[R-SIG-Finance] statistical features of equity time series

[Dirk Eddelbuettel]

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