Calculating Data Loss for Time-Series Data

Data transformations are commonly used across statistics to transform data distributions into distributions with properties that make them more user friendly. In time-series, stationarity is one of the most common assumptions that is violated because the mean and variance are time dependent. Dick and Fuller (1979) have proven that differencing data can make data stationary. It is also common to try to make data stationary through taking the natural log or using the growth rates of the data instead of the original non-stationary data. There is concern that transforming the data through differencing loses valuable information. This paper purposes a method for measuring data lost from these three types of transformations.