Simulate the stock market for back testing strategy ---R bootstrap function

Thanks for Brian's reply.
to make this  more relevant to this list, what
functions in R can do bootstrap resampling while
keeping the autocorrelation in the original data? (I
only know function of sample()). Would this resmapled
data do any good on back testing?

Thanks!




--- "Brian G. Peterson" <brian at braverock.com> wrote:

elton wang wrote:

Here is a beginner question:
what would be your perferred method if we want to
simulate the stock market for back testing a

trading

strategy?
Using sp500 daily data as example, if given the
knowledge that historical data has time varying
volatility, autocorrelations etc? just fitting a
GARCH(1,1) or doing historical resampling?

(simply

divided the data to in-sample and out sample may

not

be sufficient, am I right?)

You've bitten off one of the most complex and
studied problems in finance.

Kalman filtering is often applied to build bands and
trends, as are
straightforward standard deviation based measures
such as "Bollinger bands".

Any of the AR methods ARMA, ARIMA, GARCH allow for
time-varying changes
in level and volatility.

Refinement of those models generally involves EMM or
Bayesian evolution
of the moments.

These can all be used as one- or multiple-
step-ahead prediction methods.

In general, these predictions would be used as
inputs to *create* a
trading strategy.  You would then backtest your
strategy by setting up a
"learning period" (length depending on the frequency
of your data), and
then letting the model evolve on an out-of-sample
basis (by making one
step ahead or similar predictions).

If you then wanted to further test your models, you
could fit various
distributions to historical data and simulate
historical series from
these distributions.  I'm not really a fan of the
pure simulation
approach unless you are very careful and know what
you're doing, because
there is a huge amount of model risk (risk that you
will mis-specify
starting parameters and therefore get worthless
results) involved in
these pure simulation approaches.

Many Bayesian (and other Monte Carlo) methods use
simulation to inform
their predictions, but this is different than
constructing purely
hypothetical historical series to test a model
against.

Regards,

    - Brian