RePEc: Research Papers in Economics
Research Papers in Economics is a collaborative effort of hundreds of volunteers in many countries to enhance the dissemination of research in economics.
School of Economics and Finance Discussion Papers and Working Papers Series
2006
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#208oDownload full text
- Keywords:
- Kernel estimators; nonparametric density estimation; wavelets
Estimators of integrals of powers of density derivatives
Simple kernel-type estimators of integrals of general powers of general derivatives of probability densities are proposed. They are based on two simple properties, and in many circumstances enjoy optimal convergence rate.
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#208nDownload full text
- Keywords:
- Bandwidth; chaos; density estimation; invariant distribution; kernel method; logistic map; Lyapunov exponent; pole; stationary distribution
Properties of invariant distributions and Lyapunov exponents for chaotic logistic maps
Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling biological systems. We derive theory describing properties of the 'invariant' or 'stationary' distribution under logistic maps and apply those results in conjunction with numerical work to develop further properties of invariant distributions and Lyapunov exponents. We describe the role that poles play in determining properties of densities' iterated distributions and show how poles arise from iterated mappings of the centre of the interval to which the map is applied. Particular attention is paid to the shape of the invariant distribution in the tails or in the neighbourhood of a pole of its density. A new technique is developed for this application. it enables us to combine 'parametric' information, available from the structure of the map, with 'nonparametric' information obtainable from numerical experiments.
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#208mDownload full text
- Keywords:
- Chaos; correlation integral; invariant distribution; logistic map
Properties of distributions and correlation integrals for generalised versions of the logistic map
We study a generalised version of the logistic map of the unit interval $(0,1)$, in which the point $x$ is taken to $1-|2x-1|^nu$. Here, $nu >0$ is a parameter of the map, which has received attention only when $nu =1$ and 2. We obtain the invariant density when $nu = frac12$, and derive properties of invariant distributions in all other cases. These are obtained by a mixture of analytic and numerical argument. In particular, we develop a technique for combining "parametric" information, available from the functional form of the map, with "non-parametric" information, from a Monte Carlo study. Properties of the correlation integral under the invariant distribution are also derived. It is shown that classical behaviour of this test statistic, which demands that the logarithm of the integral have slope equal to the lag, is valid if and only if $nu leq 2$.
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#208lDownload full text
- Keywords:
- Absolutely regular; bandwidth; biased bootstrap; conditional distribution; kernel methods; local linear methods; local logistic methods; Nadaraya-Watson estimator; prediction; quantile estimation; time series analysis; weighted bootstrap
Methods for estimating a conditional distribution function
Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the Nadaraya--Watson estimator. It preserves the bias and variance properties of a class of second-order estimators introduced by Yu and Jones but has the added advantage of always being a distribution itself. Our methods also have application outside the time series setting; for example, to quantile estimation for independent data. This problem motivated the work of Yu and Jones.
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#208kDownload full text
- Keywords:
- Adaptive estimation; additive model; dependent process; mixing condition; nonlinear time series; nonparametric regression; orthogonal series; strict stationarity; truncation parameter
Adaptive orthogonal series estimation in additive stochastic regression models
In this paper, we consider additive stochastic nonparametric regression models. By approximating the nonparametric components by a class of orthogonal series and using a generalized cross-validation criterion, an adaptive and simultaneous estimation procedure for the nonparametric components is constructed. We illustrate the adaptive and simultaneous estimation procedure by a number of simulated and real examples.
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#208jDownload full text
- Keywords:
- Binary sequence; chaos; chaos communications; dependence; discretisation; invariant distribution; logistic map; randomness
Binary time series generated by chaotic logistic maps
This paper examines stochastic pairwise dependence structures in binary time series obtained from discretised versions of standard chaotic logistic maps. It is motivated by applications in communications modelling which make use of so-called chaotic binary sequences. The strength of non-linear stochastic dependence of the binary sequences is explored. In contrast to the original chaotic sequence, the binary version is non-chaotic with non-Markovian non-linear dependence, except in a special case. Marginal and joint probability distributions, and autocorrelation functions are elicited. Multivariate binary and more discretised time series from a single realisation of the logistic map are developed from the binary paradigm. Proposals for extension of the methodology to other cases of the general logistic map are developed. Finally, a brief illustration of the place of chaos-based binary processes in chaos communications is given.
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#208iDownload full text
- Keywords:
- Bootstrap; chaos; empirical likelihood; expectile; percentile
Statistical tests for Lyapunov exponents of deterministic systems
In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least deviations and asymmetric least squares methods. Asymptotic distributional properties of the estimators are established.
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#208hDownload full text
- Keywords:
- Accounting systems; conditioning; depreciation; Markov chains; Statistical Activity Cost Theory (SACT); virtual firm
Recent developments of statistical approaches in cost accounting: a review
We review and simultaneously introduce a convenient statistical concept for the mathematical representation of the Statistical Activity Cost Theory (SACT) introduced by Willett (1987 and 1988). Further, we discuss, and present a critique of, a variety of statistical models with respect to long debated accounting problems, such as the allocation of joint costs and depreciation. We finally propose that taking the effort to combine those models results in a novel statistical accounting system and this is discussed by means of the so-called virtual firm. As it has been shown that any statistical model discussed here outperforms associated deterministic counterparts, this review presents promising outcomes and useful perspectives for the accounting profession.
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#208gDownload full text
- Keywords:
- Archimedean copula; copula; correlation integral; dependence; Poisson convergence
Dependence structures in financial time series: a chaos-theoretic approach
Of much interest in financial econometrics is the recovery of joint distributional behaviour of collections of contemporaneous financial time series, e.g., two related commodity price series, or two asset returns series. An approach to model their joint behaviour is to use copulas. Essentially, copulas are selected on the basis of a measure of correlation between the two series and are made to match their marginal properties. Of course, generalisations exist for more than two series. A possible limitation of this approach is that only linear correlations between series might be captured. We consider incorporating more general dependence structures, through the use of the correlation integral (as in the BDS test), as a means to refine the choice of candidate copulas in an empirical situation.
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#208fDownload full text
- Keywords:
- Third-order moment; bispectrum; non-linear; non-stationary; time series; bootstrap; phase scrambling
A time-domain test for some types of non-linearity
The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.
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#208eDownload full text
- Keywords:
- Convergence diagnostics; higher cumulants; Markov Chain Monte Carlo; non-linear time series; stationarity; surrogate series
Phase randomisation: a convergence diagnostic test for MCMC
Most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. Potentially useful diagnostics may be borrowed from diverse areas such as time series. One such method is phase randomisation. The aim of this paper is to describe this method in the context of MCMC, summarise its characteristics, and contrast its performance with those of the more common diagnostic tests for MCMC. It is observed that the new tool contributes information about third and higher order cumulant behaviour which is important in characterising certain forms of nonlinearity and nonstationarity.
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#208dDownload full text
- Keywords:
- Metal price; mining risk; open pit design; orebody estimation; production costs; real options
Modelling the initial pit design: the first step for project valuation
One critical factor in open pit mining projects is the estimation of the recoverable reserves. The reason for this is that at the valuation stage there is a lack of information about future metal prices and production costs. Consequently, the estimation of the recoverable reserves needs to be done based on a fixed break-even cut-off grade (BECG), in which fixed expected metal prices and production costs are assumed throughout the operating life of the mine (OLM).
In this paper, an alternative technique for estimating the recoverable reserves of an open pit mining project is presented and explained in detail. The main characteristic of this technique is that it estimates the recoverable reserves of the project using mining costs as reference: this is done due to the fact that mining costs are easier to model than metal prices. Another important characteristic of this technique is that it uses the uncertainty of the geology of the orebody, given by simulations of the deposit, to make final strategic decisions, such as the selection of the operating life of the mine and the optimal production rate, which minimise the risk of not achieving future production targets while maximising the upside potential of future rewards.
As it will be shown, the final outcome of the proposed technique is the generation of a robust open pit design, that include cutbacks and ultimate pit limits, called the marginal open pit mine design (MOPMD). One characteristic of the MOPMD is that, at each production period, it will be characterised by their respective geological uncertainty, given as probability distributions of ore, waste and metal quantities, and by marginal economical project indicators, such as cut-off grades and metal prices, among others. The details follow in the paper. -
#208cDownload full text
- Keywords:
- Return; Volatility; News
Does Company Specific News Effect the US, UK, and Australian Markets within 60 minutes?
The efficient market hypothesis states that an efficient market rapidly incorporates all available information into the price of the asset. It has been well established that no market, particularly the stock market, is truly efficient as there are too many traders with differing strategies, and differing access to and interpretation of information. Despite this there is considerable evidence that the stock market does assimilate new information into prices. There has however been little research into the intraday effect of company specific news. In this paper we investigate the intraday effect of company specific news on the US, UK, and Australian markets. We use a scheme to determine whether the markets react to news by determining the likelihood of certain events occurring, and the likelihood of news occurring within 60 minutes of them, and compare the two. We find that there is strong evidence that these markets do react to news within 60 minutes, and indicate which events are most likely to correlate to news.
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#208bDownload full text
- Keywords:
- Stock Market; News; Return; Volatility; Market Reaction
What Types of Events Provide the Strongest Evidence that the Stock Market is Affected by Company Specific News?
The efficient market hypothesis states that an efficient market immediately incorporates all available information into the price of the traded entity. It is well established that the stock market is not an efficient market as it consists of numerous traders with differing strategies and interpretations of information. However there is substantial evidence to suggest that the stock market does incorporate new information into prices. Unfortunately little research has focussed on the high frequency effect of real time news, across a broad base of assets. This paper investigates how the US, UK, and Australian markets incorporate all real time news, not just Press Announcements, Annual Reports, etc. We find that there is strong evidence to suggest that the markets do incorporate news quickly.
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#208aDownload full text
- JEL-Codes:
- J24; D73; J68
- Keywords:
- Matching; education; start-up costs; venture capital; bureaucratic hurdles
(published)Reducing Start-up costs for New Firms: The Double Dividend on the Labor Market
Starting a firm with expansive potential is an option for educated and high-skilled workers. If there are labor market frictions, this additional option can be seen as reducing the chances of ending up in a low-wage job and hence as increasing the incentives for education. In a matching model, we show that reducing the start-up costs for new firms results in higher take-up rates of education. It also gives rise through a thick-market externality to higher rates of job creation for high-skilled labor as well as average match productivity. We provide empirical evidence to support our argument.
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#208Download full text
- JEL-Codes:
- C430; D290; L910; L960; O570
- Keywords:
- Purchasing Power Parity; Comparative Price Level
Output and Productivity Performance of Hong Kong and Singapore’s Transport and Communications Sector, 1990 to 2005
This paper examines the output and productivity performance of the Transport and Communication sector in Hong Kong and Singapore, from 1990 to 2005. The aim of the paper is two-fold. First, the paper introduces a method for derivation of appropriate currency converters or purchasing power parities (PPPs) to enable quantification of output and productivity at various disaggregated levels of the transport and communications sector. This method is based on the industry-of-origin approach as refined by the International Comparisons of Output and Productivity (ICOP) project based at the University of Groningen. Second, the paper will attempt to address differences in output and productivity levels between these two countries with regard to their current policies in transport and communications. It will also examine the impact of events such as the Asian financial crisis, the global downturn in 2001, the events of September 11, as well as the outbreak of the Severe Acute Respiratory Syndrome (SARS) in 2003 on the transport and communication sector.
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#207Download full text
- Keywords:
- income distributions, inequality, technology adoption, structural change
Concerning Inequality, Technology Adoption, and Structural Change
Empirical evidence suggests that there has been a divergence over time in income distributions across countries and within countries. In this paper we study a simple dynamic general equilibrium model of technology adoption which is consistent with these stylized facts. In our model, growth is endogenous, and agents are assumed to be heterogeneous in their initial holdings of wealth and capital. We find that in the presence of barriers or costs associated with the adoption of more productive technologies, inequalities in wealth and income may increase over time tending to delay the convergence in international income differences. The model is also capable of explaining the observed diversity in the growth pattern of transitional economies. According to the model, this diversity may be the result of variability in adoption costs, or the relative position of a transitional economy in the world income distribution.
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#206
Total Market Equilibria
The total market containing all assets is in equilibrium where all investors have the same utility functions and hold the same fully diversifed total market portfolio. This is not an equilibrium, however, where they have different utility functions, even if they are all risk averse. Then investors can all increase their utility by reallocating the market returns among themselves on a non pro-rata basis. Even in a perfect market the utility maximizing investment strategy for risk averse investors with different utility functions requires them to bear idiosyncratic risk, providing a role for asset transformation. The maximum or minimum asset prices at which an investor will transact in pursuance of greater portfolio utility are unique to that investor and the existing market state.