[RSIGFinance] statistical features of equity time series
Dirk Eddelbuettel
edd at debian.org
Sun Oct 28 13:41:17 CET 2012
On 28 October 2012 at 13:21, Alex Grund wrote:
 Hi,

 I would like to explore some basic investment "behaviors" (not real
 quant "strategies"), such like the cost average effect.

 Therefore, I would like to create artificial time series with similar
 statistical features as real stock price time series.


 1) How could I create them? What is a common distribution function to
 get returns from? (Without having reference data)
There are libraries full of papers and dissertations on this.
You first need to establish _which properties_ you actually want to model /
recreate. And at which time frame. Eg for daily data you may use a normal
mixture, maybe add a jump, overlay some sort of Garch or SV... but those are
"still wrong".
I'd (carefully) resample as per 4).
 2) How can I create a time series with similar features as a given time series?
See 1). Which features?
 3) How can I create a time series with statistical features that are
 similar to most of the data from a set of given time series?
See 1) and 2). Seriously :) The last paper presentation I saw was Diebold who
showed how to regenerate trade duration data, as well as high frequency vol,
from a "simple" four parameter model. And simple is a relative term  he
recaptured the features of his (SP100 equity TAQ) data set, but its not a
model you can code up in just a few lines.
 4) Is there anything valuable which could make given data more
 exhaustible? Something like bootstrapping?
Block bootstrap for time series is pretty well established, and the tseries
package even had a tsbootstrap() function for over a decade. You can (fairly
easily) extend similar schemes.
Dirk

Dirk Eddelbuettel  edd at debian.org  http://dirk.eddelbuettel.com
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