[SGM GARCH Volatility]

I'm excited to share with you a Pine Script™ that I developed to analyze GARCH (Generalized Autoregressive Conditional Heteroskedasticity) volatility. This script allows you to calculate and plot GARCH volatility on TradingView. Let's see together how it works!

Introduction

Volatility is a key concept in finance that measures the variation in prices of a financial asset. The GARCH model is a statistical method that predicts future volatility based on past volatilities and prediction residuals (errors).

Indicator settings
We define several parameters for our indicator:

length = input.int(20, title="Length")
p = input.int(1, title="Lag order (p)")
q = input.int(1, title="Degree of moving average (q)")
cluster_value = input(0.2,title="cluster value")

length: The period used for the calculations, default 20.
p: The order of the delay for the GARCH model.
q: The degree of the moving average for the GARCH model.
cluster_value: A threshold value used to color the graph.

Calculation of logarithmic returns
We calculate logarithmic returns to capture price changes:

logReturns = math.log(close) - math.log(close[1])

Initializing arrays
We initialize arrays to store residuals and volatilities:

var float[] residuals = array.new_float(length, 0)
var float[] volatilities = array.new_float(length, 0)

We add the new logarithmic returns to the tables and keep their size constant:

array.unshift(residuals, logReturns)
if (array.size(residuals) > length)
 array.pop(residuals)

We then calculate the mean and variance of the residuals:

meanResidual = array.avg(residuals)
varianceResidual = array.stdev(residuals, meanResidual)
volatility = math.sqrt(varianceResidual)

We update the volatility table with the new value:

array.unshift(volatilities, volatility)
if (array.size(volatilities) > length)
 array.pop(volatilities)

GARCH volatility is calculated from accumulated data:

var float garchVolatility = na

if (array.size(volatilities) >= length and array.size(residuals) >= length)
 alpha = 0.1 // Alpha coefficient
 beta = 0.85 // Beta coefficient
 omega = 0.01 // Omega constant

 sumVolatility = 0.0
 for i = 0 to p-1
 sumVolatility := sumVolatility + beta * math.pow(array.get(volatilities, i), 2)

 sumResiduals = 0.0
 for j = 0 to q-1
 sumResiduals := sumResiduals + alpha * math.pow(array.get(residuals, j), 2)

 garchVolatility := math.sqrt(omega + sumVolatility + sumResiduals)

Plot GARCH volatility

We finally plot the GARCH volatility on the chart and add horizontal lines for easier visual analysis:

plt = plot(garchVolatility, title="GARCH Volatility", color=color.rgb(33, 149, 243, 100))

h1 = hline(0.1)
h2 = plot(cluster_value)
h3 = hline(0.3)

colorGarch = garchVolatility > cluster_value ? color.red: color.green

fill(plt, h2, color = colorGarch)

colorGarch: Determines the fill color based on the comparison between garchVolatility and cluster_value.


Using the script in your trading

Incorporating this Pine Script™ into your trading strategy can provide you with a better understanding of market volatility and help you make more informed decisions. Here are some ways to use this script:

Identification of periods of high volatility:

When the GARCH volatility is greater than the cluster value (cluster_value), it indicates a period of high volatility. Traders can use this information to avoid taking large positions or to adjust their risk management strategies.

Anticipation of price movements:

An increase in volatility can often precede significant price movements. By monitoring GARCH volatility spikes, traders can prepare for potential market reversals or accelerations.

Optimization of entry and exit points:

By using GARCH volatility, traders can better identify favorable times to enter or exit a position. For example, entering a position when volatility begins to decrease after a peak can be an effective strategy.

Adjustment of stops and objectives:

Since volatility is an indicator of the magnitude of price fluctuations, traders can adjust their stop-loss and take-profit orders accordingly. Periods of high volatility may require wider stops to avoid being exited from a position prematurely.


That's it for the detailed explanation of this Pine Script™ script. Don’t hesitate to use it, adapt it to your needs and share your feedback! Happy analysis and trading everyone!