# What are the criteria for protocol transformations

## When does a time series have to be logged before an ARIMA model is adapted?

I used Forecast Pro before to forecast univariate time series, but switched my workflow to R. The forecasting package for R contains many useful functions, but one thing it doesn't do until it runs automatically, arima (). In some cases, Forecast Pro decides to log transformation data before making forecasts, but I still haven't figured out why.

So my question is, when should I log-transform my time series before trying ARIMA methods?

/ edit: After reading your answers, I'll use something like this, where x is my time series:

Does it make sense?

Some Precautions Before Proceeding. As I often suggest to my students, only use things as a first approximation of your bottom line, or when you want a frugal model when verifying that your competitive model does better.

Data

You need to start clearly from the description of the time series data you are working with. In macroeconometrics, you usually work with aggregated data, and geometric means have (surprisingly) more empirical evidence for macro time series data, probably because most of them are in exponentially growing trends can be disassembled.

Incidentally, Rob's suggestion works "visually" for time series clear seasonal share as slowly changing annual data for the increase in variation are less clear. Fortunately, there is typically an exponentially growing trend (if it appears to be linear, no logs are required).

model

If your analysis is based on a theory that a weighted geometric mean Y. (t) = Xα11 (t). . . Xαkk (t) ε (t)

In financial econometrics, due to the popularity of ...

Protocol transformations have nice properties

In the log-log regression model, this is the interpretation of the estimated parameter as elasticity from Y (t) to X iαichY. (t) Xich (t)

In error correction models it is more empirically assumed that the Proportions more stable ( stationary ) are than the absolute differences.

In financial econometrics it is easy to aggregate the logarithmic returns over time .

There are many other reasons not mentioned here.

At last

Note that the protocol transformation is usually applied to non-negative (level) variables. If you observe the differences between two time series (e.g. net export), it is not even possible to create the log. You need to either look for original data in layers or take the form of a common trend that has been subtracted.

[ Completion after processing ] If you continue one statistical criterion want to perform the protocol transformation, a simple solution is a test for heteroscedasticity. If the variance increases, I would recommend the Goldfeld-Quandt test or something similar. In R it is in and is denoted by function. If you don't have a regression model, this is your dependent variable.

Draw a graph of the data against time. If it looks like the variance is increasing with the level of the series, run logs. Otherwise, model the original data.

You shall recognize them by their fruit

The assumption (to be tested) is that the errors from the model have a constant variance. Note that this does not mean the flaws of an assumed model. When using simple graphical analysis, you are essentially assuming a linear time model.

So if you have an inadequate model, as suggested by a random plot of the data against time, you may be falsely inferring the need for a performance transformation. Box and Jenkins did this with their airline data example. They did not account for 3 unusual values ​​in the latest data and incorrectly concluded that there was a greater variation in residuals at the highest level of the series.