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Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.

In this study, the performance of ordinal GA-based trading strategies is evaluated under six classes of time series model, namely, the linear ARMA model, the bilinear model, the ARCH model, the GARCH model, the threshold model and the chaotic model. The performance criteria employed are the winning probability, accumulated returns, Sharpe ratio and luck coefficient. Asymptotic test statistics for these criteria are derived. The hypothesis as to the superiority of GA over a benchmark, say, buy-and-hold, can then be tested using Monte Carlo simulation. From this rigorously-established evaluation process, we find that simple genetic algorithms can work very well in linear stochastic environments, and that they also work very well in nonlinear deterministic (chaotic) environments. However, they may perform much worse in pure nonlinear stochastic cases. These results shed light on the superior performance of GA when it is applied to the two tick-by-tick time series of foreign exchange rates: EUR/USD and USD/JPY.

The Laplace-type estimator (LTE) is a simulation-based alternative to the classical extremum estimator that has gained popularity in applied research. We show that even though the estimator has desirable asymptotic properties, in small samples the point estimate provided by LTE may not necessarily converge to the extremum of the sample objective function. Furthermore, we suggest a simple test to verify if the estimator converges. We illustrate these results by estimating a prototype dynamic stochastic general equilibrium model widely used in macroeconomics research.

This paper investigates forecasting US Treasury bond and Dollar Eurocurrency rates using the stochastic unit root (STUR) model of Leybourne et al. (1996), and the stochastic cointegration (SC) model of Harris et al. (2002, 2006). Both models have time-varying parameter representations and are conceptually attractive for modelling interest rates as both allow for conditional heteroscedasticity. I find that for many of the series considered STUR and SC models generate statistically significant gains in out-of-sample forecasting accuracy relative to simple orthodox models. The results obtained highlight the usefulness of these extensions and raise some issues for future research.

The topic of volatility measurement and estimation is central to financial and more generally time-series econometrics. In this chapter, we begin by surveying models of volatility, both discrete and continuous, and then we summarize some selected empirical findings from the literature. In particular, in the first sections of this chapter, we discuss important developments in volatility models, with focus on time-varying and stochastic volatility as well as nonparametric volatility estimation. The models discussed share the common feature that volatilities are unobserved and belong to the class of missing variables. We then provide empirical evidence on “small” and “large” jumps from the perspective of their contribution to overall realized variation, using high-frequency price return data on 25 stocks in the DOW 30. Our “small” and “large” jump variations are constructed at three truncation levels, using extant methodology of Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev, and Diebold (2007), and Aït-Sahalia and Jacod (2009a, 2009b, 2009c). Evidence of jumps is found in around 22.8% of the days during the 1993–2000 period, much higher than the corresponding figure of 9.4% during the 2001–2008 period. Although the overall role of jumps is lessening, the role of large jumps has not decreased, and indeed, the relative role of large jumps, as a proportion of overall jumps, has actually increased in the 2000s.

We build three stochastic models of garbage can processes in an organization populated by boundedly rational agents. Although short-run behavior in our models can be quite chaotic, they generate systematic, testable predictions about patterns of organizational choice. These predictions are determined, in fairly intuitive ways, by the degree of preference conflict among agents in the organization, by their patterns of attention, and by their tendencies to make errors. We also show that nontrivial temporal orders can arise endogenously in one of our models, but only when some form of intentional order, based on agents’ preferences, is also present.

We analyze stochastic volatility effects in the context of the bond market. The short rate model is of Vasicek type and the focus of our analysis is the effect of multiple scale variations in the volatility of this model. Using a combined singular-regular perturbation approach we can identify a parsimonious representation of multiscale stochastic volatility effects. The results are illustrated with numerical simulations. We also present a framework for model calibration and look at the connection to defaultable bonds.