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on Econometric Time Series |
| By: | Dou, Baojun; Parrella, Maria Lucia; Yao, Qiwei |
| Abstract: | We consider a class of spatio-temporal models which extend popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) different from each other. To overcome the innate endogeneity, we propose a generalized Yule–Walker estimation method which applies the least squares estimation to a Yule–Walker equation. The asymptotic theory is developed under the setting that both the sample size and the number of locations (or panels) tend to infinity under a general setting for stationary and α-mixing processes, which includes spatial autoregressive panel data models driven by i.i.d. innovations as special cases. The proposed methods are illustrated using both simulated and real data. |
| Keywords: | α-mixing; dynamic panels; high dimensionality; least squares estimation; spatial autoregression; stationarity |
| JEL: | C13 C23 C32 |
| Date: | 2016–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:67151&r=ets |
| By: | Robinson, Peter; Taylor, Luke |
| Abstract: | This article develops statistical methodology for semiparametric models for multiple time series of possibly high dimension N. The objective is to obtain precise estimates of unknown parameters (which characterize autocorrelations and cross-autocorrelations) without fully parameterizing other distributional features, while imposing a degree of parsimony to mitigate a curse of dimensionality. The innovations vector is modelled as a linear transformation of independent but possibly non-identically distributed random variables, whose distributions are nonparametric. In such circumstances, Gaussian pseudo-maximum likelihood estimates of the parameters are typically √n-consistent, where n denotes series length, but asymptotically inefficient unless the innovations are in fact Gaussian. Our parameter estimates, which we call ‘adaptive,’ are asymptotically as first-order efficient as maximum likelihood estimates based on correctly specified parametric innovations distributions. The adaptive estimates use nonparametric estimates of score functions (of the elements of the underlying vector of independent random varables) that involve truncated expansions in terms of basis functions; these have advantages over the kernel-based score function estimates used in most of the adaptive estimation literature. Our parameter estimates are also √n -consistent and asymptotically normal. A Monte Carlo study of finite sample performance of the adaptive estimates, employing a variety of parameterizations, distributions and choices of N, is reported. |
| JEL: | J1 |
| Date: | 2017–02–08 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:68345&r=ets |
| By: | Eyal Neuman; Mathieu Rosenbaum |
| Abstract: | It has been recently established that the volatility of financial assets is rough. This means that the behavior of the log-volatility process is similar to that of a fractional Brownian motion with Hurst parameter around 0.1. Motivated by this finding, we wish to define a natural and relevant limit for the fractional Brownian motion when $H$ goes to zero. We show that once properly normalized, the fractional Brownian motion converges to a Gaussian random distribution which is very close to a log-correlated random field. |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1711.00427&r=ets |
| By: | Matteo Serafino; Andrea Gabrielli; Guido Caldarelli; Giulio Cimini |
| Abstract: | Statistical physics of complex systems exploits network theory not only to model, but also to effectively extract information from many dynamical real-world systems. A pivotal case of study is given by financial systems: market prediction represents an unsolved scientific challenge yet with crucial implications for society, as financial crises have devastating effects on real economies. Thus, nowadays the quest for a robust estimator of market efficiency is both a scientific and institutional priority. In this work we study the visibility graphs built from the time series of several trade market indices. We propose a validation procedure for each link of these graphs against a null hypothesis derived from ARCH-type modeling of such series. Building on this framework, we devise a market indicator that turns out to be highly correlated and even predictive of financial instability periods. |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1710.10980&r=ets |
| By: | McCracken, Michael W. (Federal Reserve Bank of St. Louis); McGillicuddy, Joseph (Federal Reserve Bank of St. Louis) |
| Abstract: | When constructing unconditional point forecasts, both direct- and iterated-multistep (DMS and IMS) approaches are common. However, in the context of producing conditional forecasts, IMS approaches based on vector autoregressions (VAR) are far more common than simpler DMS models. This is despite the fact that there are theoretical reasons to believe that DMS models are more robust to misspecification than are IMS models. In the context of unconditional forecasts, Marcellino, Stock, and Watson (MSW, 2006) investigate the empirical relevance of these theories. In this paper, we extend that work to conditional forecasts. We do so based on linear bivariate and trivariate models estimated using a large dataset of macroeconomic time series. Over comparable samples, our results reinforce those in MSW: the IMS approach is typically a bit better than DMS with significant improvements only at longer horizons. In contrast, when we focus on the Great Moderation sample we find a marked improvement in the DMS approach relative to IMS. The distinction is particularly clear when we forecast nominal rather than real variables where the relative gains can be substantial. |
| Keywords: | Prediction; forecasting; out-of-sample |
| JEL: | C12 C32 C52 C53 |
| Date: | 2017–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2017-040&r=ets |
| By: | Guglielmo Maria Caporale; Luis A. Gil-Alana |
| Abstract: | In this paper we propose a new modelling framework for the analysis of macro series that includes both stochastic trends and stochastic cycles in addition to deterministic terms such as linear and non-linear trends. We examine four US macro series, namely annual and quarterly real GDP and GDP per capita. The results indicate that the behaviour of US GDP can be captured accurately by a model incorporating both stochastic trends and stochastic cycles that allows for some degree of persistence in the data. Both appear to be mean-reverting, although the stochastic trend is nonstationary whilst the cyclical component is stationary, with cycles repeating themselves every 6 – 10 years. |
| Keywords: | GDP, GDP per capita, trends, cycles, long memory, fractional integration |
| JEL: | C22 E32 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_6728&r=ets |
| By: | Raihan, Tasneem |
| Abstract: | This paper seeks to uncover the non-linear characteristics of uncertainty underlying the US inflation rates over the period 1971-2015 within a regime-switching framework. Accordingly, we employ two variants of a Markov regime-switching GARCH model, one with normally distributed errors (MS-GARCH-N) and another with t-distributed errors (MS-GARCH-t), and compare their relative in-sample as well as out-of-sample performances with those of their standard single-regime counterparts. Consistent with the findings in existing studies, both of our regime-switching models are successful in identifying the year 1984 as the breakpoint in inflation volatility. Among other interesting results is a new finding that the process of switching to the low volatility regime started around April, 1979 and continued until mid 1983. This time frame is matched with the period of aggressive monetary policy changes implemented by the then Fed chairman Paul Volcker. As regards the performance in forecasting uncertainty, for shorter horizons spanning 1 to 5 months, MS-GARCH-N forecasts are found to outperform all other models whereas for 8 to 12-month ahead forecasts MS-GARCH-t appears superior. |
| Keywords: | Markov switching, GARCH, inflation uncertainty |
| JEL: | C01 C53 E31 |
| Date: | 2017–10–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:82343&r=ets |
| By: | Güriş, Burak |
| Abstract: | Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autoregressive (ESTAR) model. The simulation results indicate that the proposed unit root test is more powerful than the Kruse (2011) and KSS(2003) tests. |
| Keywords: | Flexible Fourier Form, Unit Root Test, Nonlinearity |
| JEL: | C12 C22 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:82260&r=ets |
| By: | Burak Eroglu (Istanbul Bilgi University); Kemal Caglar Gogebakan (Bilkent University); Mirza Trokic (Bilkent University and IHS Markit) |
| Abstract: | This paper introduces a non-parametric variance ratio testing procedure for seasonal unit roots by utilizing the fractional integration operator. This procedure includes unit root tests at zero, Nyquist, harmonic and joint frequencies. Different from the widely used seasonal unit root tests of Hylleberg et al. (1990)[HEGY], the proposed tests are free from any nuisance and tuning parameters. Furthermore, we develop a new bootstrap technique for the fractional seasonal variance ratio tests by utilizing wavelet filters. This technique allows the practitioners to test for the seasonal unit roots without estimating a parametric regression model. The Monte Carlo simulation evidence reveals that, our proposed fractional seasonal variance ratio [FSVR] tests and the wavelet based bootstrap counterparts have desirable size and power properties. |
| Keywords: | Seasonal unit roots; Fractional integration; Wavelets; Wavestrapping |
| JEL: | C14 C22 |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:bli:wpaper:1707&r=ets |
| By: | Francisco (F.) Blasques (VU Amsterdam; Tinbergen Institute, The Netherlands); Andre (A.) Lucas (VU Amsterdam; Tinbergen Institute, The Netherlands); Andries van Vlodrop (VU Amsterdam; Tinbergen Institute, The Netherlands) |
| Abstract: | We study optimality properties in finite samples for time-varying volatility models driven by the score of the predictive likelihood function. Available optimality results for this class of models suffer from two drawbacks. First, they are only asymptotically valid when evaluated at the pseudo-true parameter. Second, they only provide an optimality result `on average' and do not provide conditions under which such optimality prevails. We show in a finite sample setting that score-driven volatility models have optimality properties when they matter most. Score-driven models perform best when the data is fat-tailed and robustness is important. Moreover, they perform better when filtered volatilities differ most across alternative models, such as in periods of financial distress. These results are confirmed by an empirical application based on U.S. stock returns. |
| Keywords: | Volatility models; score-driven dynamics; finite samples; Kullback-Leibler divergence; optimality. |
| JEL: | C01 C18 C20 |
| Date: | 2017–11–24 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20170111&r=ets |
| By: | Burak Eroglu (Istanbul Bilgi University) |
| Abstract: | In this paper, I propose a wavelet based cointegration test for fractionally integrated time series. This proposed test is non-parametric and asymptotically invariant to different forms of short run dynamics. The use of wavelets allows one to take advantage of the wavelet based bootstrapping method particularly known as wavestrapping. In this regard, I introduce a new wavestrapping algorithm for multivariate time series processes, specifically for cointegration tests. The Monte Carlo simulations indicate that this new wavestrapping procedure can alleviate the severe size distortions which are generally observed in cointegration tests with time series containing innovations that possess highly negative MA parameters. Additionally, I apply the proposed methodology to analyse the long run co-movements in the credit default swap market of European Union countries. |
| Keywords: | Fractional integration; Cointegration; Wavelet; Wavestrapping |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:bli:wpaper:1706&r=ets |