Assessing Random-Walk Models for Weekly Company Turnover
Summary
The document raises whether a random walk with drift, commonly used for price-like series, is appropriate for weekly company turnover. Turnover is a flow measured over an interval, while a share price is a stock observed at a point in time. The question highlights that turnover can change sharply between weeks, including falling to zero, and asks whether this distinction rules out applying similar stochastic models.
The text does not provide an answer, fitted model, or empirical evidence. Instead, it frames the modelling issue and identifies the goal of comparing estimated drifts across companies. Its useful contribution is the distinction between stock and flow variables and the need to justify a model for the specific data-generating process. In particular, ordinary random-walk assumptions may need scrutiny for nonnegative, intermittent turnover series with zeros; the document leaves model choice and diagnostics unresolved.
Key ideas
- Weekly turnover is a flow variable, whereas a share price is a stock variable.
- The question asks whether a random walk with drift can describe turnover despite abrupt week-to-week changes.
- The intended analysis is to compare drift estimates across company turnover series.
- No modelling answer or empirical validation is supplied, so suitability remains unresolved.
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Full text
# Modelling turnovers with a random walk. Is it right? # Modelling turnovers with 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. 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. 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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.