    Box-Ljung test

data:  Squared.Residuals
X-squared = 15.6938, df = 1, p-value = 7.447e-05

Call:
garch(x = data2, order = c(1, 2))

Model:
GARCH(1,2)

Residuals:
      Min        1Q    Median        3Q       Max 
-3.301812 -0.268550  0.006167  0.257807  2.279465 

Coefficient(s):
    Estimate  Std. Error  t value Pr(>|t|)  
a0 3.327e+00   2.675e+00    1.244    0.214  
a1 1.341e-01   7.183e-02    1.866    0.062 .
a2 1.299e-01   1.559e-01    0.833    0.405  
b1 1.113e-13   7.818e-01    0.000    1.000  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Diagnostic Tests:
    Jarque Bera Test

data:  Residuals
X-squared = 470.4355, df = 2, p-value < 2.2e-16


    Box-Ljung test

data:  Squared.Residuals
X-squared = 60.2426, df = 1, p-value = 8.438e-15
$\endgroup$
  • $\begingroup$ Can you post your data? $\endgroup$ – tchakravarty May 11 '14 at 9:47
  • $\begingroup$ The data looks like it might be consistent with GARCH. You could fit a GARCH model and then look to see if there's substantive structure left in standardized residuals. $\endgroup$ – Glen_b -Reinstate Monica May 11 '14 at 10:19
  • $\begingroup$ I posted my data . Here is the result of garch(0,1). Can you help me interpret the results? $\endgroup$ – arke May 11 '14 at 18:29
1
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There are several ways of testing for (G)ARCH effects in time series, and using your data, I am reporting two of the most commonly used two-sided tests:

  1. Engle's LM test (implemented in ArchTest() from the FinTS package)
  2. McLeod-Li test (implemented in McLeod.Li.test() from the TSA package)

In both cases, using your data, the null of no ARCH effects is strongly rejected when checking up to lag 12.

library(FinTS)
library(TSA)

dfGARCH = read.table(textConnection('[1]   0.187415738   0.477868164   0.295777631   0.575167970   0.469157108
  [6]   0.328171826   1.292894322  -0.847711535   0.392077876   0.116540719
 [11]   0.314835442  -0.131731938   0.090753214   0.326724648  -0.504309863
                          [16]   0.522419894  -0.458490815  -0.922188177   1.312544072  -0.124784861
                          [21]  -0.440201131  -0.376074075   0.484759007  -0.544084907   0.184140601
                          [26]   0.634605831  -1.015191304  -0.392407326   0.069140836   0.837570607
                          [31]  -0.734046990   0.009650584  -0.297811017  -0.894844413   1.254269251
                          [36]  -2.202675529   3.181080668   2.738269460  -1.531934991  -0.441972078
                          [41]  -0.111205739   0.347052040   0.812613401   1.056684583  -0.498294836
                          [46]  -0.318961547  -0.109851318  -0.118844912   0.404173405  -0.910582285
                          [51]  -0.353860467  -0.750922999  -0.703591979  -0.637060347  -0.282754755
                          [56]  -0.953784737   1.576556620   4.151024359  -5.425327217  -6.103292196
                          [61]   7.943888186 -13.463531790   5.869748465 -14.205872960  -5.045698842
                          [66]   6.001954472   4.930371803  -1.892510511   1.850741003  -0.954016972
                          [71]  -0.077456198   0.040999835  -0.446823649   0.127273533   0.127966102
                          [76]   0.216028033   0.626917525   0.282341328   0.328576480  -0.157644004
                          [81]  -0.937382208   1.287429037   0.900623061  -0.677630409   0.427116916
                          [86]   0.246673589   0.204713960  -0.177800003   0.290096733   0.758407267
                          [91]  -0.328556185  -0.330455346  -0.526235619  -0.489013356   0.475158246
                          [96]   0.430567333  -0.775044149   0.139062847   0.374927797  -0.528934679
                          [101]   0.217091044  -0.019686328   0.690038054  -0.450631659   0.530362959
                          [106]  -0.466588401   0.895308589   0.013337137  -0.257514294  -0.346425256
                          [111]   0.002790152   0.565433354  -1.038591166   1.439547986  -0.475994171
                          [116]  -0.573993908   0.844415185  -0.778530803  -0.743884821   1.258147231
                          [121]  -0.088087152   0.508910627  -0.071854449   0.410070978   0.471372207
                          [126]   0.094210278   1.334666193  -0.010790060  -0.305813138  -0.347626733
                          [131]  -0.467378439   0.372987762   0.481824018   0.415398181  -0.180618112
                          [136]   1.013615048  -0.156073342   0.356076568   0.169108466   0.275734683
                          [141]  -0.648042994   0.269037495   0.669168433  -0.239254253   0.796882449
                          [146]   1.336804388  -0.354919126  -0.525481668  -0.066679296  -0.645930518
                          [151]   0.415104329   1.070218821   2.305348685  -3.405189139  -3.799563891
                          [156]   0.721310801  -0.864861449  -1.169885359   0.052965774  -0.681096223
                          [161]  -0.227592654   0.538791441   0.123075072   0.471443863  -0.598493272
                          [166]  -0.575874729  -0.497991275  -1.149177081  -0.391882551  -0.724743988
                          [171]   0.151001413  -0.596898412   0.762378302  -1.740324011   0.255643898
                          [176]   0.417552215  -0.641130460  -0.775619616   0.968210920  -0.110971587
                          [181]  -0.143987039  -0.041898461   0.384757277   0.303919564   0.367943147
                          [186]  -0.123326308   0.506591242   0.631918157  -0.265859230   0.325193212
                          [191]   0.532946942   0.633710920   0.590115624   0.307122036   0.391484459
                          [196]  -0.036289366  -0.614109628  -0.638930907   0.881656376  -1.584292446'))

dfGARCH$V1 = NULL
tsGARCH = as.ts(c(t(as.matrix(dfGARCH))))

#==========================================================
# Engle's LM test for ARCH effects
#==========================================================
ArchTest(tsGARCH, lags = 12, demean = FALSE)

#==========================================================
# McLeod-Li test for ARCH effects
#==========================================================
McLeod.Li.test(y = tsGARCH, gof.lag = 12, plot = FALSE)$p.values
$\endgroup$
  • $\begingroup$ Thank you for your answer. What do you think about GARCH(0,1), GARCH(1,1) AND GARCH(1,2) results I put abve? $\endgroup$ – arke May 11 '14 at 19:00

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