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I need to analyse a bunch of weekly time series that reflect the turnovers of various companies. I already read that return rates or share prices show stochastic patterns that can be modelled by a random walk. However, such time series usually correspond to continuous functions (curves), whereas turnover values can go up and down dramatically between two successive weeks. For example:

Week t: 1 mio Euros

Week t+1: 0 Euros

QUESTION: So my question is whether the choice of a random walk model would still be justified or not.

My plan is to model the timely courses of turnover figures by a random walk model that allows for a drift because analyzing the distribution of drifts is my final goal.

My apologies for weaknesses in the explanation - I am not from finance originally.

Best regards

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    $\begingroup$ Could you elaborate on what a "turnover" is and what you understand a "random walk model" to be? $\endgroup$ – whuber Apr 29 '15 at 18:38
  • $\begingroup$ Sure! So, turnover is also called revenue. [Wikipedia] Revenue - en.m.wikipedia.org/wiki/Revenue A random walk model is a linear time series model. $\endgroup$ – CodingButStillAlive Apr 29 '15 at 18:50
  • $\begingroup$ Thank you. I believe that what most people consider a "linear time series model" to be would encompass far more than what is ordinarily considered to be a "random walk," so your uses of these terms are confusing. Regardless, I can't find any information in your question that looks like it could be useful for providing an objective statistical answer: you tell us too little about your data and how they might behave. Perhaps you could edit it to include more details to make it answerable? $\endgroup$ – whuber Apr 29 '15 at 18:56
  • $\begingroup$ Random walk is a series of uncorrelated increments. If you take a cumulative sum of weekly turnovers(i.e. t(1) = w1, t(2) = w1+w2, t(3) = w1+w2+w3,...), this may be modeled like a random walk (though it won't be very useful for prediction). Or alternatively the weekly turnovers themselves can be modeled by an ARMA model. $\endgroup$ – Cagdas Ozgenc Apr 30 '15 at 7:58
  • $\begingroup$ Thanks a lot, Cagdas. I think that brings me in the right direction. I will try. $\endgroup$ – CodingButStillAlive May 1 '15 at 18:37
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In the meantime, I figured out that the core of my question refers to the distinction between so-called stock and flow variables. The revenue per week is a flow variable, whereas a share price at a specific point in time is a stock variable.

[Wikipedia] Stock and flow - https://en.m.wikipedia.org/wiki/Stock_and_flow

However, it remains unclear to me whether both types of variables can be treated with the same stochastic models.

The random walk with drift model is described in 'Introductory Time Series with R (Use R!)' by Paul S. P. Cowpertwait. In the book it is applied to a time series of stock variables (share prices). It allows to analyse whether there exists a positive drift (i.e. a mean increase of prices) in a time series of prices, which is mainly determined by unknown and unpredictable (i.e. stochastic) effects. But the question remains, whether this model can also be used for flow variables.

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