Luke De Clerk, Sergey Savel'ev
arXiv 23 Feb 2021 · Econometrics · 1 citations (OpenAlex)
arXiv:2102.11627 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | T. Bollerslev, “Generalised autoregressive conditional heteroskedast… (1986) Generalised autoregressive conditional heteroskedasticity | 0.874 | 6 | 2 | 100% |
| 2 | R. Mantegna and H. Stanley, An Introduction to Econophysics, C. U. P… (2000) vol | 0.737 | 3 | 2 | 100% |
| 3 | T. Bali and P. Theodossiou, “A conditional sgt-var approach with alt… (2006) A conditional sgt-var approach with alternative garch models | 0.644 | 2 | 2 | 100% |
| 4 | R. Engle, “Autoregressive conditional heteroscedasticity with estima… (1982) Autoregressive conditional heteroscedasticity with estimates of variance in the united kingdom inflation | 0.405 | 1 | 1 | 100% |
| 5 | F. Drost and B. Werker, “Closing the garch gap: Continuous time garc… (1996) Closing the garch gap: Continuous time garch modelling | 0.405 | 1 | 1 | 100% |
| 6 | T. Economist, “Crash course,” (2013) Crash course | 0.405 | 1 | 1 | 100% |
| 7 | R. Baille and T. Bollerslev, “Conditional forecast densities from dy… (1992) Conditional forecast densities from dynamical models with garch innovations | 0.405 | 1 | 1 | 100% |
| 8 | K. Wallis, “The two-piece normal, binormal, or double gaussian distr… (2014) The two-piece normal, binormal, or double gaussian distribution: Its origin and rediscoveries | 0.405 | 1 | 1 | 100% |
| 9 | Z. Ding, R. Engle, and C. Granger, “A long memory property of stock… (1993) A long memory property of stock market return and a new model | 0.405 | 1 | 1 | 100% |
| 10 | C. Conrad and B. Haag, “Inequality constraints in the fractionally i… (2006) Inequality constraints in the fractionally integrated garch models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 23 scored citations.