Testing stability in a spatial unilateral autoregressive model

Least squares estimator of the stability parameter $\varrho := |\alpha| + |\beta|$ for a spatial unilateral autoregressive process $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\varepsilon_{k,\ell}$ is investigated. Asymptotic normality with a scaling factor $n^{5/4}$ is shown in the unstable case, i.e., when $\varrho = 1$, in contrast to the AR(p) model $X_k=\alpha_1 X_{k-1}+... +\alpha_p X_{k-p}+ \varepsilon_k$, where the least squares estimator of the stability parameter $\varrho :=\alpha_1 + ... + \alpha_p$ is not asymptotically normal in the unstable, i.e., in the unit root case

Modelling and forecasting the UK tourism growth cycle in Algarve

Over the past three decades, Portugal has developed a strong economic dependence on tourism, which has several implications for the country's overall economic development. Tourism is an activity that is interrelated strongly with the economic system since Portugal as a whole and specific regions in particular rely on the performance of tourism for their economic activity. Moreover, because economic cycles affect tourism development, it is highly vulnerable to economic fluctuations. Most tourists who visit Portugal are from the European Union, especially Western Europe. Statistics are based on the number of overnight stays in hotel accommodation and other similar establishments. In 2005, the main source markets were the UK (30.7%), Germany (16.5%), Spain (11.5%), the Netherlands (6.8%), France (4.7%), Ireland (3.6%) and Italy (3.1%). These values show that the UK has the greatest share of visitors to Algarve. The purpose of this paper is to propose a modelling approach that best fits the tourism flow pattern in order to support forecasting. The paper contributes to our understanding of the relationship between economic cycles and tourism flows to Portugal (Algarve) and explores the potential of applying the diffusion index model proposed by Stock and Watson (1999, 2002) for tourism demand forecasting

G\"odel Type Metrics in Three Dimensions

We show that the G{\" o}del type Metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations. There exists only one first order partial differential equation satisfied by the components of fluid's velocity vector field. We then show that the same metrics solve the field equations of the topologically massive gravity where the two dimensional background geometry is a space of constant negative Gaussian curvature. We discuss the possibility that the G{\" o}del Type Metrics to solve the Ricci and Cotton flow equations. When the vector field $u^{\mu}$ is a Killing vector field we finally show that the stationary G{\" o}del Type Metrics solve the field equations of the most possible gravitational field equations where the interaction lagrangian is an arbitrary function of the electromagnetic field and the curvature tensors.Comment: 17 page

Missing data imputation of high-resolution temporal climate time series data

© 2020 The Authors. Meteorological Applications published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society. Analysis of high-resolution data offers greater opportunity to understand the nature of data variability, behaviours, trends and to detect small changes. Climate studies often require complete time series data which, in the presence of missing data, means imputation must be undertaken. Research on the imputation of high-resolution temporal climate time series data is still at an early phase. In this study, multiple approaches to the imputation of missing values were evaluated, including a structural time series model with Kalman smoothing, an autoregressive integrated moving average (ARIMA) model with Kalman smoothing and multiple linear regression. The methods were applied to complete subsets of data from 12 month time series of hourly temperature, humidity and wind speed data from four locations along the coast of Western Australia. Assuming that observations were missing at random, artificial gaps of missing observations were studied using a five-fold cross-validation methodology with the proportion of missing data set to 10%. The techniques were compared using the pooled mean absolute error, root mean square error and symmetric mean absolute percentage error. The multiple linear regression model was generally the best model based on the pooled performance indicators, followed by the ARIMA with Kalman smoothing. However, the low error values obtained from each of the approaches suggested that the models competed closely and imputed highly plausible values. To some extent, the performance of the models varied among locations. It can be concluded that the modelling approaches studied have demonstrated suitability in imputing missing data in hourly temperature, humidity and wind speed data and are therefore recommended for application in other fields where high-resolution data with missing values are common

The Impact of new Execution Venues on European Equity Markets’ Liquidity – The Case of Chi-X

With the Markets in Financial Instruments Directive in effect since November 2007, new trading venues have emerged in European equities trading, among them Chi-X. This paper analyzes the impact of this new market entrant on the home market as well as on consolidated liquidity of French blue chip equities, newly tradable on Chi-X. Our findings suggest that owing to this new competition the home market’s liquidity has enhanced. This is apparently due to the battle for order flow which results in narrower spreads and increased market depth. These results imply that overall liquidity in a virtually consolidated order book is in the French case higher than without the new competitor

Information ontrol and the exercise of power in the obstetrical encounter

Interactions between doctor and patient involve participants with unequal power and possibly different interests. While a number of studies have focused upon the doctor/patient relationship, few have examined the utility of the concept of power and its capacity to help us understand the outcome of these interactions. The information sought by pregnant women from their obstetricians is used to provide a case study of one conceptualization and test of the utility of the concept of power. Pregnant women and their obstetricians are found to have different perceptions of the information that should be exchanged during their interactions. Women generally fail to obtain the information they want. Lower social class patients desire more and obtain less information than their higher status counterparts

Consistent Anisotropic Repulsions for Simple Molecules

We extract atom-atom potentials from the effective spherical potentials that suc cessfully model Hugoniot experiments on molecular fluids, e.g., $O_2$ and $N_2$. In the case of $O_2$ the resulting potentials compare very well with the atom-atom potentials used in studies of solid-state propertie s, while for $N_2$ they are considerably softer at short distances. Ground state (T=0K) and room temperatu re calculations performed with the new $N-N$ potential resolve the previous discrepancy between experimental and theoretical results.Comment: RevTeX, 5 figure