This document refers to Macrobond 1.13 and later.

## Overview

The Rate of change analysis calculates the change of a series of over a period of values expressed as a percentage or as the change of the value. The change can be expression in an annualized form.

The calculation is made over a period length, or horizon, called h below.

## Settings

#### Method

###### Change over period value

Calculate the change in value over the time period.

$y\left(t\right)=z\left(t\right)-z\left(t-h\right)$
###### Change over period %

Calculate the percentage change over the time period.

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

Calculate the sum of the values over the time period and then scale the result to a yearly level.

$y\left(t\right)=\frac{c}{h}\sum _{i=1}^{h}\text{z}\left(t+1-i\right)$

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

###### Annual rate %

Calculate the percentage change over the time period and then annualize.

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

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

###### Logarithmic change over period %

Calculate the logarithmic percentage change over the time period.

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

#### Unit

The unit of the Length property.

#### Length

The period length, or horizon, measured in the units specified by the Units property.

#### Mode

The Mode determines how the period length is measured. If Fixed length is selected, the horizon will be a constant number of observations that is determined only from the frequency. Select this option is it is important to use a constant period length and that each value of the past is used only once.

When the mode is Calendar date is selected, the period length is determined for each observation based on the calendar date so that an observation with a corresponding date in the past is selected. Select this option when it is important to compare values of corresponding dates even if it means that some values in the past might be used twice and some not used at all. A common case when you want to use this mode is when you have converted the series from a lower frequency.

#### Force

The application attempts detect of the series is already expressed as a rate of change and will give you an error if you attempt to calculate it twice. You can bypass this check by selecting the Force option.