Mixed effect models for absolute log returns of ultra high frequency data

Continuous‐time autoregressive moving average (CARMA) processes have recently been used widely in the modelling of non‐uniformly spaced data and as a tool for dealing with high‐frequency data of the form ,n = 0, 1, 2,…, where Δ is small and positive. Such data occur in many fields of application, particularly in finance and in the study of turbulence. This article is concerned with the characteristics of the process , when Δ is small and the underlying continuous‐time process is a specified CARMA process.

On continuous-time threshold ARMA processes

We review some applications of continuous-time ARMA processes in the modelling of time series observed at discrete times t 1,…, t N . The problem of finding a continuous-time ARMA process in which a given discrete-time ARMA process can be “embedded” is discussed and some of the properties of a family of continuous-time analogues of Tong’s SETARMA models are considered. An approach to inference for such models is described and illustrated with reference to a variety of data sets.KeywordsAutocorrelation FunctionStochastic Differential EquationTime Series AnalysisARMA ModelTransition DistributionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A general approach for modeling the volatility process in continuous-time is based on the convolution of a kernel with a non-decreasing Levy process, which is non-negative if the kernel is non-negative. Within the framework of Continuous-time Auto-Regressive Moving-Average (CARMA) processes, we derive a necessary condition for the kernel to be non-negative, and propose a numerical method for checking the non-negativity of a kernel function. These results can be lifted to solving a similar problem with another approach to modeling volatility via the COntinuous-time Generalized Auto-Regressive Conditional Heteroscedastic (COGARCH) processes.

Abstract: Econometric models involving a discrete outcome dependent variable abound in the finance and accounting literatures. However, much of the literature to date utilises a basic or standard logit model. Capitalising on recent developments in the discrete choice literature, we examine three advanced (or non‐IID) logit models, namely: nested logit, mixed logit and latent class MNL. Using an illustration from corporate takeovers research, we compare the explanatory and predictive performance of each class of advanced model relative to the standard model. We find that in all cases the more advanced logit model structures, which correct for the highly restrictive IID and IIA conditions, provide significantly greater explanatory power than standard logit. Mixed logit and latent class MNL models exhibited the highest overall predictive accuracy on a holdout sample, while the standard logit model performed the worst. Moreover, the analysis of marginal effects of all models indicates that use of advanced models can lead to more insightful and behaviourally meaningful interpretations of the role and influence of explanatory variables and parameter estimates in model estimation. The results of this paper have implications for the use of more optimal logit structures in future research and practice.

Distribution patterns and conservation status of four bustard species (Family Otididae) in a montane grassland of South Africa

This paper demonstrates the potential advantage of using a linear, mixed-effect state-space model for statistical downscaling of climate variables compared to the frequently used approach of linear regression. This comparison leads to the development of a method for estimation of model parameters using the EM algorithm approach. The model is applied to the prediction of temperature and rainfall statistics at both a sub-tropical and temperate location in Australia. The results indicate that for lead times of 1–10 years this state-space approach is able to predict observed seasonal temperature and rainfall means with substantially greater precision than climatology, multivariate linear regression (MLR) or a standard linear state-space (LSS) approach. The model is seen as a first step in the development of a short-term climate change projection system that will utilise both historical climate data as well as dynamically derived mean climate change projection information obtained from global climate models (GCMs). Copyright © 2010 John Wiley & Sons, Ltd.

PurposeThe main purpose of this paper is to examine the asymmetry and long memory properties in the volatility of the stock indices of the PIIGS economies (Portugal, Ireland, Italy, Greece and Spain).Design/methodology/approachThe paper utilizes the wavelets approach (based on Haar, Daubechies‐4, Daubechies‐12 and Daubechies‐20 wavelets) and the GARCH class of models (namely, ARFIMA (p,d′,q)‐GARCH (1,1), IGARCH (1,1), FIGARCH (1,d,0), FIGARCH (1,d,1), EGARCH (1,1) and FIEGARCH (1,d,1)) to accomplish the desired goals.FindingsThe findings provide evidence in support of the presence of long range dependence in the various proxies of volatility of the PIIGS economies. The results from the wavelet approach also support the Taylor effect in the volatility proxies. The results show that ARFIMA (p,d′,q)‐FIGARCH (1,d,0) model specification is better able to capture the long memory property of conditional volatility than the conventional GARCH and IGARCH models. In addition, the ARFIMA (p,d′,q)‐FIEGARCH (1,d,1) model is better able to capture the asymmetric long memory feature in the conditional volatility.Originality/valueThis paper has both methodological and empirical originality. On the methodological side, the study applies the wavelet technique on the major proxies of volatility (squared returns, absolute returns, logarithm squared returns and the range) because the wavelet‐based estimator exhibits superior properties in modeling the behavior of the volatility of stock returns. On the empirical side, the paper finds asymmetry and long range dependence in the conditional volatility of the stock returns in PIIGS economies using the GARCH family of models.

Abstract. Embedding a discrete‐time autoregressive moving average (DARMA) process in a continuous‐time ARMA (CARMA) process has been discussed by many authors. These authors have considered the relationship between the autocovariance structures of continuous‐time and related discrete‐time processes. In this article, we treat the problem from a slightly different point of view. We define embedding in a more rigid way by taking account of the probability structure. We consider Gaussian processes. First we summarize the necessary and sufficient condition for a DARMA process to be able to be embedded in a CARMA process. Secondly, we show a concrete condition such that a DARMA process can be embeddable in a CARMA process. This condition is new and general. Thirdly, we show some special cases including new examples. We show how we can examine embeddability for these special cases.

PurposeAluminium alloys can be used as lightweight and high-strength materials in combination with the technology of laser beam welding, an efficient joining method, in the manufacturing of automotive parts. The purposes of this paper are to conduct laser welding experiments with Al2024 in the lap joint configuration, model the laser welding process parameters of Al2024 alloys and use propounded models to optimize the process parameters.Design/methodology/approachLaser welding of Al2024 alloy has been conducted in the lap joint configuration. Then, the influences of explanatory variables (laser peak power, scanning speed and frequency) on outcome variables (weld width [WW], throat length [TL] and breaking load [BL]) have been investigated with Poisson regression analysis of the data set derived from experimentation. Thereafter, a multi-objective genetic algorithm (MOGA) has been used using MATLAB to find the optimum solutions. The effects of various input process parameters on the responses have also been analysed using response surface plots.FindingsThe promulgated statistical models, derived with Poisson regression analysis, are evinced to be well-fit ones using the analysis of deviance approach. Pareto fronts have been used to demonstrate the optimization results, and the maximized load-bearing capacity is computed to be 1,263 N, whereas the compromised WW and TL are 714 µm and 760 µm, respectively.Originality/valueThis work of conducting laser welding of lap joint of Al2024 alloy incorporating the Taguchi method and optimizing the input process parameters with the promulgated statistical models proffers a neoteric perspective that can be useful to the manufacturing industry.

General‐to‐Specific (GETS) modelling has witnessed major advances thanks to the automation of multi‐path GETS specification search. However, the estimation complexity associated with financial models constitutes an obstacle to automated multi‐path GETS modelling in finance. Making use of a recent result we provide and study simple but general and flexible methods that automate financial multi‐path GETS modelling. Starting from a general model where the mean specification can contain autoregressive terms and explanatory variables, and where the exponential volatility specification can include log‐ARCH terms, asymmetry terms, volatility proxies and other explanatory variables, the algorithm we propose returns parsimonious mean and volatility specifications.

<p>By modelling and forecasting  of meteorological  time  series it is possible to  improve   understanding  of  the  weather dynamics and fluctuations as a result of climate change . The most frequently used forecasting models are exponential smoothing, ARIMA models (Box and Jenkins, 1970), state-space models (Harvey, 1989) and innovations State Space Models (Hyndman et al., 2008).</p><p>The aim of this study was to check the effectiveness of the coupled TBATS and Support Vector Machines (SVM) model, supplied with some measured meteorological quantities to forecast air temperature for six years for four climatic localizations in Europe. The study was calculated from northern (Jokioinen in Finland), central (Dikopshof located in the west part of Germany and Nossen in the south part of Germany) and southern (Lleida in Spain) Europe to present different climatic conditions. Jokioinen city has a subarctic climate that has severe winters, with cool and short summers and strong seasonality. Lleida has a semi-arid climate with Mediterranean. Dikopshof represents maritime temperate climate. There are significant precipitation throughout the year in Dikopshof and Nossen. In the study we study on air temperature dataset collected on a daily basis from January 1st 1980 to December 31st 2010 (11322 days).</p><p>For all the studied sites coupled TBATS/SVM models occurred to be effective in predicting air temperature courses, giving an improved precision (up to 25%) in forecasting of the seasonality and local temperature variations, compared to pure SVM or TBATS modelling. The precision of prediction of the maximum and minimum air temperatures strongly depended on the dynamics of the weather conditions, and varied for different climatic zones.</p><p>This study has been partly financed from the funds of the Polish National Centre for Research and Development in frame of the project: MSINiN, contract number: BIOSTRATEG3/343547/8/NCBR/2017.</p><p> </p><p>Reference to a journal publication:</p><p>BOX, G.E.P. – Jenkins, G. 1970. Time Series Analysis: forecasting and control. Holden-Day, p. 20-31.</p><p>HARVEY A. 1989. Forecasting Structural Time Series Model and the Kalman Filter. New York, Cambridge University press., p. 32-41.</p><p>HYNDMAN, R.J. – KOEHLER, A.B. – ORD, J.K. – SNYDER, R.D. 2008. Forecasting with Exponential Smoothing: The State Space Approach. Springer-Verlag, p. 50-62.</p>

Assessing spatial dynamics of a Pinus nigra subsp. salzmannii natural stand combining point and polygon patterns analysis

BackgroundGlobally, HIV/AIDS remains a significant public health issue particularly in Sub-Saharan Africa. Media exposure plays a significant role in raising community knowledge about HIV. Therefore, this study aimed to investigate the effect of media on comprehensive knowledge of HIV and its spatial distribution among reproductive-age women in Ethiopia.MethodsA secondary data analysis was done based on the 2016 Ethiopian Demographic and Health Surveys (EDHS). A total weighted sample of 15,683 reproductive-age women was included for analysis. For the spatial analysis, ArcGIS version 10.3 and SaTScan version 9.6 software were employed to explore the spatial distribution of comprehensive knowledge of HIV/AIDS and for identifying significant hotspot areas. For associated factors, the mixed-effect logistic regression model was fitted. Deviance and ICC were used for model comparison. In the multivariable analysis, Adjusted Odds Ratio (AOR) with 95% Confidence Interval (CI) was reported to declare significantly associated factors of comprehensive knowledge of HIV/AIDS.ResultsThe spatial analysis revealed that the spatial distribution of comprehensive knowledge of HIV/AIDS among reproductive-age women was significantly varied across the country. The SaTScan analysis identified significant clusters in the entire Somali region, the eastern part of Dire Dawa and Harari regions. Being rural (AOR = 1.52,95% CI:1.21–1.91), maternal age 25–34 years (AOR = 1.26,95% CI:1.14–1.40), aged ≥35 years (AOR = 1.20,95%CI:1.07–1.35), being Muslim (AOR = 0.68,95% CI:0.60–0.78), being protestant (AOR = 0.83,95% CI:0.71–0.96), poorer wealth (AOR = 1.26,95%CI:1.06–1.51), middle wealth (AOR = 1.34,95%CI:1.11–1.60), richer wealth (AOR = 1.36,95% CI:1.12–1.63), richest wealth (AOR = 1.72,95% CI:1.37–2.15), reading newspaper (AOR = 1.20,95%CI: 1.06–1.37), listening radio (AOR = 1.24,95% CI:1.10, 1.41), covered by health insurance (AOR = 1.23,95%CI:1.01–1.51), having primary education (AOR = 1.77,95% CI:1.57–1.99), having secondary education (AOR = 2.45,95%CI:2.10–2.86) and having higher education (AOR = 3.04,95%CI:2.52–3.65) were significantly associated with comprehensive knowledge of HIV/AIDS.ConclusionSpatial distribution of comprehensive knowledge of HIV/AIDS among reproductive-age women was significantly varied across the country with significant hotspot areas with poor comprehensive knowledge of HIV/AIDS identified in the Somali region, the eastern part of Dire Dawa and Harari Regions. media exposure was a significant predictor of comprehensive knowledge of HIV/AIDS among reproductive-age women in Ethiopia. Therefore, the government should scale up public health programs in the hot spot areas and provide health information using different media.

Statistics is a branch of mathematics concerned with the collection, quantification, analysis, interpretation, and presentation of real-world data, and the use of probability theory to estimate population parameters with these data. Spatial statistics is a subset of statistics that is concerned with handling the special problems associated with geographically distributed data, which include spatial point patterns, regional and lattice measurement aggregations, irregularly spaced site-specific measurements on a surface, and image analysis. Meanwhile, econometrics is concerned with the application of statistical methods to the study of economic data and problems. When coining the term spatial econometrics in 1979, Paelinck and Klaassen characterized it as a subset of econometrics that is concerned with the role of spatial dependence in regional economic model response and explanatory variables, asymmetries in spatial relationships, the specification of geographic structure governing spatial interactions, and the explicit modeling of space. We outline and discuss principal similarities (e.g., testing for the presence of spatial autocorrelation) and differences (e.g., map generalization) between spatial statistics and spatial econometrics. In doing so, our goal is to help clarify past, present, and future relationships between these two subfields.