arXiv subjects

Luke De Clerk

Publications and source records attributed to Luke De Clerk.

3 recordsLinked to original sources

arXiv2022

A machine learning search for optimal GARCH parameters

Here, we use Machine Learning (ML) algorithms to update and improve the efficiencies of fitting GARCH model parameters to empirical data. We employ an Artificial Neural Network (ANN) to predict the parameters of these models. We present a fitting algorithm for GARCH-normal(1,1) models to predict one of the model's parameters, $α_1$ and then use the analytical expressions for the fourth order standardised moment, $Γ_4$ and the unconditional second order moment, $σ^2$ to fit the other two parameters; $β_1$ and $α_0$, respectively. The speed of fitting of the parameters and quick implementation of this approach allows for real time tracking of GARCH parameters. We further show that different inputs to the ANN namely, higher order standardised moments and the autocovariance of time series can be used for fitting model parameters using the ANN, but not always with the same level of accuracy.

econ.EM↗

arXiv2021

An investigation of higher order moments of empirical financial data and the implications to risk

Here, we analyse the behaviour of the higher order standardised moments of financial time series when we truncate a large data set into smaller and smaller subsets, referred to below as time windows. We look at the effect of the economic environment on the behaviour of higher order moments in these time windows. We observe two different scaling relations of higher order moments when the data sub sets' length decreases; one for longer time windows and another for the shorter time windows. These scaling relations drastically change when the time window encompasses a financial crisis. We also observe a qualitative change of higher order standardised moments compared to the gaussian values in response to a shrinking time window. We extend this analysis to incorporate the effects these scaling relations have upon risk. We decompose the return series within these time windows and carry out a Value-at-Risk calculation. In doing so, we observe the manifestation of the scaling relations through the change in the Value-at-Risk level. Moreover, we model the observed scaling laws by analysing the hierarchy of rare events on higher order moments.

econ.EM↗

arXiv2021

Non-stationary GARCH modelling for fitting higher order moments of financial series within moving time windows

Here, we have analysed a GARCH(1,1) model with the aim to fit higher order moments for different companies' stock prices. When we assume a gaussian conditional distribution, we fail to capture any empirical data when fitting the first three even moments of financial time series. We show instead that a double gaussian conditional probability distribution better captures the higher order moments of the data. To demonstrate this point, we construct regions (phase diagrams), in the fourth and sixth order standardised moment space, where a GARCH(1,1) model can be used to fit these moments and compare them with the corresponding moments from empirical data for different sectors of the economy. We found that the ability of the GARCH model with a double gaussian conditional distribution to fit higher order moments is dictated by the time window our data spans. We can only fit data collected within specific time window lengths and only with certain parameters of the conditional double gaussian distribution. In order to incorporate the non-stationarity of financial series, we assume that the parameters of the GARCH model have time dependence.

econ.EM↗