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

Matthew Gilbert matthew.douglas.gilbert at gmail.com
Sun Oct 28 14:43:37 CET 2012

```The books "Analysis of Financial Time Series" by Ruey Tsay and
"Statistics of Financial Markets" by Franke, Hardle and Hafner are both
good references.

But ultimately if the end goal is to test a trading strategy why
simulate your own data? It seems like a lot of work and the end result
would be to generate a profitable strategy on fictitious data?

On 10/28/2012 09:22 AM, Alex Grund wrote:
> Hi Dirk,
>
>
> 2012/10/28 Dirk Eddelbuettel <edd at debian.org>:
>
>> There are libraries full of papers and dissertations on this.
> Okay, could you please mention a few valuable papers? So that I can search more
>
>> See 1). Which features?
> Basically, I started from the naive question: "How to create a time
> series that "looks" like a stock price process over time".
> So, the basic features I came through has been a) the distribution of
> the (daily) returns, b) their auto-correl features and c) binominal
> features.
> To explain what I mean by c):
> Imagine you create normal-distributed (N(0,1)) returns. Then the
> generated time series of prices (price[i] = price[i-1]*(returns[i]+1))
> will slightly tend to fall. This is obviously because of this: Imagine
> you have three returns generated, [-.5; 0; .5], then the series will
> fall. It should be [-.5;0;1] for the series to hold it's level,
> however P(X<-.5) > P(X>1), X~N(0,1), so the series with returns mean 0
> is obviously to fall.
>
> Additionally, one could think of volatility features (such as
> suggested by GARCH).
>
>> | 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.
> Okay, are there models to start with? They don't need to be perfect,
> because I want to use them for learning...
>
>> | 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.
> Ok, thanks
>
>
> --a
>
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