On conditions in central limit theorems for martingale difference arrays

An alternative central limit theorem for martingale difference arrays is presented. It can be deduced from the literature but it is not stated as such. It can be very useful for statisticians and econometricians. An illustration is given in the context of ARMA models with time-dependent coefficients. This note ends with a discussion about the conditions.     

A reexamination of trends in primary commodity prices

This paper conducts a reexamination of the Prebisch-Singer hypothesis by employing the unit root test proposed by Lee and Strazicich (2003) and Lee and Strazicich (2004) that allow for up to two structural breaks. Given the higher power of these tests compared to the Zivot and Andrews (1992) and Lumsdaine and Papell (1997) tests, rejection of the null can be considered as genuine evidence of stationarity. The main findings of this paper are that eleven out of twenty-four commodity prices are found to be difference stationary implying that shocks to these commodities tend to be permanent in nature. The remaining thirteen prices are found to exhibit trend stationary behavior with either one or two structural breaks. Most of the commodities that do not exhibit difference stationary behavior seem to contain no significant trends. There are fewer cases, in relation to past studies, of commodities that display negative trends thereby weakening the case for the Prebisch-Singer hypothesis.     

On general periodic time-varying bilinear processes

We study in this note the class of bilinear processes with periodic time-varying coefficients. We give necessary and sufficient conditions ensuring the existence of strict and second order stationary solutions (in periodic sense) and for the existence of higher order moments. The given conditions can be applied to periodic ARMA or periodic GARCH models. The central limit theorem and the law of iterated logarithm (LIL) for higher order sample moments are showed.     

How useful is yet another data-driven bandwidth in long-run variance estimation?: A simulation study on cointegrating regressions

This paper investigates how bandwidth choice rules in long-run variance estimation affect finite-sample performance of efficient estimators for cointegrating regression models. Monte Carlo results indicate that Hirukawa's (2010) bandwidth choice rule contributes bias reduction in the estimators.     

Pricing Nikkei 225 Options Using Realized Volatility

This article examines option pricing performance using realized volatilities with or without handling microstructure noise, non‐trading hours and large jumps. The dynamics of realized volatility is specified by ARFIMA(X) and HAR(X) models. The main results using put options on the Nikkei 225 index are that: (i) the ARFIMAX model performs best; (ii) the Hansen and Lunde (2005a) adjustment for non‐trading hours improves the performance; (iii) methods for reducing microstructure noise‐induced bias yield better performance, while if the Hansen–Lunde adjustment is used, the other methods are not necessarily needed; and (iv) the performance is unaffected by removing large jumps from realized volatility.     

Volatility spill-overs in commodity spot prices: New empirical results

The classical rational expectations model of commodity markets implies that expected spot price risk is an explanatory variable in spot price regressions; and also that inventory carryover, which is reduced by a larger price variance, creates autoregressive conditional heteroscedastic processes in spot prices. In order to falsify/verify this theory, it has typically been assumed that the square root of the conditional variance of spot prices, a proxy for spot price risk, enters the conditional mean function of spot prices. Based on this simple representation, a typical but counter intuitive outcome has been that spot price risk has an insignificant impact on spot prices, see, e.g., Beck (Beck, S., 1993. A Rational Expectations Model of Time Varying Risk Premia in Commodities Futures Markets: Theory and Evidence. International Economic Review 34, 149–168, Beck, S., 2001. Autoregressive Conditional Heteroskedasticity in Commodity Spot Prices. Journal of Applied Econometrics 16, 115–132). In this paper, we propose an alternative functional relationship (from GARCH(1,1) to GARCH(1,1)-AR(m)) between spot price risk and spot prices that is fully supported by the classical rational expectations model, and based on this new representation we are able to provide stronger empirical support for Muth's rational expectation theory.     

Modified Quasi‐Likelihood Ratio Test for Regime Switching

In this paper we propose a modified quasi‐likelihood ratio test of the null hypothesis of one regime against the alternative of two regimes in Markov regime‐switching models. The asymptotic distribution of the proposed test statistic is a simple function of Gaussian random variables, and the inference is no more complicated than in the standard case. Our simulations show that the proposed test has good finite sample size and power that are comparable to the quasi‐likelihood ratio test of Cho and White. We apply our test to stock returns and Japanese policy functions.     

Estimation of the business cycle: A modified Hodrick-Prescott filter

Hodrick-Prescott (HP) filtering of (most often, seasonally adjusted) quarterly series is analysed. Some of the criticism to the filter are adressed. It is seen that, while filtering strongly affects autocorrelations, it has little effect on crosscorrelations. It is argued that the criticism that HP filtering induces a spurious cycle in the series is unwarranted. The filter, however, presents two serious drawbacks: First, poor performance at the end periods, due to the size of the revisions in preliminary estimators, and, second, the amount of noise in the cyclical signal, which seriously disturbs its interpretation. We show how the addition of two model-based features (in particular, applying the filter to the series extended with proper ARIMA forecasts and backcasts, and using as input to the filter the trend-cycle component instead of the seasonally adjusted series) can considerably improve the filter performance. Throughout the discussion, we use a computationally and analytically convenient alternative derivation of the HP filter, and illustrate the results with an example consisting of 4 Spanish economic indicators.     

An in-sample and out-of-sample empirical investigation of the nonlinearity in house prices of South Africa

This paper tests whether housing prices in the five segments of the South African housing market, namely large-middle, medium-middle, small-middle, luxury and affordable, exhibit non-linearity based on smooth transition autoregressive (STAR) models estimated using quarterly data from 1970:Q2 to 2009:Q3. Findings point to an overwhelming evidence of non-linearity in these five segments based on in-sample evaluation of the linear and non-linear models. We next provide further support for non-linearity by comparing one- to four-quarters-ahead out-of-sample forecasts of the non-linear time series model with those of the classical and Bayesian versions of the linear autoregressive (AR) models for each of these segments, for the out-of-sample horizon 2001:Q1 to 2009:Q3, using the in-sample period 1970:Q2 to 2000:Q4. Our results indicate that barring the one-, two and four-step(s)-ahead forecasts of the small segment, the non-linear model always outperforms the linear models. In addition, given the existence of strong causal relationship amongst the house prices of the five segments, the multivariate versions of the linear (classical and Bayesian) and STAR (MSTAR) models were also estimated. The MSTAR always outperformed the best performing univariate and multivariate linear models. Thus, our results highlight the importance of accounting for non-linearity, as well as the possible interrelationship amongst the variables under consideration, especially for forecasting.     

Loafing or learning?—the demand for informal education

Using detailed time use data for Germany a positive correlation is found between the level of schooling and time investments in informal education. Two hypotheses explain this observation: (1) highly educated people have higher opportunity costs of their leisure time and thus prefer leisure activities which add to their market productivity (wage effect) and (2) highly educated people have a preference for ‘high quality’ leisure (taste effect). The demand for informal education is derived in a household production model accounting for both explanations. An empirical investigation finds evidence for both effects with the taste effect being more important.     

Poverty trap and global indeterminacy in a growth model with open-access natural resources

In this paper we use global analysis techniques to analyze an economic growth model with environmental negative externalities, giving rise to a three-dimensional dynamic system (the framework is the one introduced by Wirl (1997) [53]). The dynamics of our model admits a locally attracting stationary state , which is, in fact, a poverty trap, coexisting with another stationary state possessing saddle-point stability. Global dynamical analysis shows that, under some conditions on the parameters, if the initial values of the state variables are close enough to the coordinates of , then there exists a continuum of equilibrium trajectories approaching and one trajectory approaching . Therefore, our model exhibits global indeterminacy, since either or can be selected according to agent expectations. Moreover, we prove that conditions guaranteeing the attractivity of also imply the saddle-point stability of . However, when is not attractive, numerical simulations show the possible existence of one or two limit cycles: an attractive one surrounding and one endowed with a two-dimensional stable manifold surrounding .     

Can we reject linearity in an HAR-RV model for the S&P 500? Insights from a nonparametric HAR-RV

This article tests the linearity assumption underlying the popular heterogeneous autoregressive model for realized volatility (HAR-RV). We implement a consistent model specification test that is robust to both distributional and model misspecification. We find that, using a nonparametric HAR-RV (NPHAR-RV), we are unable to reject the null of linearity.     

Endogenous market structure and the cooperative firm

When the threat of entry by followers includes cooperative firms, the maximum fixed cost that a profit maximizing leader can endure is endogenous. The aggressive strategy required for entry-deterrence curtails the leader’s expected profit and can discourage its initial entry. In such circumstances a cooperative firm may yet be viable, despite having a cost handicap and no first-mover advantage.     

Some properties of periodically collapsing bubbles

This paper explores some properties of periodically collapsing bubbles, which are a very popular model in the bubbles literature. We first demonstrate that complicated nonlinear bubbles can be represented as a time-varying parameter linear model of order 1. We demonstrate that the bubbles are explosive and nonstationary. We also derive conditions under which the bubbles are strictly stationary. We also demonstrate that the bubbles cannot be weakly stationary by deriving the tail indices of the strictly stationary distribution.