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

Sun Oct 28 14:22:42 CET 2012

```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

```