Fixed bandwidth inference for fractional cointegration

In a fractional cointegration setting we derive the fixed bandwidth limiting theory of a class of estimators of the cointegrating parameter which are constructed as ratios of weighted periodogram averages. These estimators offer improved limiting properties over those of more standard approaches like OLS or NBLS estimation. These advantages have been justified by means of traditional asymptotic theory and here we explore whether these improvements still hold when considering the alternative fixed bandwidth theory and, more importantly, whether this latter approach provides a more accurate approximation to the sampling distribution of the corresponding test statistics. This appears to be relevant, especially in view of the typical oversizing displayed by Wald statistics when confronted to the standard limiting theory. A Monte Carlo study of finite-sample behaviour is included

Boundary limit theory for functional local to unity regression

This paper studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary and explosive directions. Such models enhance the flexibility of the LUR framework by including break point, trending, and multi-directional departures from unit autoregressive coefficients. We study the behavior of this model as the localizing function diverges, thereby determining the impact on the time series and on inference from the time series as the limits of the domain of definition of the autoregressive coefficient are approached. This boundary limit theory enables us to characterize the asymptotic form of power functions for associated unit root tests against functional alternatives. Both sequential and simultaneous limits (as the sample size and localizing coefficient diverge) are developed. We find that asymptotics for the process, the autoregressive estimate, and its $t$ statistic have boundary limit behavior that differs from standard limit theory in both explosive and stationary cases. Some novel features of the boundary limit theory are the presence of a segmented limit process for the time series in the stationary direction and a degenerate process in the explosive direction. These features have material implications for autoregressive estimation and inference which are examined in the paper

Frequency Domain Estimation of Continuous Time Cointegrated Models with Mixed Frequency and Mixed Sample Data

Recent work by the author on mixed frequency data analysis has focused on the estimation of cointegrated systems in continuous time based on a fully specified dynamic system of equations, while the estimation of cointegrating vectors in a discrete time system has been approached using a semiparametric frequency domain estimator. We extend the latter approach to cover the continuous time case, establishing the asymptotic properties of the frequency domain estimator and explore, in a simulation study, the effects of misspecifying the continuous time dynamic model in discrete time compared to treating the dynamics non‐parametrically. An empirical illustration is also provided

The US stock market leads the Federal funds rate and Treasury bond yields

Using a recently introduced method to quantify the time varying lead-lag dependencies between pairs of economic time series (the thermal optimal path method), we test two fundamental tenets of the theory of fixed income: (i) the stock market variations and the yield changes should be anti-correlated; (ii) the change in central bank rates, as a proxy of the monetary policy of the central bank, should be a predictor of the future stock market direction. Using both monthly and weekly data, we found very similar lead-lag dependence between the S&P500 stock market index and the yields of bonds inside two groups: bond yields of short-term maturities (Federal funds rate (FFR), 3M, 6M, 1Y, 2Y, and 3Y) and bond yields of long-term maturities (5Y, 7Y, 10Y, and 20Y). In all cases, we observe the opposite of (i) and (ii). First, the stock market and yields move in the same direction. Second, the stock market leads the yields, including and especially the FFR. Moreover, we find that the short-term yields in the first group lead the long-term yields in the second group before the financial crisis that started mid-2007 and the inverse relationship holds afterwards. These results suggest that the Federal Reserve is increasingly mindful of the stock market behavior, seen at key to the recovery and health of the economy. Long-term investors seem also to have been more reactive and mindful of the signals provided by the financial stock markets than the Federal Reserve itself after the start of the financial crisis. The lead of the S&P500 stock market index over the bond yields of all maturities is confirmed by the traditional lagged cross-correlation analysis.Comment: 12 pages, 7 figures, 1 tabl

Dynamic modeling of mean-reverting spreads for statistical arbitrage

Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. Building on previous work, we embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean-reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds.Comment: 34 pages, 6 figures. Submitte

Multiple shifts and fractional integration in the us and uk unemployment rates

This paper analyses the long-run behaviour of the US and UK unemployment rates by testing for possibly fractional orders of integration and multiple shifts using a sample of over 100 annual observations. The results show that the orders of integration are higher than 0 in both series, which implies long memory. If we assume that the underlying disturbances are white noise, the values are higher than 0.5, i.e., nonstationary. However, if the disturbances are autocorrelated, the orders of integration are in the interval (0, 0.5), implying stationarity and mean-reverting behaviour. Moreover, when multiple shifts are taken into account, unemployment is more persistent in the US than in the UK, implying the need for stronger policy action in the former to bring unemployment back to its original level

Is eco-efficiency in greenhouse gas emissions converging among European Union countries?

Eco-efficiency refers to the ability to produce more goods and services with less impact on the environment and less consumption of natural resources. This issue has become a matter of concern that is receiving increasing attention from politicians, scientists and researchers. Furthermore, greenhouse gases emitted as a result of production processes have a marked impact on the environment and are also the foremost culprit of global warming and climate change. This paper assesses convergence in eco-efficiency in greenhouse gas emissions in the European Union. Eco-efficiency is assessed at both country and greenhouse-gas-specific levels using Data Envelopment Analysis techniques and directional distance functions, as recently proposed by Picazo-Tadeo et al. (Eur J Oper Res, 220:798–809, 2012). Convergence is then evaluated using the Phillips and Sul (Econometrica, 75:1771–1855, 2007) approach that allows testing for the existence of convergence groups. Although the results point to the existence of different convergence clubs depending on the specific pollutant considered, they signal the existence of at least four clear groups of countries. The first two groups are core European Union high-income countries (Benelux, Germany, Italy, Austria, the United Kingdom and Scandinavian countries). A third club is made up of peripheral countries (Spain, Ireland, Portugal and Greece) together with some Eastern countries (Latvia and Slovenia), while the remaining clubs consist of groups containing Eastern European countries

Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

An important issue in modelling economic time series is whether key unobserved components representing trends, seasonality and calendar components, are deterministic or evolutive. We address it by applying a recently proposed Bayesian variable selection methodology to an encompassing linear mixed model that features, along with deterministic effects, additional random explanatory variables that account for the evolution of the underlying level, slope, seasonality and trading days. Variable selection is performed by estimating the posterior model probabilities using a suitable Gibbs sampling scheme. The paper conducts an extensive empirical application on a large and representative set of monthly time series concerning industrial production and retail turnover. We find strong support for the presence of stochastic trends in the series, either in the form of a time-varying level, or, less frequently, of a stochastic slope, or both. Seasonality is a more stable component, although in at least 60 % of the cases we were able to select one or more stochastic trigonometric cycles. Most frequently the time variation is found in correspondence with the fundamental and the first harmonic cycles. An interesting and intuitively plausible finding is that the probability of estimating time-varying components increases with the sample size available. However, even for very large sample sizes we were unable to find stochastically varying calendar effects

Economic factors and suicide rates: associations over time in four countries

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