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on Econometric Time Series |
| By: | Francisco Blasques (Vrije Universiteit Amsterdam); Siem Jan Koopman (Vrije Universiteit Amsterdam); Gabriele Mingoli (Vrije Universiteit Amsterdam) |
| Abstract: | This paper proposes a novel time-series model with a non-stationary stochastic trend, locally explosive mixed causal non-causal dynamics and fat-tailed innovations. The model allows for a description of financial time-series that is consistent with financial theory, for a decomposition of the time-series in trend and bubble components, and for meaningful real-time forecasts during bubble episodes. We provide sufficient conditions for strong consistency and asymptotic normality of the maximum likelihood estimator. The model-based filter for extracting the trend and bubbles is shown to be invertible and the extracted components converge to the true trend and bubble paths. A Monte Carlo simulation study confirms the good finite sample properties. Finally, we consider an empirical study of Nickel monthly price series and global mean sea level data. We document the forecasting accuracy against competitive alternative methods and conclude that our model-based forecasts outperform all these alternatives. |
| Keywords: | observation-driven filter, non-stationary time-series, mixed causal non- causal models |
| JEL: | C22 C51 C53 |
| Date: | 2023–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230065&r=ets |
| By: | Mirko Armillotta (Vrije Universiteit Amsterdam); Paolo Gorgi (Vrije Universiteit Amsterdam) |
| Abstract: | We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series. |
| Keywords: | Double-bounded time series, integer-valued autoregressions, quasi-maximum likelihood. |
| JEL: | C32 C52 C58 |
| Date: | 2023–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230054&r=ets |
| By: | Jakub Micha\'nk\'ow; {\L}ukasz Kwiatkowski; Janusz Morajda |
| Abstract: | In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily logarithmic returns on the S&P 500 index as well as gold price Bitcoin prices, with the three assets representing quite distinct volatility dynamics. As the main volatility estimator, also underlying the target function of our hybrid models, we use the price-range-based Garman-Klass estimator, modified to incorporate the opening and closing prices. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets' risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. In general, it can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior VaR and ES forecasts. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.01063&r=ets |
| By: | Jakub Michańków (Cracow University of Economics, Department of Informatics; University of Warsaw, Faculty of Economic Sciences, Quantitative Finance Research Group, Department of Quantitative Finance); Paweł Sakowski (University of Warsaw, Faculty of Economic Sciences, Quantitative Finance Research Group, Department of Quantitative Finance); Robert Ślepaczuk (University of Warsaw, Faculty of Economic Sciences, Quantitative Finance Research Group, Department of Quantitative Finance) |
| Abstract: | This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the level of ensemble algorithmic investment strategies (AIS) built based on the prices of these assets. We employ four types of diverse theoretical models (LSTM - Long Short-Term Memory, ARIMA-GARCH - Autoregressive Integrated Moving Average - Generalized Autoregressive Conditional Heteroskedasticity, momentum, and contrarian) to generate price forecasts, which are then used to produce investment signals in single and complex AIS. In such a way, we are able to verify the diversification potential of different types of investment strategies consisting of various assets (energy commodities, precious metals, cryptocurrencies, or soft commodities) in hedging ensemble AIS built for equity indices (S&P 500 index). Empirical data used in this study cover the period between 2004 and 2022. Our main conclusion is that LSTM-based strategies outperform the other models and that the best diversifier for the AIS built for the S&P 500 index is the AIS built for Bitcoin. Finally, we test the LSTM model for a higher frequency of data (1 hour). We conclude that it outperforms the results obtained using daily data. |
| Keywords: | machine learning, recurrent neural networks, long short-term memory, algorithmic investment strategies, testing architecture, loss function, walk-forward optimization, over-optimization |
| JEL: | C4 C14 C45 C53 C58 G13 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2023-25&r=ets |
| By: | Qinmeng Luan; James Hamp |
| Abstract: | Recent work has proposed Wasserstein k-means (Wk-means) clustering as a powerful method to identify regimes in time series data, and one-dimensional asset returns in particular. In this paper, we begin by studying in detail the behaviour of the Wasserstein k-means clustering algorithm applied to synthetic one-dimensional time series data. We study the dynamics of the algorithm and investigate how varying different hyperparameters impacts the performance of the clustering algorithm for different random initialisations. We compute simple metrics that we find are useful in identifying high-quality clusterings. Then, we extend the technique of Wasserstein k-means clustering to multidimensional time series data by approximating the multidimensional Wasserstein distance as a sliced Wasserstein distance, resulting in a method we call `sliced Wasserstein k-means (sWk-means) clustering'. We apply the sWk-means clustering method to the problem of automated regime detection in multidimensional time series data, using synthetic data to demonstrate the validity of the approach. Finally, we show that the sWk-means method is effective in identifying distinct market regimes in real multidimensional financial time series, using publicly available foreign exchange spot rate data as a case study. We conclude with remarks about some limitations of our approach and potential complementary or alternative approaches. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.01285&r=ets |