# Intrabar Efficiency Ratio

█  OVERVIEW

This indicator displays a directional variant of Perry​ Kaufman's​ Efficiency​ Ratio​, designed to gauge the "efficiency" of intrabar price movement by comparing the sum of movements of the lower timeframe bars composing a chart bar with the respective bar's movement on an average basis.

█  CONCEPTS

Efficiency Ratio (ER)

Efficiency Ratio​ was first introduced by Perry Kaufman in his 1995 book, titled "Smarter Trading". It is the ratio of absolute price change to the sum of absolute changes on each bar over a period. This tells us how strong the period's trend is relative to the underlying noise. Simply put, it's a measure of price movement efficiency. This ratio is the modulator utilized in Kaufman's​ Adaptive​ Moving​ Average​ (KAMA​), which is essentially an Exponential​ Moving​ Average​ (EMA​) that adapts its responsiveness to movement efficiency.

ER's output is bounded between 0 and 1. A value of 0 indicates that the starting price equals the ending price for the period, which suggests that price movement was maximally inefficient. A value of 1 indicates that price had travelled no more than the distance between the starting price and the ending price for the period, which suggests that price movement was maximally efficient. A value between 0 and 1 indicates that price had travelled a distance greater than the distance between the starting price and the ending price for the period. In other words, some degree of noise was present which resulted in reduced efficiency over the period.

As an example, let's say that the price of an asset had moved from \$15 to \$14 by the end of a period, but the sum of absolute changes for each bar of data was \$4. ER would be calculated like so:
` ER = abs(14 - 15)/4 = 0.25`
This suggests that the trend was only 25% efficient over the period, as the total distanced travelled by price was four times what was required to achieve the change over the period.

Intrabars

Intrabars are chart bars at a lower timeframe than the chart's. Each 1H chart bar of a 24x7 market will, for example, usually contain 60 intrabars at the ​LTF of 1min, provided there was market activity during each minute of the hour. Mining information from intrabars can be useful in that it offers traders visibility on the activity inside a chart bar.

Lower timeframes (LTFs)

A lower timeframe is a timeframe that is smaller than the chart's timeframe. This script determines which ​LTF to use by examining the chart's timeframe. The ​LTF determines how many intrabars are examined for each chart bar; the lower the timeframe, the more intrabars are analyzed, but fewer chart bars can display indicator information because there is a limit to the total number of intrabars that can be analyzed.

Intrabar precision

The precision of calculations increases with the number of intrabars analyzed for each chart bar. As there is a 100K limit to the number of intrabars that can be analyzed by a script, a trade-off occurs between the number of intrabars analyzed per chart bar and the chart bars for which calculations are possible.

Intrabar Efficiency Ratio (IER)

Intrabar Efficiency Ratio applies the concept of ER on an intrabar level. Rather than comparing the overall change to the sum of bar changes for the current chart's timeframe over a period, IER compares single bar changes for the current chart's timeframe to the sum of absolute intrabar changes, then applies smoothing to the result. This gives an indication of how efficient changes are on the current chart's timeframe for each bar of data relative to LTF​ bar changes on an average basis. Unlike the standard ER calculation, we've opted to preserve directional information by not taking the absolute value of overall change, thus allowing it to be utilized as a momentum oscillator. However, by taking the absolute value of this oscillator, it could potentially serve as a replacement for ER in the design of adaptive moving averages.

Since this indicator preserves directional information, IER can be regarded as similar to the Chande​ Momentum​ Oscillator​ (CMO​), which was presented in 1994 by Tushar​ Chande​ in "The New Technical Trader". Both CMO​ and ER​ essentially measure the same relationship between trend and noise. CMO simply differs in scale, and considers the direction of overall changes.

█  FEATURES

Display

Three different display types are included within the script:
• Line: Displays the middle length MA of the IER as a line.
Color for this display can be customized via the "Line" portion of the "Visuals" section in the script settings.
• Candles: Displays the non-smooth IER and two moving averages of different lengths as candles.
The `open` and `close` of the candle are the longest and shortest length MAs of the IER respectively.
The `high` and `low` of the candle are the max and min of the IER, longest length MA of the IER, and shortest length MA of the IER respectively.
Colors for this display can be customized via the "Candles" portion of the "Visuals" section in the script settings.
• Circles: Displays three MAs of the IER as circles.
The color of each plot depends on the percent rank of the respective MA over the previous 100 bars.
Different colors are triggered when ranks are below 10%, between 10% and 50%, between 50% and 90%, and above 90%.
Colors for this display can be customized via the "Circles" portion of the "Visuals" section in the script settings.

With either display type, an optional information box can be displayed. This box shows the LTF​ that the script is using, the average number of lower timeframe bars per chart bar, and the number of chart bars that contain LTF​ data.

Specifying intrabar precision

Ten options are included in the script to control the number of intrabars used per chart bar for calculations. The greater the number of intrabars per chart bar, the fewer chart bars can be analyzed.

The first five options allow users to specify the approximate amount of chart bars to be covered:
• Least Precise (Most chart bars): Covers all chart bars by dividing the current timeframe by four.
This ensures the highest level of intrabar precision while achieving complete coverage for the dataset.
• Less Precise (Some chart bars) & More Precise (Less chart bars): These options calculate a stepped ​LTF in relation to the current chart's timeframe.
• Very precise (2min intrabars): Uses the second highest quantity of intrabars possible with the 2min ​LTF.
• Most precise (1min intrabars): Uses the maximum quantity of intrabars possible with the 1min ​LTF.

The stepped lower timeframe for "Less Precise" and "More Precise" options is calculated from the current chart's timeframe as follows:
```Chart Timeframe            Lower Timeframe

Less Precise     More Precise

< 1hr               1min            1min
< 1D                15min           1min
< 1W                ​2hr​             30min
> 1W                1D              60min```

The last five options allow users to specify an approximate fixed number of intrabars to analyze per chart bar. The available choices are 12, 24, 50, 100, and 250. The script will calculate the LTF​ which most closely approximates the specified number of intrabars per chart bar. Keep in mind that due to factors such as the length of a ticker's sessions and rounding of the LTF​, it is not always possible to produce the exact number specified. However, the script will do its best to get as close to the value as possible.

Specifying MA type

Seven MA types are included in the script for different averaging effects:
• Simple
• Exponential
• Wilder (RMA)
• Weighted
• Volume-Weighted
• Arnaud Legoux with `offset` and `sigma` set to 0.85 and 6 respectively.
• Hull

Weighting

This script includes the option to weight IER values based on the percent rank of absolute price changes on the current chart's timeframe over a specified period, which can be enabled by checking the "Weigh using relative close changes" option in the script settings. This places reduced emphasis on IER values from smaller changes, which may help to reduce noise in the output.

█  FOR Pine Script™ CODERS

• This script imports the recently published lower_ltf library for calculating intrabar statistics and the optimal lower timeframe in relation to the current chart's timeframe.
• This script uses the recently released request.security_lower_tf() Pine Script™ function discussed in this blog post.
It works differently from the usual request.security() in that it can only be used on LTFs, and it returns an array containing one value per intrabar.
This makes it much easier for programmers to access intrabar information.
• This script implements a new recommended best practice for tables which works faster and reduces memory consumption.
Using this new method, tables are declared only once with var, as usual. Then, on the first bar only, we use table.cell() to populate the table.
Finally, table.set_*() functions are used to update attributes of table cells on the last bar of the dataset.
This greatly reduces the resources required to render tables.

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