# Overview

The Rate of change analysis is used to calculate the change in value or in percentage over periods of time. These changes can also be annualized. The analysis will help you visualize and compare how series are changing over time and is commonly used to calculate differences before applying regressions or correlations

# Settings

## Method

### Change over period value

Calculates the difference in value over the time. This can also be called “momentum”.

$y\left(t\right)=z\left(t\right)-z\left(t-h\right)$

### Change over period %

Calculates the percentage change over the time.

$y\left(t\right)=100\frac{\text{z}\left(t\right)-z\left(t-h\right)}{\left|z\left(t-h\right)\right|}$

### Annual rate value

Calculates the sum of the values over the time and then scales the result to a yearly level.

$y\left(t\right)=100\cdot \text{ln}\frac{z\left(t+h\right)}{z\left(t\right)}$

where c is the typical number of observations for one year.

### Annual rate %

Calculates the percentage change over the time and then annualizes.

$y\left(t\right)=\text{100}·\left({\left(\frac{\text{z}\left(t\right)}{\text{z}\left(t-h\right)}\right)}^{\frac{c}{h}}-1\right)$

where c is the typical number of observations for one year.

### Logarithmic change over period %

Calculates the logarithmic percentage change over the time.

$y\left(t\right)=100\cdot \text{ln}\frac{z\left(t\right)}{z\left(t-h\right)}$

# Example

Change over period value

In this example, we calculated by how many persons the jobless claims have increased or decreased compared to a year ago. We did this by selecting change over period value for a length of 1 year.

Annual rate (value or percentage)

Here, we compared two different growth rates of the German GDP. The line displays year on year growth rates and the columns represent annualized quarterly growth rates.