[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 = naif (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.greenfill(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!