[R] ARCH LM test for univariant time series

[Spencer Graves]

Dear Tom: 

      Your revised function eliminates the discrepancy in the degrees of 
freedom but is still very different from the numbers reports on Tsay, p. 
102: 

 archTest(log(1+as.numeric(m.intc7303)), lag=12)

    ARCH test (univariate)

data:  Residual of y1 equation
Chi-squared = 13.1483, df = 12, p-value = 0.3584

Warning message:
In VAR(s, p = 1, type = "const") :
  No column names supplied in y, using: y1, y2, y3, y4, y5, y6, y7, y8, 
y9, y10, y11, y12 , instead.

     
      TOM:  What can you tell me about the warning message? 

      Thanks for your help with this. 
      Spencer Graves

tom soyer wrote:
> Spencer,
>
> Sorry, I forgot that the default lag in arch is 16. Here is the fix. Can you
> try it again and see if it gives the correct (or at least similar compared
> to a true LM test) result?
>
> archTest=function(x, lags=12){
>  #x is a vector
>  require(vars)
>  s=embed(x,lags)
>  y=VAR(s,p=1,type="const")
>  result=arch(y,lags.single=lags,multi=F)$arch.uni[[1]]
>  return(result)
> }
>
> Thanks and sorry about the bug.
>
>
> On 2/2/08, Spencer Graves <spencer.graves at pdf.com> wrote:
>   
>> Dear Tom, Bernhard, Ruey:
>>
>>      I can't get that to match Tsay's example, but I have other
>> questions about that.
>>
>>      1.  I got the following using Tom's 'archTest' function (below):
>>
>>     
>>> archTest(log(1+as.numeric(m.intc7303)), lags=12)
>>>       
>>    ARCH test (univariate)
>>
>> data:  Residual of y1 equation
>> Chi-squared = 10.8562, df = 16, p-value = 0.8183
>>
>> Warning message:
>> In VAR(s, p = 1, type = "const") :
>> No column names supplied in y, using: y1, y2, y3, y4, y5, y6, y7, y8,
>> y9, y10, y11, y12 , instead.
>>
>>     
>>           ** First note that the answer has df = 16, even though I
>> supplied lags = 12.
>>
>>      2.  For (apparently) this example, S-Plus FinMetrics 'archTest'
>> function returned "Test for ARCH Effects:  LM Test.  Null Hypothesis:
>> no ARCH effects.  Test Stat 43.5041, p.value 0.0000.  Dist. under Null:
>> chi-square with 12 degrees of freedom".
>>
>>      3.  Starting on p. 101, Ruey mentioned "the Lagrange multiplier
>> test of Engle (1982)", saying "This test is equivalent to the usual F
>> test for" no regression, but refers it to a chi-square, not an F
>> distribution.  Clearly, there is a gap here, because the expected value
>> of the F distribution is close to 1 [d2/(d2-2), where d2 = denominator
>> degrees of freedom;  http://en.wikipedia.org/wiki/F-distribution], while
>> the expected value for a chi-square is the number of degrees of freedom
>>
>>      Unfortunately, I don't feel I can afford the time to dig into this
>> further right now.
>>
>>      Thanks for your help.
>>      Spencer Graves
>>
>> tom soyer wrote:
>>     
>>> Spencer, how about something like this:
>>>
>>> archTest=function (x, lags= 16){
>>>  #x is a vector
>>>  require(vars)
>>>  s=embed(x,lags)
>>>  y=VAR(s,p=1,type="const")
>>>  result=arch(y,multi=F)$arch.uni[[1]]
>>>  return(result)
>>> }
>>>
>>> can you, or maybe Bernhard, check and see whether this function gives
>>> the correct result?
>>>
>>> thanks,
>>>
>>> On 2/1/08, *Spencer Graves* <spencer.graves at pdf.com
>>> <mailto:spencer.graves at pdf.com>> wrote:
>>>
>>>     Hi, Tom:
>>>
>>>          The 'arch' function in the 'vars' package is supposed to be
>>>       
>> able
>>     
>>>     to do that.  Unfortunately, I was unable to make it work for a
>>>     univariate series.  Bernhard Pfaff, the author of 'vars', said
>>>     that if I
>>>     read the code for 'arch', I could easily retrieve the necessary
>>>       
>> lines
>>     
>>>     and put them in my own function;  I have not so far found the time
>>>       
>> to
>>     
>>>     try that.  If you do, or if you get a better answer than this,
>>>     would you
>>>     please let me know?  I would like to have this capability for the
>>>     'FinTS' package, and I would happily write a help page if someone
>>>     would
>>>     contribute the function -- or use a function in another
>>>       
>> package.  Tsay
>>     
>>>     (2005) Analysis of Financial Time Series, 2nd ed. (Wiley) includes
>>>       
>> an
>>     
>>>     example on p. 103 that could be used for a reference.
>>>
>>>          Hope this helps.
>>>          Spencer Graves
>>>
>>>     tom soyer wrote:
>>>     > Hi,
>>>     >
>>>     > Does anyone know if R has a Lagrange multiplier (LM) test for ARCH
>>>     > effects for univariant time series?
>>>     >
>>>     > Thanks!
>>>     >
>>>     >
>>>
>>>
>>>
>>>
>>> --
>>> Tom
>>>       
>
>
>
>