# Modelling turnovers by a random walk. Is it right?

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

• Could you elaborate on what a "turnover" is and what you understand a "random walk model" to be? – whuber Apr 29 '15 at 18:38
• 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. – CodingButStillAlive Apr 29 '15 at 18:50
• 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? – whuber Apr 29 '15 at 18:56
• 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. – Cagdas Ozgenc Apr 30 '15 at 7:58
• Thanks a lot, Cagdas. I think that brings me in the right direction. I will try. – CodingButStillAlive May 1 '15 at 18:37