# Analytical performance indicators

Calculation of derived analytical indicators of time series

**Time series** is a series arranged in chronological order of indicators characterizing the change of any quantity over time. Time series includes two main elements: time value - t and the corresponding value indicators - Y.

Time series is divided into **state series** и **interval series**.

.

State series indicate the state of the value at a certain moment. Interval series indicate the state of the value for certain time intervals.

Here is the example. On January 1st, bread cost 13 rubles, on February 1st - 14 rubles, on March 1st - 15 rubles - that's the state series. If in January we bought 10 loaves of bread, in February - 12 loaves, in March - 14 loaves - that's interval series. Note that we can add the parameters and come to something meaningful, for example, bread consumption for three months.

With series of indicators, it is possible to calculate various analytical derivative indicators. Derivative indicators can be calculated in two basic ways - **chain** and **base**.

With the chain method, each subsequent indicator compared with the previous, with the base method - with the same indicator, taken as a comparison base. This is usually the first indicator of the series.

Let's discuss some of the analytical derivative indicators:

**Analytical derivative indicators**

**1.** **Absolute increment**

The difference between the values of two parameters of time series.

Absolute basic increment - the difference between the current value and the value used for the permanent base of comparison

Absolute chain increment - the difference between the current and previous values.

**2.** **Growth rate**

Two levels of the series ratio (can be expressed in percentage).

Base growth rate - current value and the value received for the permanent base of comparison ratio.

Chain growth rate - current and previous value ratio.

**3.** **Increment rate**

Absolute increment to compared indicator ratio

Base increment rate - absolute base increment to the value received for the permanent base of comparison ratio.

Chain increment rate - absolute chain increment to the previous value ratio.

**4.** **Acceleration**

Absolute acceleration - the difference between absolute increment for the given period and the absolute increment of the equal duration. Calculated with the chain method only.

Relative acceleration - chain increment rate for the current period to the chain increment rate for the previous period ratio.

**5.** **Build-up rate**

The ratio of the absolute chain increment level and the level is taken as a permanent base of comparison.

**6.** **Absolute value of 1% increment**

The ratio of absolute increment to the rate of increment is expressed as a percentage.

The formula is simplified to:

For the generalized dynamics characteristics of the given series **average performance indicators** are used.

**average performance indicators**

**1.** *Average level*

Characterizes the typical value of indicators

In the interval time series, it's calculated as the simple arithmetic average.

In the state series with **equal** time interval between the indications, it's calculated as a chronological average.

**2.** **Absolute average increment**

Generalizing indicator of the rate of change of absolute values of the time series.

**3.** **Average growth rate**

Generalizing characteristic of the time series growth rate.

( i - 1 root)

**4.** **Average increment rate**

The same as the growth and increment rates ratio.

All derivatives and average indicators are given here are calculated in the calculator below, as the user inputs values in the table.

## Comments