[R] C/C++/Fortran Rolling Window Regressions
Mark Leeds
markleeds2 at gmail.com
Fri Jul 22 06:48:51 CEST 2016
Hi Jeremiah: I think I wasn't that clear. I'm not suggesting the kalman
filter to deal with time varying coefficients. As Roy pointed out, one can
use the kalman filter to do regular regression where one "sees" a new data
point as each time unit passes. It can be assumed that the coefficients do
not vary ( basically by having no variance in the system equation ).
The problem as I see it, is that Duncan and Horn's approach ( and Roy
alluded
to this problem also ), only deals with adding one point at a time to the
front of the data set. It doesn't handle the fact that you want to drop
the nth observation and everything older than that observation also.
don't know how easy it would be to modify their approach to deal with the
fact that you are using a moving window rather than just adding one point
at a time.
The main point I wanted to get across here is that I was not suggesting the
KF as a way to handle varying coefficients. You can assume that they're
fixed and still use it. See the reference I pointed out for more on this
approach and my apologies for the confusion.
On Thu, Jul 21, 2016 at 5:43 PM, jeremiah rounds <roundsjeremiah at gmail.com>
wrote:
> I agree that when appropriate Kalman Filter/Smoothing the higher-quality
> way to go about estimating a time-varying coefficient (given that is what
> they do), and I have noted that both the R package "dlm" and the function
> "StructTS" handle these problems quickly. I am working on that in
> parallel.
>
> One of the things I am unsure about with Kalman Filters is how to estimate
> variance parameters when the process is unusual in some way that isn't in
> the model and it is not feasible to adjust the model by-hand. dlm's dlmMLE
> seems to produce non-sense (not because of the author's work but because of
> assumptions). At least with moving window regressions after the unusual
> event is past your window the influence of that event is gone. That
> isn't really a question for this group it is more about me reading more.
> When I get that "how to handle all the strange things big data throws at
> you" worked out for Kalman Filters, I will go back to those because I
> certainly like what I see when everything is right. There is a plethora of
> related topics right? Bayesian Model Averaging, G-ARCH models for
> heteroscedasticity, etc.
>
> Anyway... roll::roll_lm, cheers!
>
> Thanks,
> Jeremiah
>
>
>
> On Thu, Jul 21, 2016 at 2:08 PM, Mark Leeds <markleeds2 at gmail.com> wrote:
>
>> Hi Jermiah: another possibly faster way would be to use a kalman
>> filtering framework. I forget the details but duncan and horne have a paper
>> which shows how a regression can be re-computed each time a new data point
>> is added .I
>> forget if they handle taking one off of the back also which is what you
>> need.
>>
>> The paper at the link below isn't the paper I'm talking about but it's
>> reference[1] in that paper. Note that this suggestion might not be a better
>> approach than the various approaches already suggested so I wouldn't go
>> this route unless you're very interested.
>>
>>
>> Mark
>>
>> https://www.le.ac.uk/users/dsgp1/COURSES/MESOMET/ECMETXT/recurse.pdf
>>
>>
>>
>>
>>
>>
>> On Thu, Jul 21, 2016 at 4:28 PM, Gabor Grothendieck <
>> ggrothendieck at gmail.com> wrote:
>>
>>> I would be careful about making assumptions regarding what is faster.
>>> Performance tends to be nonintuitive.
>>>
>>> When I ran rollapply/lm, rollapply/fastLm and roll_lm on the example
>>> you provided rollapply/fastLm was three times faster than roll_lm. Of
>>> course this could change with data of different dimensions but it
>>> would be worthwhile to do actual benchmarks before making assumptions.
>>>
>>> I also noticed that roll_lm did not give the same coefficients as the
>>> other two.
>>>
>>> set.seed(1)
>>> library(zoo)
>>> library(RcppArmadillo)
>>> library(roll)
>>> z <- zoo(matrix(rnorm(10), ncol = 2))
>>> colnames(z) <- c("y", "x")
>>>
>>> ## rolling regression of width 4
>>> library(rbenchmark)
>>> benchmark(fastLm = rollapplyr(z, width = 4,
>>> function(x) coef(fastLm(cbind(1, x[, 2]), x[, 1])),
>>> by.column = FALSE),
>>> lm = rollapplyr(z, width = 4,
>>> function(x) coef(lm(y ~ x, data = as.data.frame(x))),
>>> by.column = FALSE),
>>> roll_lm = roll_lm(coredata(z[, 1, drop = F]), coredata(z[, 2, drop =
>>> F]), 4,
>>> center = FALSE))[1:4]
>>>
>>>
>>> test replications elapsed relative
>>> 1 fastLm 100 0.22 1.000
>>> 2 lm 100 0.72 3.273
>>> 3 roll_lm 100 0.64 2.909
>>>
>>> On Thu, Jul 21, 2016 at 3:45 PM, jeremiah rounds
>>> <roundsjeremiah at gmail.com> wrote:
>>> > Thanks all. roll::roll_lm was essentially what I wanted. I think
>>> maybe
>>> > I would prefer it to have options to return a few more things, but it
>>> is
>>> > the coefficients, and the remaining statistics you might want can be
>>> > calculated fast enough from there.
>>> >
>>> >
>>> > On Thu, Jul 21, 2016 at 12:36 PM, Achim Zeileis <
>>> Achim.Zeileis at uibk.ac.at>
>>> > wrote:
>>> >
>>> >> Jeremiah,
>>> >>
>>> >> for this purpose there are the "roll" and "RcppRoll" packages. Both
>>> use
>>> >> Rcpp and the former also provides rolling lm models. The latter has a
>>> >> generic interface that let's you define your own function.
>>> >>
>>> >> One thing to pay attention to, though, is the numerical reliability.
>>> >> Especially on large time series with relatively short windows there
>>> is a
>>> >> good chance of encountering numerically challenging situations. The QR
>>> >> decomposition used by lm is fairly robust while other more
>>> straightforward
>>> >> matrix multiplications may not be. This should be kept in mind when
>>> writing
>>> >> your own Rcpp code for plugging it into RcppRoll.
>>> >>
>>> >> But I haven't check what the roll package does and how reliable that
>>> is...
>>> >>
>>> >> hth,
>>> >> Z
>>> >>
>>> >>
>>> >> On Thu, 21 Jul 2016, jeremiah rounds wrote:
>>> >>
>>> >> Hi,
>>> >>>
>>> >>> A not unusual task is performing a multiple regression in a rolling
>>> window
>>> >>> on a time-series. A standard piece of advice for doing in R is
>>> >>> something
>>> >>> like the code that follows at the end of the email. I am currently
>>> using
>>> >>> an "embed" variant of that code and that piece of advice is out
>>> there too.
>>> >>>
>>> >>> But, it occurs to me that for such an easily specified matrix
>>> operation
>>> >>> standard R code is really slow. rollapply constantly returns to R
>>> >>> interpreter at each window step for a new lm. All lm is at its
>>> heart is
>>> >>> (X^t X)^(-1) * Xy, and if you think about doing that with Rcpp in
>>> rolling
>>> >>> window you are just incrementing a counter and peeling off rows (or
>>> >>> columns
>>> >>> of X and y) of a particular window size, and following that up with
>>> some
>>> >>> matrix multiplication in a loop. The psuedo-code for that Rcpp
>>> >>> practically writes itself and you might want a wrapper of something
>>> like:
>>> >>> rolling_lm (y=y, x=x, width=4).
>>> >>>
>>> >>> My question is this: has any of the thousands of R packages out there
>>> >>> published anything like that. Rolling window multiple regressions
>>> that
>>> >>> stay in C/C++ until the rolling window completes? No sense and
>>> writing it
>>> >>> if it exist.
>>> >>>
>>> >>>
>>> >>> Thanks,
>>> >>> Jeremiah
>>> >>>
>>> >>> Standard (slow) advice for "rolling window regression" follows:
>>> >>>
>>> >>>
>>> >>> set.seed(1)
>>> >>> z <- zoo(matrix(rnorm(10), ncol = 2))
>>> >>> colnames(z) <- c("y", "x")
>>> >>>
>>> >>> ## rolling regression of width 4
>>> >>> rollapply(z, width = 4,
>>> >>> function(x) coef(lm(y ~ x, data = as.data.frame(x))),
>>> >>> by.column = FALSE, align = "right")
>>> >>>
>>> >>> ## result is identical to
>>> >>> coef(lm(y ~ x, data = z[1:4,]))
>>> >>> coef(lm(y ~ x, data = z[2:5,]))
>>> >>>
>>> >>> [[alternative HTML version deleted]]
>>> >>>
>>> >>> ______________________________________________
>>> >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> >>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> >>> PLEASE do read the posting guide
>>> >>> http://www.R-project.org/posting-guide.html
>>> >>> and provide commented, minimal, self-contained, reproducible code.
>>> >>>
>>> >>>
>>> >
>>> > [[alternative HTML version deleted]]
>>> >
>>> > ______________________________________________
>>> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> > https://stat.ethz.ch/mailman/listinfo/r-help
>>> > PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> > and provide commented, minimal, self-contained, reproducible code.
>>>
>>>
>>>
>>> --
>>> Statistics & Software Consulting
>>> GKX Group, GKX Associates Inc.
>>> tel: 1-877-GKX-GROUP
>>> email: ggrothendieck at gmail.com
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>
[[alternative HTML version deleted]]
More information about the R-help
mailing list