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I would like to determine, whether two products are complementary. I have one year of data (day by day), where I have prices and demands for both products.

Can I use cross elasticity of demand? I guess it's too simple "model". For example I've noticed big variation of demand during a month, which I guess might be related to the payday. There might huge amounts of variables determining demand for product Y. I was event trying to compare similar days from different months, to avoid that "payday seasonality".

Is there any model, which helps to determine, whether two goods are complementary based on time series data?

I know, I'm might be quite naive, that I could use a cross elasticity for that.

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Most models that assess the cross-price elasticity with non-experimental data do so using time series data. With any regression model, the cross-price elasticity will be biased if you omit relevant variables. So, you need to include variables that capture seasonality, pay day effects, lagged effects, and anything else.

Many, many, models have been developed for this type of problem. The simplest is to have a regression with the dependent variable being the log of demand, and the log of the prices of both products as independent variables, along with all the other variables you need. More complex approaches include using time series models with transfer functions, converting the demand into share data and then use some type of model that can model shares (e.g., variants of logit),simultaneously model multiple dependent variables, etc. There would be many hundreds, and perhaps many thousands, of papers and books in the marketing and econometrics literatures on this.

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