Cycle Indicators

Cycle indicators use the Hilbert Transform to identify dominant cycles in price data. These indicators are based on the work of John Ehlers and are useful for identifying cyclical patterns and trend vs. cycle modes.

HT_DCPERIOD - Dominant Cycle Period

The Dominant Cycle Period identifies the length (in bars) of the dominant cycle in the price data using the Hilbert Transform.

Formula

The Hilbert Transform is applied to price data to extract the dominant cycle period. The algorithm:

Applies Hilbert Transform to create InPhase and Quadrature components
Calculates the period from the phase relationship
Smooths the period estimate

Characteristics

Property	Value
Input	Close price
Output	Single value (period in bars)
Lookback	63
Memory	O(1)

API Usage

Python

from techkit import HT_DCPERIOD

dcperiod = HT_DCPERIOD()
result = dcperiod.update(close_price)
if result.valid:
    print(f"Dominant Cycle Period: {result.value:.1f} bars")

Node.js

const tk = require('techkit');

const dcperiod = tk.htDcperiod();
const result = dcperiod.update(close);

C++

#include <techkit/techkit.hpp>

techkit::HT_DCPERIOD dcperiod;
auto result = dcperiod.update(close);

C

tk_indicator dcperiod = tk_ht_dcperiod_new();
tk_result r = tk_update(dcperiod, close);
tk_free(dcperiod);

Trading Usage

Cycle Length: Typical values range from 10-50 bars
Adaptive Indicators: Use period to set adaptive moving average periods
Entry Timing: Enter trades at cycle extremes
Trend vs. Cycle: Combine with HT_TRENDMODE to determine market state

HT_DCPHASE - Dominant Cycle Phase

The Dominant Cycle Phase returns the current phase of the dominant cycle in degrees (0-360).

Formula

The phase is calculated from the InPhase and Quadrature components:

\[\text{phase} = \arctan2(\text{Quadrature}, \text{InPhase}) \times \frac{180}{\pi}\]

Phase is normalized to 0-360 degrees.

Characteristics

Property	Value
Input	Close price
Output	Single value (phase in degrees, 0-360)
Lookback	63
Memory	O(1)

API Usage

from techkit import HT_DCPHASE

dcphase = HT_DCPHASE()
result = dcphase.update(close_price)
if result.valid:
    phase = result.value
    if phase < 90:
        print("Early cycle")
    elif phase < 180:
        print("Mid cycle up")
    elif phase < 270:
        print("Late cycle")
    else:
        print("Mid cycle down")

Trading Usage

Cycle Position:
- 0-90°: Early cycle (potential buy)
- 90-180°: Mid cycle up
- 180-270°: Late cycle (potential sell)
- 270-360°: Mid cycle down
Entry/Exit Timing: Use phase extremes for entries
Cycle Confirmation: Combine with HT_SINE for cycle confirmation

HT_PHASOR - Phasor Components

The HT_PHASOR returns the InPhase and Quadrature components of the Hilbert Transform, which represent the cycle in complex number form.

Formula

The Hilbert Transform extracts:

InPhase (I1): Real component of the cycle
Quadrature (Q1): Imaginary component of the cycle

These components are 90 degrees out of phase.

Characteristics

Property	Value
Input	Close price
Output	Two values (inphase, quadrature)
Lookback	63
Memory	O(1)

API Usage

from techkit import HT_PHASOR

phasor = HT_PHASOR()
result = phasor.update(close_price)
if result.valid:
    print(f"InPhase: {result.inphase:.4f}")
    print(f"Quadrature: {result.quadrature:.4f}")
    
    # Calculate amplitude
    amplitude = (result.inphase**2 + result.quadrature**2)**0.5
    print(f"Amplitude: {amplitude:.4f}")

Trading Usage

Cycle Amplitude: Calculate from I1² + Q1²
Cycle Phase: Calculate from atan2(Q1, I1)
Advanced Analysis: Use for custom cycle indicators
Filtering: Use to filter noise from price data

HT_SINE - SineWave

The HT_SINE returns the Sine and LeadSine of the dominant cycle phase. LeadSine is 45 degrees ahead of Sine.

Formula

\[\text{Sine} = \sin(\text{phase})\]

\[\text{LeadSine} = \sin(\text{phase} + 45°)\]

where phase is calculated from HT_PHASOR components.

Characteristics

Property	Value
Input	Close price
Output	Two values (sine, leadsine)
Lookback	63
Memory	O(1)

API Usage

from techkit import HT_SINE

sine = HT_SINE()
result = sine.update(close_price)
if result.valid:
    print(f"Sine: {result.sine:.4f}")
    print(f"LeadSine: {result.leadsine:.4f}")
    
    # Buy signal: Sine crosses above LeadSine
    if result.sine > result.leadsine:
        print("Bullish signal")
    # Sell signal: Sine crosses below LeadSine
    elif result.sine < result.leadsine:
        print("Bearish signal")

Trading Usage

Buy Signal: Sine crosses above LeadSine
Sell Signal: Sine crosses below LeadSine
Cycle Extremes:
- Sine near +1: Cycle peak (potential sell)
- Sine near -1: Cycle trough (potential buy)
Trend Following: Use in trending markets (confirmed by HT_TRENDMODE)

Common Strategy

# Combined cycle strategy
sine = HT_SINE()
trendmode = HT_TRENDMODE()

for price in prices:
    sine_result = sine.update(price)
    trend_result = trendmode.update(price)
    
    if sine_result.valid and trend_result.valid:
        # Only trade in cycle mode (not trending)
        if trend_result.value == 0:  # Cycle mode
            if sine_result.sine > sine_result.leadsine:
                # Buy signal
                pass
            elif sine_result.sine < sine_result.leadsine:
                # Sell signal
                pass

HT_TRENDLINE - Instantaneous Trendline

The HT_TRENDLINE returns the instantaneous trendline based on the dominant cycle. It’s smoother than a simple moving average and adapts to the cycle.

Formula

The trendline is calculated from the InPhase component, filtered to remove cycle components and leave only the trend.

Characteristics

Property	Value
Input	Close price
Output	Single value (trendline price)
Lookback	63
Memory	O(1)

API Usage

from techkit import HT_TRENDLINE

trendline = HT_TRENDLINE()
result = trendline.update(close_price)
if result.valid:
    print(f"Trendline: {result.value:.2f}")
    
    # Price above trendline = uptrend
    if close_price > result.value:
        print("Uptrend")
    else:
        print("Downtrend")

Trading Usage

Trend Identification: Price above trendline = uptrend
Support/Resistance: Trendline acts as dynamic S/R
Entry Signals: Buy when price crosses above trendline
Comparison: Smoother than EMA, adapts to cycles

HT_TRENDMODE - Trend vs. Cycle Mode

The HT_TRENDMODE determines whether the market is in trending mode (1) or cycling mode (0).

Formula

The indicator compares the strength of the trend component to the cycle component. If trend dominates, returns 1; if cycle dominates, returns 0.

Characteristics

Property	Value
Input	Close price
Output	Single value (1 = trending, 0 = cycling)
Lookback	63
Memory	O(1)

API Usage

from techkit import HT_TRENDMODE

trendmode = HT_TRENDMODE()
result = trendmode.update(close_price)
if result.valid:
    if result.value == 1:
        print("Market is trending - use trend-following indicators")
    else:
        print("Market is cycling - use cycle indicators")

Trading Usage

Indicator Selection:
- Trending (1): Use trend-following indicators (MA, ADX)
- Cycling (0): Use cycle indicators (HT_SINE, oscillators)
Strategy Adaptation: Switch strategies based on mode
Filter: Filter cycle signals when in trending mode

Combined Strategy Example

from techkit import HT_TRENDMODE, HT_SINE, HT_TRENDLINE, ADX

trendmode = HT_TRENDMODE()
sine = HT_SINE()
trendline = HT_TRENDLINE()
adx = ADX(period=14)

for bar in bars:
    mode = trendmode.update(bar.close)
    sine_result = sine.update(bar.close)
    trend_result = trendline.update(bar.close)
    adx_result = adx.update_ohlcv(bar)
    
    if all results valid:
        if mode.value == 1:  # Trending
            # Use trend-following logic
            if bar.close > trend_result.value and adx_result.adx > 25:
                # Strong uptrend
                pass
        else:  # Cycling
            # Use cycle logic
            if sine_result.sine > sine_result.leadsine:
                # Cycle buy signal
                pass

Hilbert Transform Overview

The Hilbert Transform is a mathematical technique that:

Separates trend from cycle components
Identifies the dominant cycle period
Calculates cycle phase and amplitude
Determines market mode (trending vs. cycling)

Advantages

Adaptive: Automatically adapts to changing cycle lengths
No Lag: Instantaneous calculation (no look-ahead bias)
Mode Detection: Identifies when to use trend vs. cycle strategies

Limitations

Requires Warmup: Needs 63 bars before valid output
Noise Sensitivity: Can be affected by market noise
Complex: Requires understanding of cycle analysis

Cycle Indicators

HT_DCPERIOD - Dominant Cycle Period

Formula

Characteristics

API Usage

Trading Usage

HT_DCPHASE - Dominant Cycle Phase

Formula

Characteristics

API Usage

Trading Usage

HT_PHASOR - Phasor Components

Formula

Characteristics

API Usage

Trading Usage

HT_SINE - SineWave

Formula

Characteristics

API Usage

Trading Usage

Common Strategy

HT_TRENDLINE - Instantaneous Trendline

Formula

Characteristics

API Usage

Trading Usage

HT_TRENDMODE - Trend vs. Cycle Mode

Formula

Characteristics

API Usage

Trading Usage

Combined Strategy Example

Hilbert Transform Overview

Advantages

Limitations

Related Indicators

Further Reading