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on Econometric Time Series |
| By: | Gordon V. Chavez |
| Abstract: | We propose a family of stochastic volatility models that enable direct estimation of time-varying extreme event probabilities in time series with nonlinear dependence and power law tails. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, this process has an explicit, closed-form expression for its conditional probability density function, which enables straightforward estimation of dynamically changing extreme event probabilities. The process and volatility are conditionally Pareto-tailed, with tail exponent given by the reciprocal of the log-volatility's mean absolute innovation. These models thus can accommodate conditional power law-tail behavior ranging from very weakly non-Gaussian to Cauchy-like tails. Closed-form expressions for the models' conditional polynomial moments also allows for volatility modeling. We provide a straightforward, probabilistic method-of-moments estimation procedure that uses an asymptotic result for the process' conditional large deviation probabilities. We demonstrate the estimator's usefulness with a simulation study. We then give empirical applications to financial time series data, which show that this simple modeling method can be effectively used for dynamic tail inference in nonlinear, heavy-tailed time series. |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1901.02419&r=all |
| By: | Chappell, Daniel |
| Abstract: | Markov regime-switching (MRS) models, also known as hidden Markov models (HMM), are used extensively to account for regime heteroskedasticity within the returns of financial assets. However, we believe this paper to be one of the first to apply such methodology to the time series of cryptocurrencies. In light of Molnar and Thies (2018) demonstrating that the price data of Bitcoin contained seven distinct volatility regimes, we will �fit a sample of Bitcoin returns with six m-state MRS estimations, with m between 2 and 7. Our aim is to identify the optimal number of states for modelling the regime heteroskedasticity in the price data of Bitcoin. Goodness-of-�fit will be judged using three information criteria, namely: Bayesian (BIC); Hannan-Quinn (HQ); and Akaike (AIC). We determined that the restricted 5-state model generated the optimal estimation for the sample. In addition, we found evidence of volatility clustering, volatility jumps and asymmetric volatility transitions whilst also inferring the persistence of shocks in the price data of Bitcoin. |
| Keywords: | Bitcoin; Markov regime-switching; regime heteroskedasticity; volatility transitions. |
| JEL: | C01 C22 C26 C50 |
| Date: | 2018–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:90682&r=all |
| By: | George Kapetanios; M. Hashem Pesaran; Simon Reese |
| Abstract: | The importance of units with pervasive impacts on a large number of other units in a network has become increasingly recognized in the literature. In this paper we propose a new method to detect such influential or dominant units by basing our analysis on unit-specific residual error variances in the context of a standard factor model, subject to suitable adjustments due to multiple testing. Our proposed method allows us to estimate and identify the dominant units without the a priori knowledge of the interconnections amongst the units, or using a short list of potential dominant units. It is applicable even if the cross section dimension exceeds the time dimension, and most importantly it could end up with none of the units selected as dominant when this is in fact the case. The sequential multiple testing procedure proposed exhibits satisfactory small-sample performance in Monte Carlo simulations and compares well relative to existing approaches. We apply the proposed detection method to sectoral indices of US industrial production, US house price changes by states, and the rates of change of real GDP and real equity prices across the world’s largest economies. |
| Keywords: | dominant units, factor models, systemic risk, cross-sectional dependence, networks |
| JEL: | C18 C23 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7401&r=all |
| By: | Arnoud Stevens (National Bank of Belgium); Joris Wauters (National Bank of Belgium and Ghent University) |
| Abstract: | Inflation has been persistently weak in the euro area despite the economic recovery since 2013. We investigate the sources behind this protracted low inflation by building a time-varying parameter model that jointly explains the dynamics of inflation and inflation expectations from the ECB’s Survey of Professional Forecasters. We find that the inclusion of survey data strengthens the view that low inflation was mainly due to cyclical drivers. In particular, the model with survey expectations finds a more muted decline of trend inflation in recent years and a larger degree of economic slack. The impact of economic slack and import prices on inflation is found to have increased in recent years. We also find that survey expectations have become less persistent over the financial crisis period, and that including survey data improves the model’s out-of-sample forecasting performance. |
| Keywords: | in?ation dynamics, trend in?ation, survey-based in?ation expectations, ECB Survey of Pro- fessional Forecasters, nonlinear state space model, Bayesian estimation, euro area |
| JEL: | E31 C11 C32 |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbb:reswpp:201810-355&r=all |
| By: | Luisa Bisaglia; Matteo Grigoletto |
| Abstract: | In this work we propose a new class of long-memory models with time-varying fractional parameter. In particular, the dynamics of the long-memory coefficient, $d$, is specified through a stochastic recurrence equation driven by the score of the predictive likelihood, as suggested by Creal et al. (2013) and Harvey (2013). We demonstrate the validity of the proposed model by a Monte Carlo experiment and an application to two real time series. |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1812.07295&r=all |
| By: | Stauskas, Ovidijus (Department of Economics, Lund University) |
| Abstract: | In this paper we re-visit a recent theoretical idea introduced by Phillips and Lee (2015). They examine an empirically relevant situation when multiple time series under consideration exhibit different degrees of non-stationarity. By bridging the asymptotic theory of the local to unity and mildly explosive processes, they construct a Wald test for the commonality of the long-run behavior of two series. Therefore, a vector autoregressive (VAR) setup is natural. However, inference is complicated by the fact that the statistic is degenerate under the null and divergent under the alternative. This is true if the parameters of the data generating process are known and re-normalizing function can be constructed. If the parameters are unknown, as is in practice, the test statistic may be divergent even under the null. We solve this problem by converting the original setting of one vector time series in a panel setting with N individual vector series. We consider asymptotics with fixed N and large T and extend the results to sequential asymptotics when T passes to infinity before N. We show that the Wald test statistic converges to nuisance parameter-free Chi-squared distribution under the null hypothesis. |
| Keywords: | Local to unity; mildly explosive; panel; weak dependence; Wald test |
| JEL: | C12 C32 C33 |
| Date: | 2019–01–14 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2019_002&r=all |
| By: | Francisco Blasques; Vladim\'ir Hol\'y; Petra Tomanov\'a |
| Abstract: | In finance, durations between successive transactions are usually modeled by the autoregressive conditional duration model based on a continuous distribution omitting frequent zero values. Zero durations can be caused by either split transactions or independent transactions. We propose a discrete model allowing for excessive zero values based on the zero-inflated negative binomial distribution with score dynamics. We establish the invertibility of the score filter. Additionally, we derive sufficient conditions for the consistency and asymptotic normality of the maximum likelihood of the model parameters. In an empirical study of DJIA stocks, we find that split transactions cause on average 63% of zero values. Furthermore, the loss of decimal places in the proposed model is less severe than incorrect treatment of zero values in continuous models. |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1812.07318&r=all |
| By: | Aknouche, Abdelhakim; Francq, Christian |
| Abstract: | We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in the present paper. |
| Keywords: | Absolute regularity, Autoregressive Conditional Duration, Count time series models, Distance covariance test, Ergodicity, Integer GARCH |
| JEL: | C18 C5 C58 |
| Date: | 2018–11–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:90838&r=all |
| By: | NYONI, THABANI |
| Abstract: | Using annual time series data on GDP per capita in Kenya from 1960 to 2017, the study analyzes GDP per capita using the Box – Jenkins ARIMA technique. The diagnostic tests such as the ADF tests show that Kenyan GDP per capita data is I (2). Based on the AIC, the study presents the ARIMA (3, 2, 1) model. The diagnostic tests further show that the presented parsimonious model is stable and reliable. The results of the study indicate that living standards in Kenya will improve over the next decade, as long as the prudent macroeconomic management continues in Kenya. Indeed, Kenya’s economy is growing. The study offers 3 policy prescriptions in an effort to help policy makers in Kenya on how to promote and maintain the much needed growth. |
| Keywords: | GDP per capita; forecasting; Kenya |
| JEL: | C53 E37 O47 |
| Date: | 2019–01–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91395&r=all |
| By: | NYONI, THABANI |
| Abstract: | Using annual time series data on GDP per capita in Nigeria from 1960 to 2017, I model and forecast GDP per capita using the Box – Jenkins ARIMA technique. My diagnostic tests such as the ADF tests show that Nigerian GDP per capita data is I (1). Based on the AIC, the study presents the ARIMA (2, 1, 0) model. The diagnostic tests further reveal that the presented optimal model is stable and hence reliable. The results of the study indicate that living standards in Nigeria will tumble over the next decade, as long as the current economic policy stance is not reviewed. Indeed, Nigeria’s economy is backsliding again!!! In order to improve the living standards of an ordinary Nigerian, this study has put forward four-fold policy prescriptions. |
| Keywords: | GDP per capita; forecasting; Nigeria |
| JEL: | C53 E37 O47 |
| Date: | 2019–01–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91396&r=all |
| By: | NYONI, THABANI |
| Abstract: | Employing annual time series data on total population in Bangladesh from 1960 to 2017, I model and forecast total population over the next 3 decades using the Box – Jenkins ARIMA technique. Diagnostic tests such as the ADF tests show that Bangladesh annual total population is neither I (1) nor I (2) but for simplicity purposes, the researcher has assumed it is I (2). Based on the AIC, the study presents the ARIMA (4, 2, 1) model. The diagnostic tests further indicate that the presented model is very stable and quite reliable. The results of the study reveal that total population in Bangladesh will continue to sharply rise in the next three decades. In order to deal with the threats posed by a large population, 3 policy recommendations have been suggested. |
| Keywords: | Population; forecasting; Bangladesh |
| JEL: | C53 Q56 R23 |
| Date: | 2019–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91394&r=all |
| By: | Halkos, George; Tzirivis, Apostolos |
| Abstract: | The current study emphasizes on the importance of the development of an effective price risk management strategy regarding energy products, as a result of the high volatility of that particular market. The study provides a thorough investigation of the energy price volatility, through the use of GARCH type model variations and the Markov-Switching GARCH methodology, as they are presented in the most representative academic researches. A large number of GARCH type models are exhibited together with the methodology and all the econometric procedures and tests that are necessary for developing a robust and precise forecasting model regarding energy price volatility. Nevertheless, the present research moves another step forward, in an attempt to cover also the probability of potential shifts in the unconditional variance of the models due to the effect of economic crises and several unexpected geopolitical events into the energy market prices. |
| Keywords: | Energy commodities, WTI oil, Brent oil, electricity, natural gas, gasoline, risk management, volatility modeling, ARCH-GARCH models, Markov-Switching GARCH models. |
| JEL: | C01 C58 D8 G3 O13 P28 Q43 Q47 Q58 |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:90781&r=all |