A multi-harmonic (or multi-tone) trigonometric model of a price series x[i], i=1..n, is given by:

x[i] = m + Sum( a[h]*Cos(w[h]*i) + b[h]*Sin(w[h]*i), h=1..H )

where:

This digital filter shows a trend by changing the color.

The Hodrick-Prescott filter is used in macroeconomics, especially in real business cycle theory to separate the cyclical component of a time series from raw data. It has a zero lag. There is a common disadvantage of such zero lag filters - the recent values are recalculated.

I have tried to apply this filter for the different purposes: for price channels, to use it as the trend changes indicator, etc, but I have found that it hasn't any significant advantages compared with EMA, LWMA or AMA.

The Heiken-Ashi indicator is looks like the candlestick chart, but it has some difference. Instead of the use of the standard OHLC values for candles, it uses another formulas:

Close = (Open+High+Low+Close)/4
Open = [Open (previous bar) + Close (previous bar)]/2
High = Max (High,Open,Close)
Low = Min (Low,Open, Close)

in other words, the indicator shows the "synthetic" candlesticks, which are different from the standard.

The indicator plots Pivot levels for all the available history. It doesn't uses any objects.

There are 5 variants of Pivot levels is supported.  There are 3 calculation periods: daily, weekly, monthly. For the daily pivot levels it's possible to specify the GMT time shift.

The formulas, used for the calculation, are:

PIVOT_CLASSIC

A multi-harmonic (or multi-tone) trigonometric model of a price series x[i], i=1..n, is given by:

x[i] = m + Sum( a[h]*Cos(w[h]*i) + b[h]*Sin(w[h]*i), h=1..H )

where:

x[i] - past price at i-th bar, total n past prices

m - bias

a[h] and b[h] - scaling coefficients of harmonics

w[h] - frequency of a harmonic

h - harmonic number

H - total number of fitted harmonics

Candlestick Momentum Index (CMI, based on Candlestick Momentum Indicator) is described by William Blau in the book "Momentum, Direction, and Divergence: Applying the Latest Momentum Indicators for Technical Analysis".

WilliamBlau.mqh must be placed in terminal_data_folder\MQL5\Include\

Blau_CMI.mq5 must be placed in terminal_data_folder\MQL5\Indicators\