Machine learning in trading: theory, models, practice and algo-trading - page 3717
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I'm going to formalise this topic, and at the same time share a useful link https://link.springer.com/article/10.1007/s10959-022-01225-6. If you are interested, google the title and you will find it :-)
up
I can't get to practice in the near future, so a small portion of theory for now.
I still can not get to practice, so another portion of thoughts about probabilistic MoM)
Another possible use of WMO is to divide random fluctuations into stationary and non-stationary components. But it is still not very clear how to realise it in practice for trading to make any sense.
Another possible use of WMO is to divide random fluctuations into stationary and non-stationary components. However, it is still not very clear how to implement it in practice for trading to make any sense.
I could be wrong, but isn't heteroskedasticity autoregression about the same thing?
GARCH? It is a stationary model (with appropriate conditions on the coefficients). Only the conditional variance changes there, and the unconditional variance remains constant.
In fact, it is an attempt to drive the observed non-stationarity (in the sense of volatility fluctuations) into the framework of a stationary model.
GARCH?
Answer deeoseek
Is the GARCH model applicable for time series (non-stationary) like currency or stock prices
Great question. You have touched on a key topic in modern econometrics and financial market analysis.
Short answer: Yes, the GARCH model is extremely well applicable and widely used for volatility analysis of non-stationary series such as stock and currency quotes. However, there is a very important nuance: GARCH is not applied to the prices themselves, but to thestationary series of their returns.
Let's break it down in detail.
1. The problem of non-stationarity of price series
A series of quotes (for example, S(t) is the price of Apple stock at time t ) is usuallynon-stationary. It manifests itself in:
Trend: A general directional movement (up or down).
Varying variance: Periods of calm alternate with periods of high volatility (volatility clustering).
ARIMA or GARCH type models cannot deal directly with such series as they requirestationarity.
2. Solution: Switching to returns
To solve the non-stationarity problem, we convert prices intologarithmicreturns ( log returns):
r(t) = ln(S(t) / S(t-1)) * 100%
or simple percentage returns.
Why it works.
A series of returns r(t) is usually stationary:
Constant mean: On average, the returns fluctuate around zero (or some small constant).
Autocorrelation: Often absent or very weak (the series is close to "white noise").
Heteroskedasticity: The variance (volatility) of returns istime-varying - the very volatility clusters that the GARCH model is designed to explain.
Thus, we are not modelling prices, but the process of price change.
3. How exactly is GARCH applied?
The GARCH model is built for theerrors (residuals) ofa model describing the mean of returns.
Typical application algorithm:
Calculate returns from a price series.
Check the stationarity of the series of returns (Dickey-Fuller test, KPSS). Typically, the returns are stationary.
Determine the model for the mean. Often it is simply a constant ( r(t) = μ + ε(t) ), or a simple ARMA model if the returns show signs of autocorrelation.
Analyse the residuals ( ε(t) ) of the model for the mean:
Check forautocorrelation ( Lewng-Box test). There should be none.
Check forvolatility clustering effect ( e.g., look at the residuals squares plot or apply the ARCH-LM test). If this effect is present, it is time to apply GARCH.
Select a GARCH model for the variance of the residuals. The most popular one is GARCH(1,1):
σ²(t) = ω + α * ε²(t-1) + β * σ²(t-1)
σ²(t) is an estimate of the volatility at time t .
ε²(t-1) is yesterday's "news" (shock). The parameter α indicates how much yesterday's shocks affect today's volatility.
σ²(t-1) - yesterday's volatility. The parameter β shows the "inertia" of volatility.
Check the model adequacy: the residuals of the full model (ARMA + GARCH) should no longer have autocorrelation and ARCH effects.
4. Practical usefulness of GARCH for trading and analysis
Volatility forecasting: This is the main application. GARCH allows for accurate short-term volatility forecasts, which is critical for:
Risk management (Value at Risk - VaR calculation).
Option pricing (volatility is a key parameter in models like Black-Scholes).
Optimisation of trading strategies.
Detection of risk periods: The model clearly shows when the market goes into high uncertainty mode.
Dependency modelling: Multivariate models (e.g. DCC-GARCH) allow us to analyse how the correlation between different assets (e.g. dollar and oil) changes over time.
5. Developments and alternatives to classical GARCH
Classical GARCH(1,1) is often sufficient, but there are modifications for more complex cases:
EGARCH: Takes into accountasymmetric effects ( "markets fear falls more than they enjoy rises" - bad news increases volatility more than good news).
TGARCH: Similarly, models the asymmetric effect.
GARCH-M: Incorporates volatility as a factor directly into the equation for average returns (investors demand a risk premium).
Multivariate GARCH: For analysing the covariance and correlation of multiple assets.
Bottom line
The GARCH model is not just applicable to non-stationary series of quotes - it is one of the main tools for their analysis. It is important to remember that the object of modelling is not the prices themselves, but the stationary series of returns calculated from them. GARCH copes brilliantly with the task of describing and forecasting their main feature - volatility clustering.
Is GARCH applicable for modelling non-stationary processes?
Answer Perplexity:
The GARCH (Generalised Autoregressive Conditional Heteroskedasticity) model in its classical formulation applies to stationary time processes, in particular stationary series of conditional heteroskedasticity. For a GARCH process to be covariance stationary, an inequality must be satisfied where the sum of the autoregressive and moving average coefficients in the model is less than 1: ∑ α i + ∑ β i < 1 ∑ α i + ∑ β i < 1. In this case, the unconditional variance of the process remains constant in time.
If the sum of the coefficients is equal to one, the so-called integrated GARCH model (IGARCH) arises, for which the unconditional variance is theoretically infinite, which corresponds to a non-stationary process.
Thus, standard GARCH models are designed for stationary series, while to deal with non-stationary processes, data preprocessing (e.g., differentiation, transformation) is often applied, or special extensions and generalisations of the GARCH model are used (e.g., IGARCH, other integrated versions or structural change models).
Bottom line: GARCH is used for modelling stationary processes. For non-stationary ones, either pre-processing or specialised extensions are used, e.g. IGARCH, which models integrated non-stationarity in the variation of a series.
An explanation after AI, as the questioners understand it, would be nice. To me it seems like some kind of assumption that there are some averaged or otherwise derived derivatives of the data in the sb and they are almost stationary. That's a bit of a stretch.
An explanation after AI, as the questioners understand it, would be nice. To me it seems like some kind of assumption that there are some averaged or otherwise derived derivatives of the data in the sb and they are almost stationary. That doesn't sound right to me.
I have seen quite a few publications on the success of garches that, for some reason, have not found their way onto this site.
There are over a hundred varieties of garches.
The meaning of all of them is the same: explicit modelling of different aspects of non-stationarity in the increment of financial time series, i.e. this is the fundamental difference from MO. So to speak, explicitly trying to solve the problem of non-stationarity in the increments, both in the form of eigenvalue increments via ARIFMA, as well as modelling the non-stationarities that are revealed in the distributions of the increments.
Saw an article (too lazy to look) on choosing a specific gARCH model using ALL stocks in the S&p500 as an example - the best IGARCH model.
Seen quite a few publications on the success of garcia applications that, for some reason, have not found their way onto this site.
There are more than a hundred varieties of garça.
The meaning of all of them is the same: explicit modelling of different aspects of non-stationarity in the increment of financial time series, i.e. this is the fundamental difference from MO. So to speak, we are explicitly trying to solve the problem of non-stationarity of increments, both in the form of eigenvalue increments via ARIFMA, as well as modelling non-stationarities that are detected in the distributions of increments.
Saw an article (too lazy to look) on choosing a specific gARCH model using ALL stocks in the S&p500 as an example - the best IGARCH model.