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on Econometric Time Series |
| By: | Enzo D'Innocenzo; Alessandra Luati; Mario Mazzocchi |
| Abstract: | A novel multivariate score-driven model is proposed to extract signals from noisy vector processes. By assuming that the conditional location vector from a multivariate Student's t distribution changes over time, we construct a robust filter which is able to overcome several issues that naturally arise when modeling heavy-tailed phenomena and, more in general, vectors of dependent non-Gaussian time series. We derive conditions for stationarity and invertibility and estimate the unknown parameters by maximum likelihood. Strong consistency and asymptotic normality of the estimator are proved and the finite sample properties are illustrated by a Monte-Carlo study. From a computational point of view, analytical formulae are derived, which consent to develop estimation procedures based on the Fisher scoring method. The theory is supported by a novel empirical illustration that shows how the model can be effectively applied to estimate consumer prices from home scanner data. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.01517&r=all |
| By: | Carlo Campajola; Fabrizio Lillo; Piero Mazzarisi; Daniele Tantari |
| Abstract: | Binary random variables are the building blocks used to describe a large variety of systems, from magnetic spins to financial time series and neuron activity. In Statistical Physics the Kinetic Ising Model has been introduced to describe the dynamics of the magnetic moments of a spin lattice, while in time series analysis discrete autoregressive processes have been designed to capture the multivariate dependence structure across binary time series. In this article we provide a rigorous proof of the equivalence between the two models in the range of a unique and invertible map unambiguously linking one model parameters set to the other. Our result finds further justification acknowledging that both models provide maximum entropy distributions of binary time series with given means, auto-correlations, and lagged cross-correlations of order one. |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2008.10666&r=all |
| By: | Yicong Lin; Hanno Reuvers |
| Abstract: | The Environment Kuznets Curve (EKC) predicts an inverted U-shaped relationship between economic growth and environmental pollution. Current analyses frequently employ models which restrict the nonlinearities in the data to be explained by the economic growth variable only. We propose a Generalized Cointegrating Polynomial Regression (GCPR) with flexible time trends to proxy time effects such as technological progress and/or environmental awareness. More specifically, a GCPR includes flexible powers of deterministic trends and integer powers of stochastic trends. We estimate the GCPR by nonlinear least squares and derive its asymptotic distribution. Endogeneity of the regressors can introduce nuisance parameters into this limiting distribution but a simulated approach nevertheless enables us to conduct valid inference. Moreover, a subsampling KPSS test can be used to check the stationarity of the errors. A comprehensive simulation study shows good performance of the simulated inference approach and the subsampling KPSS test. We illustrate the GCPR approach on a dataset of 18 industrialised countries containing GDP and CO2 emissions. We conclude that: (1) the evidence for an EKC is significantly reduced when a nonlinear time trend is included, and (2) a linear cointegrating relation between GDP and CO2 around a power law trend also provides an accurate description of the data. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.02262&r=all |
| By: | Gianluca Cubadda; Alain Hecq |
| Abstract: | This paper aims to decompose a large dimensional vector autoregessive (VAR) model into two components, the first one being generated by a small-scale VAR and the second one being a white noise sequence. Hence, a reduced number of common factors generates the entire dynamics of the large system through a VAR structure. This modelling extends the common feature approach to high dimensional systems, and it differs from the dynamic factor models in which the idiosyncratic components can also embed a dynamic pattern. We show the conditions under which this decomposition exists, and we provide statistical tools to detect its presence in the data and to estimate the parameters of the underlying small-scale VAR model. We evaluate the practical value of the proposed methodology by simulations as well as by empirical applications on both economic and financial time series. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.03361&r=all |
| By: | Cassim, Lucius |
| Abstract: | In this paper I derive a test of Multicointegration of I (2) series that takes into account both structural breaks and threshold adjustment to steady state. I extend the I(2) –multicointegration test proposed by Berenguer-Rico and Carrion-i-Silvestre (2005), by relaxing the assumption of symmetric adjustment. In a way, I adapt the Engsted et al. (1997) approach to the concept of multicointegration and following Enders and Siklos (2001) I model the multicointegration relation while allowing for asymmetric adjustment to long run equilibrium. Further, use is made of the multivariate invariance principle, the weak convergence to stochastic integrals for dependent heterogeneous processes, and the continuous mapping theorem in order to derive an augmented Dickey-Fuller type of multicointegration test for I (2) series. I find that the limiting distributions of the estimators and test statistics associated with multicointegration depend on the cut-off point of the asymmetric response and the break point. I illustrate the test by applying it to understanding interest rate pass-through in Malawi. The derived multicointegration test confirms the presence of multicointegration among lending rates, policy rate and Treasury bill rates in Malawi in which lending rates adjust asymmetrically to steady state following a positive or negative policy rate adjustment. |
| Keywords: | Multicointegration; Threshold Adjustment; I (2) series; ADF test |
| JEL: | C10 C12 C4 C5 C50 |
| Date: | 2020–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:101453&r=all |
| By: | Marius Lux; Wolfgang Karl H\"ardle; Stefan Lessmann |
| Abstract: | Appropriate risk management is crucial to ensure the competitiveness of financial institutions and the stability of the economy. One widely used financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear and parametric models can lead to biased results or even underestimation of risk due to time varying volatility, skewness and leptokurtosis of financial return series. The paper proposes a nonlinear and nonparametric framework to forecast VaR that is motivated by overcoming the disadvantages of parametric models with a purely data driven approach. Mean and volatility are modeled via support vector regression (SVR) where the volatility model is motivated by the standard generalized autoregressive conditional heteroscedasticity (GARCH) formulation. Based on this, VaR is derived by applying kernel density estimation (KDE). This approach allows for flexible tail shapes of the profit and loss distribution, adapts for a wide class of tail events and is able to capture complex structures regarding mean and volatility. The SVR-GARCH-KDE hybrid is compared to standard, exponential and threshold GARCH models coupled with different error distributions. To examine the performance in different markets, one-day-ahead and ten-days-ahead forecasts are produced for different financial indices. Model evaluation using a likelihood ratio based test framework for interval forecasts and a test for superior predictive ability indicates that the SVR-GARCH-KDE hybrid performs competitive to benchmark models and reduces potential losses especially for ten-days-ahead forecasts significantly. Especially models that are coupled with a normal distribution are systematically outperformed. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.06910&r=all |
| By: | Asim Kumer Dey; Toufiqul Haq; Kumer Das; Yulia R. Gel |
| Abstract: | We investigate the impact of Covid-19 cases and deaths, local spread spreads of Covid-19, and Google search activities on the US stock market. We develop a temporal complex network to quantify US county level spread dynamics of Covid-19. We conduct the analysis by using the following sequence of methods: Spearman's rank correlation, Granger causality, Random Forest (RF) model, and EGARCH (1,1) model. The results suggest that Covid-19 cases and deaths, its local spread spreads, and Google searches have impacts on the abnormal stock price between January 2020 to May 2020. However, although a few of Covid-19 variables, e.g., US total deaths and US new cases exhibit causal relationship on price volatility, EGARCH model suggests that Covid-19 cases and deaths, local spread spreads of Covid-19, and Google search activities do not have impacts on price volatility. |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2008.10885&r=all |