Normalizing Trends with Percentage Changes and Forecast Models

# Standard way to represent trend in an a-dimensional way


# Standard way to represent trend in an a-dimensional way












Let us suppose that a factory needs to know when certain products are increasing the profit. This factory produces an huge number of products each with different targets. So the factory need to compare their trend in a relative fashion.

So, the `trend` itself is not so good when comparing more products. For instance, explore this scenario:

- product A: goes from 50 sold pieces in January to 100 sold pieces in December.

- product B: goes from 100 sold pieces in January to 150 sold pieces in December.

- product C: goes from 100 sold pieces in January to 200 sold pieces in December.

(for simplicity let us suppose the unit price is the same for all products and does not varies in time)

`Trend` of product A equals the `trend` of product B, but product A doubled the sold pieces. Also, `trend` of product B is greater than the `trend` of product A, while both have doubled their sold pieces.

I wonder what is a good standard indicator to capture such behaviour: an indicator that have the same value for products which double their profit. So that A and C have the same value which is greater than B.

I guess representing the trend a-dimensionally should resolve this problem: this would prevent the dependency of the number of pieces and should result in a more relative indicator.

Thanks.

EDIT: I don't have only two points: not only January and December, but let's say, a set of points for each month. Currently, as trend I use linear regression. I know that dividing this trend (which has dimension of pieces/month) by the first point will normalize it. But I find the using of the first point arbitrary. Why not the second one? why not the average?

## Answer by user2763361 (score 2)

https://quant.stackexchange.com/a/10542

I can't really understand anything after the first paragraph (-1 therefore).

Making an assumption about what you meant with your first sentence, your question is how to determine whether product $A$ is going to be profitable in the future. You therefore need a forecasting model that gives $Q[Profits(t)|decision]$ (quantiles) or $E[Profits(t)|decision]$ (expectation) for each $t \in \mathbb{R}^+$ which you can discount.

This could be a combination of subjective factors (upcoming legislation that's relevant to your product, new competitor is starting up, etc) and statistical models. The model attempt that you're talking about would be the (very) beginning of an investigation on the statistical side. You would need to collect a lot of data and map this data to the next-period outcome (number of products sold of each time period, or profit from that product of each time period) using a regression/supervised learning model, and then extrapolate into the future. A simple approach would be something like ARIMA-X with seasonality and with sufficient data you can look into non-linear machine learning models. If you have insufficient time-series you can only use seasonality and time features to extrapolate since you will not be able to reduce the frequency sufficiently to achieve your objectives with exogenous features. Panel approaches may be good due to insufficient data in a univariate setting, if the products are similar.

## Answer by Mau (score 1)

https://quant.stackexchange.com/a/10539

So why not

```
trend = (sales_period_end - sales_period_start) / sales_period_start
```

?

## Answer by mcisse (score 1)

https://quant.stackexchange.com/a/10543

Look into indices, like the consumer price index. Your question needs more clarification though because a positive change in quantity does not necessarly translate into a positive change in profit. You need to take into account the unit price. Do all products have the same price? If not, you need compare profits not quanties. Do the prices stay constant over the observation period? If so, then a percent change in profits is enough to compare them.if the prices changed over time, then you need to build an index.