[R] Switching log(J) to log(J+1) to avoid log(0) in HAR-RVJ model

[Joshua Ulrich]

Cross-posted on Stack Overflow:
http://stackoverflow.com/q/11567745/271616
--
Joshua Ulrich  |  FOSS Trading: www.fosstrading.com


On Thu, Jul 19, 2012 at 12:23 PM, cursethiscure
<caolan.harvey6 at mail.dcu.ie> wrote:
> I am working with xts dependent data, and my code is as follows (the problem
> is explained throughout):
>
> dat <- getdat("prices")
> dat <- read.zoo(dat, sep = "",format="%d/%m/%Y %H:%M",
>                 tz="", FUN=NULL, regular=TRUE,
>               header=TRUE, index.column=1, colClasses=c("character",
> "numeric"))
> dat <- as.xts(dat)
> ## cleaned data here to get
> daylist <- lapply(split(dat, "days"), function(x) {
>   if(NROW(x) >= 10) x
> })
> do.call(rbind, daylist) -> dat
> makeReturns(dat) -> dat
>
> the code I am running to get the HAR regressions (full code for it shown
> below) is
>
> x = harModel(dat, periods = c(1,5,22), periodsJ=c(1), RVest =
> c("RCov","RBPCov"),
>              type="HARRVJ", h=5, transform="log") ; # Estimate the HAR model
> of type HARRVJ
>
> The three HAR models on paper are:
>
> 1.〖RV〗_(t,t+h) = β_0+ β_D 〖RV〗_t+ β_W 〖RV〗_(t-5)+ β_M 〖RV〗_(t-22)  + β_J J_t
> + ε_(t,t+h) # NULL model in code at bottom
>
> 2.  (RV〗_(t,t+h) )^(1/2) = β_0+ β_D 〖〖RV〗_t〗^(1/2)+ β_W (〖RV〗_(t-5) )^(1/2)+
> β_M (〖RV〗_(t-22) )^(1/2)  + β_J (〖 J〗_t )^(1/2)  + ε_(t,t+h)
>
> 3. log(RV〗_(t,t+h) )= β_0+ β_D.log(〖RV〗_t )+ β_W.log(〖RV〗_(t-5) )+
> β_M.log(〖RV〗_(t-22) )  + β_J  log(J_t  + 1)  + ε_(t,t+h)
>
> Basically the harModel in the code allows you to transform the regressions
> from NULL  to "sqrt" or "log", but when `transform="log"` is chosen it gives
> the following error message.
>
> x = harModel(dat, periods = c(1,5,22), periodsJ=c(1), RVest =
> c("RCov","RBPCov"),
> +              type="HARRVJ", h=22, transform="log") ; # Estimate ....
> [TRUNCATED]
> Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
>   NA/NaN/Inf in foreign function call (arg 1)
>
>  which is due to it taking the log(0), the actual log model should take
> log(J + 1) in case of a 0 value for the J in the time series ( if J does not
> occur it should return a 0, otherwise it should return J), but unfortunately
> I do not know how to rectify this. I was wondering if any one could tell me
> how how I can achieve this as I am very naive with R still.  I have tried
> some modifications you will see at the bottom of the question, but they do
> not compute the regression correctly though they do allow it to run without
> 'error'
>
> A sample of the xts returns are
>
<snip>
>
> The full code is just below this code and what I have tried to do within it
> is change the following two lines when running transform="log" but this
> gives unrealistic regression output such as values over 3:
>
>   if( type == "HARRVJ" ){
>     J = J[(maxp:(n-h)),];
>     *x = cbind(x1,J);*              # bind jumps to RV data
>     if(!is.null(transform)){ y = Ftransform(y); x = Ftransform(x); }
>     x = cbind(x,rmin);
>     model = estimhar(y=y,x=x);
>     model$transform = transform; model$h = h; model$type = "HARRVJ";
> model$dates = alldates[(maxp+h):n];
>     class(model) = c("harModel","lm");
>     return( model )
>   }#End HAR-RV-J if cond
>
> to
>
> if( type == "HARRVJ" ){
>     J = J[(maxp:(n-h)),];
>     *x = cbind(x1,J+1); *             # bind jumps to RV data
>     if(!is.null(transform)){ y = Ftransform(y); x = Ftransform(x); }
>     x = cbind(x,rmin);
>     model = estimhar(y=y,x=x);
>     model$transform = transform; model$h = h; model$type = "HARRVJ";
> model$dates = alldates[(maxp+h):n];
>     class(model) = c("harModel","lm");
>     return( model )
>   }#End HAR-RV-J if cond
>
> and this
>
>  if( type == "HARRVCJ" ){
>     # Are the jumps significant? if not set to zero:
>     if( jumptest=="ABDJumptest" ){
>       TQ = apply.daily(data, TQfun);
>       J = J[,1];
>       teststats    = ABDJumptest(RV=RM1,BPV=RM2,TQ=TQ );
>     }else{ jtest = match.fun(jumptest); teststats = jtest(data,...) }
>     Jindicators  = teststats > qnorm(1-alpha);
>     *J[!Jindicators] = 0;*
>  to
> if( type == "HARRVCJ" ){
>     # Are the jumps significant? if not set to zero:
>     if( jumptest=="ABDJumptest" ){
>       TQ = apply.daily(data, TQfun);
>       J = J[,1];
>       teststats    = ABDJumptest(RV=RM1,BPV=RM2,TQ=TQ );
>     }else{ jtest = match.fun(jumptest); teststats = jtest(data,...) }
>     Jindicators  = teststats > qnorm(1-alpha);
>   *  J[!Jindicators] = 1;*
>
> the full code is (which I take no credit for):
>
<snip>
>
> If anyone could help me with as to how J should be modified when the model
> is in log form it would be hugely appreciated, Thanks in advance.
>
> --
> View this message in context: http://r.789695.n4.nabble.com/Switching-log-J-to-log-J-1-to-avoid-log-0-in-HAR-RVJ-model-tp4637088.html
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>
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