Using Principal Components to Forecast Firm Sales
Summary
The question concerns forecasting sales for a large panel of firms using sector industrial production and lagged financial statement variables. The response suggests using principal component analysis (PCA) to reduce the many firm-level series to a smaller set of common factors, then using those factors to help predict individual firms. As an alternative, it proposes constructing capital-weighted indexes and estimating each firm's relationship to an index, with industrial production potentially informing the indexes.
The material offers a dimensionality-reduction idea, not a tested forecasting procedure. It provides no comparison with ARIMA, ARIMAX, exponential smoothing, or other methods, and gives no evidence about forecast accuracy. PCA is described in general terms as an eigenvalue and eigenvector decomposition used to find factors that explain much of a dataset's variation. The suitability of either approach would depend on the data structure, validation design, and whether factors that explain historical variation also predict future sales.
Key ideas
- PCA can summarize many firm series with a smaller number of common factors.\nThe suggested factors could be used as predictors for individual firms' sales.\nCapital-weighted indexes offer an alternative way to build shared predictors.\nThe response proposes methods but reports no empirical forecast results.
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Full text
# Forecasting sales from balance sheet data # Forecasting sales from balance sheet data I have got a database with balance sheet and income statement data of 150.000 firms for the period 1995-2014. I need to get a good forecast of each firm's sales. As exogenous variables I can use the industrial production index of the relative industrial sector and the lagged other balance sheet variables. I would be grateful if you could suggest me the best methodology to use. I was thinking to try ARIMA, ARIMAX and exponential smoothing. ## Answer by horseless (score 2) https://quant.stackexchange.com/a/24661 [Sorry, I'm new here and accidently posted this as an answer and its just meant as a comment responding to a question, but it does not let me delete answers to put it under comments. If I last long enough, I'm sure I'll figure out how to edit things.] PCA is an eigenvalue/eigenvector decomposition of the data frequently applied in risk management to look for systemic factors effecting a large portfolio. My favorite introduction to the concept is an excellent efficient and very focused chapter in Carol Alexander's Market Risk Analysis vol 2 (and the volume number is critical since there are 4 books). This can give you factors that explain the majority of the variability in your series and it reduces your problem from 150,000 series down to a few factors. There are lots of articles on this if you search. Alternatively, and less techy, you could create your own capital weighted indexes and use those to predict the 150,000 individual series, using betas estimated off that index for each firm. Your IP index could influence these indexes.
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