Econometric Modelling with Time Series : Specification, Estimation and Testing

This book provides a general framework for specifying, estimating, and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalized method of moments estimation, nonparametric estimation, and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.

Self excitation in equity indices

A "self-exciting" market is one in which the probability of observing a crash increases in response to the occurrence of a crash. It essentially describes cases where the initial crash serves to weaken the system to some extent, making subsequent crashes more likely. This thesis investigates if equity markets possess this property. A self-exciting extension of the well-known jump-based Bates (1996) model is used as the workhorse model for this thesis, and a particle-filtering algorithm is used to facilitate estimation by means of maximum likelihood. The estimation method is developed so that option prices are easily included in the dataset, leading to higher quality estimates. Equilibrium arguments are used to price the risks associated with the time-varying crash probability, and in turn to motivate a risk-neutral system for use in option pricing. The option pricing function for the model is obtained via the application of widely-used Fourier techniques. An application to S&P500 index returns and a panel of S&P500 index option prices reveals evidence of self excitation.

Investigation into the bond between CFRP and steel tubes

CFRP material has been widely used to strengthen concrete structures. There is an increasing trend of using CFRP in strengthening steel structures. The bond between steel and CFRP is a key issue. Relatively less work has been done on the bond between CFRP and a curved surface which is often found in tubular structures. This paper reports a study on the bond between CFRP and steel tubes. A series of tensile tests were conducted with different bond lengths and number of layers. The types of adhesive and specimen preparation methods varied in the testing program. High modulus CFRP was used. Tests were carried out to measure the modulus and tensile strength of CFRP. Strain gages were mounted on different layers of CFRP. The stress distributions across the layers of the CFRP were established. Models were developed to estimate the maximum load for a given CFRP arrangement.

A model of workplace safety incorporating worker interactions and simple interventions

Although there was substantial research into the occupational health and safety sector over the past forty years, this generally focused on statistical analyses of data related to costs and/or fatalities and injuries. There is a lack of mathematical modelling of the interactions between workers and the resulting safety dynamics of the workplace. There is also little work investigating the potential impact of different safety intervention programs prior to their implementation. In this article, we present a fundamental, differential equation-based model of workplace safety that treats worker safety habits similarly to an infectious disease in an epidemic model. Analytical results for the model, derived via phase plane and stability analysis, are discussed. The model is coupled with a model of a generic safety strategy aimed at minimising unsafe work habits, to produce an optimal control problem. The optimal control model is solved using the forward-backward sweep numerical scheme implemented in Matlab.

Factorial validity and invariance of questionnaires measuring social-cognitive determinants of physical activity among adolescent girls

Background There are few theoretically derived questionnaires of physical activity determinants among youth, and the existing questionnaires have not been subjected to tests of factorial validity and invariance, The present study employed confirmatory factor analysis (CFA) to test the factorial validity and invariance of questionnaires designed to be unidimensional measures of attitudes, subjective norms, perceived behavioral control, and self-efficacy about physical activity. Methods Adolescent girls in eighth grade from two cohorts (N = 955 and 1,797) completed the questionnaires at baseline; participants from cohort 1 (N = 845) also completed the questionnaires in ninth grade (i.e., 1-year follow-up). Factorial validity and invariance were tested using CFA with full-information maximum likelihood estimation in AMOS 4.0, Initially, baseline data from cohort 1 were employed to test the fit and, when necessary, to modify the unidimensional models. The models were cross-validated using a multigroup analysis of factorial invariance on baseline data from cohorts 1 and 2, The models then were subjected to a longitudinal analysis of factorial invariance using baseline and follow-up data from cohort i, Results The CFAs supported the fit of unidimensional models to the four questionnaires, and the models were cross-validated, as indicated by evidence of multigroup factorial invariance, The models also possessed evidence of longitudinal factorial invariance. Conclusions Evidence was provided for the factorial validity and the invariance of the questionnaires designed to be unidimensional measures of attitudes, subjective norms, perceived behavioral control, and self-efficacy about physical activity among adolescent girls, (C) 2000 American Health Foundation and academic Press.

Development and validation of the ankle fracture outcome of rehabilitation measure (A-FORM)

Study Design Delphi panel and cohort study. Objective To develop and refine a condition-specific, patient-reported outcome measure, the Ankle Fracture Outcome of Rehabilitation Measure (A-FORM), and to examine its psychometric properties, including factor structure, reliability, and validity, by assessing item fit with the Rasch model. Background To our knowledge, there is no patient-reported outcome measure specific to ankle fracture with a robust content foundation. Methods A 2-stage research design was implemented. First, a Delphi panel that included patients and health professionals developed the items and refined the item wording. Second, a cohort study (n = 45) with 2 assessment points was conducted to permit preliminary maximum-likelihood exploratory factor analysis and Rasch analysis. Results The Delphi panel reached consensus on 53 potential items that were carried forward to the cohort phase. From the 2 time points, 81 questionnaires were completed and analyzed; 38 potential items were eliminated on account of greater than 10% missing data, factor loadings, and uniqueness. The 15 unidimensional items retained in the scale demonstrated appropriate person and item reliability after (and before) removal of 1 item (anxious about footwear) that had a higher-than-ideal outfit statistic (1.75). The “anxious about footwear” item was retained in the instrument, but only the 14 items with acceptable infit and outfit statistics (range, 0.5–1.5) were included in the summary score. Conclusion This investigation developed and refined the A-FORM (Version 1.0). The A-FORM items demonstrated favorable psychometric properties and are suitable for conversion to a single summary score. Further studies utilizing the A-FORM instrument are warranted. J Orthop Sports Phys Ther 2014;44(7):488–499. Epub 22 May 2014. doi:10.2519/jospt.2014.4980

Tensor-based analysis of genetic influences on brain integrity using DTI in 100 twins

Information from the full diffusion tensor (DT) was used to compute voxel-wise genetic contributions to brain fiber microstructure. First, we designed a new multivariate intraclass correlation formula in the log-Euclidean framework. We then analyzed used the full multivariate structure of the tensor in a multivariate version of a voxel-wise maximum-likelihood structural equation model (SEM) that computes the variance contributions in the DTs from genetic (A), common environmental (C) and unique environmental (E) factors. Our algorithm was tested on DT images from 25 identical and 25 fraternal twin pairs. After linear and fluid registration to a mean template, we computed the intraclass correlation and Falconer's heritability statistic for several scalar DT-derived measures and for the full multivariate tensors. Covariance matrices were found from the DTs, and inputted into SEM. Analyzing the full DT enhanced the detection of A and C effects. This approach should empower imaging genetics studies that use DTI.

The multivariate A/C/E model and the genetics of fiber architecture

We present a new algorithm to compute the voxel-wise genetic contribution to brain fiber microstructure using diffusion tensor imaging (DTI) in a dataset of 25 monozygotic (MZ) twins and 25 dizygotic (DZ) twin pairs (100 subjects total). First, the structural and DT scans were linearly co-registered. Structural MR scans were nonlinearly mapped via a 3D fluid transformation to a geometrically centered mean template, and the deformation fields were applied to the DTI volumes. After tensor re-orientation to realign them to the anatomy, we computed several scalar and multivariate DT-derived measures including the geodesic anisotropy (GA), the tensor eigenvalues and the full diffusion tensors. A covariance-weighted distance was measured between twins in the Log-Euclidean framework [2], and used as input to a maximum-likelihood based algorithm to compute the contributions from genetics (A), common environmental factors (C) and unique environmental ones (E) to fiber architecture. Quanititative genetic studies can take advantage of the full information in the diffusion tensor, using covariance weighted distances and statistics on the tensor manifold.

Quantification of stability in an agility drill using linear and nonlinear measures of variability

This study implemented linear and nonlinear methods of measuring variability to determine differences in stability of two groups of skilled (n = 10) and unskilled (n = 10) participants performing 3m forward/backward shuttle agility drill. We also determined whether stability measures differed between the forward and backward segments of the drill. Finally, we sought to investigate whether local dynamic stability, measured using largest finite-time Lyapunov exponents, changed from distal to proximal lower extremity segments. Three-dimensional coordinates of five lower extremity markers data were recorded. Results revealed that the Lyapunov exponents were lower (P < 0.05) for skilled participants at all joint markers indicative of higher levels of local dynamic stability. Additionally, stability of motion did not differ between forward and backward segments of the drill (P > 0.05), signifying that almost the same control strategy was used in forward and backward directions by all participants, regardless of skill level. Furthermore, local dynamic stability increased from distal to proximal joints (P < 0.05) indicating that stability of proximal segments are prioritized by the neuromuscular control system. Finally, skilled participants displayed greater foot placement standard deviation values (P < 0.05), indicative of adaptation to task constraints. The results of this study provide new methods for sport scientists, coaches to characterize stability in agility drill performance.

An alternative approach to describing agility in sports through establishment of a relationship between velocity and radius of curvature

Agility is an essential part of many athletic activities. Currently, agility drill duration is the sole criterion used for evaluation of agility performance. The relationship between drill duration and factors such as acceleration, deceleration and change of direction, however, has not been fully explored. This paper provides a mathematical description of the relationship between velocity and radius of curvatures in an agility drill through implementation of a power law (PL). Two groups of skilled and unskilled participants performed a cyclic forward/backward shuttle agility test. Kinematic data was recorded using motion capture system at a sampling rate of 200 Hz. The logarithmic relationship between tangential velocity and radius of curvature of participant trajectories in both groups was established using the PL. The slope of the regression line was found to be 0.26 and 0.36, for the skilled and unskilled groups, respectively. The magnitudes of regression line slope for both groups were approximately 0.3 which is close to the expected 1/3 value. Results are an indication of how the PL could be implemented in an agility drill thus opening the way for establishment of a more representative measure of agility performance instead of drill duration.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual's previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag-recapture data and tag-recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

An extravariation model for improving confidence intervals of population size estimates from removal data

We propose a new model for estimating the size of a population from successive catches taken during a removal experiment. The data from these experiments often have excessive variation, known as overdispersion, as compared with that predicted by the multinomial model. The new model allows catchability to vary randomly among samplings, which accounts for overdispersion. When the catchability is assumed to have a beta distribution, the likelihood function, which is refered to as beta-multinomial, is derived, and hence the maximum likelihood estimates can be evaluated. Simulations show that in the presence of extravariation in the data, the confidence intervals have been substantially underestimated in previous models (Leslie-DeLury, Moran) and that the new model provides more reliable confidence intervals. The performance of these methods was also demonstrated using two real data sets: one with overdispersion, from smallmouth bass (Micropterus dolomieu), and the other without overdispersion, from rat (Rattus rattus).

Stock-recruitment relationships of the tiger prawns (Penaeus esculentus and Penaeus semisulcatus) in the Australian Northern Prawn Fishery

This paper investigates the stock-recruitment and equilibrium yield dynamics for the two species of tiger prawns (Penaeus esculentus and Penaeus semisulcatus) in Australia's most productive prawn fishery: the Northern Prawn Fishery. Commercial trawl logbooks for 1970-93 and research surveys are used to develop population models for these prawns. A population model that incorporates continuous recruitment is developed. Annual spawning stock and recruitment indices are then estimated from the population model. Spawning stock indices represent the abundance of female prawns that are likely to spawn; recruitment indices represent the abundance of all prawns less than a certain size. The relationships between spawning stock and subsequent recruitment (SRR), between recruitment and subsequent spawning stock (RSR), and between recruitment and commercial catch were estimated through maximum-likelihood models that incorporated autoregressive terms. Yield as a function of fishing effort was estimated by constraining to equilibrium the SRR and RSR. The resulting production model was then used to determine maximum sustainable yield (MSY) and its corresponding fishing effort (f(MSY)). Long-term yield estimates for the two tiger prawn species range between 3700 and 5300 t. The fishing effort at present is close to the level that should produce MSY for both species of tiger prawns. However, current landings, recruitment and spawning stock are below the equilibrium values predicted by the models. This may be because of uncertainty in the spawning stock-recruitment relationships, a change in carrying capacity, biased estimates of fishing effort, unreliable catch statistics, or simplistic assumptions about stock structure. Although our predictions of tiger prawn yields are uncertain, management will soon have to consider new measures to counteract the effects of future increases in fishing effort.

Genetic variation and responses in reproductive performance of sows in lines selected for growth rate under restricted feeding

The objective of this study was to examine genetic changes in reproduction traits in sows (total number born (TNB), number born alive (NBA), average piglet birth weight (ABW) and number of piglets weaned (NW), body weight prior to mating (MW), gestation length (GL) and daily food intake during lactation (DFI)) in lines of Large White pigs divergently selected over 4 years for high and low post-weaning growth rate on a restricted ration. Heritabilities and repeatabilities of the reproduction traits were also determined. The analyses were carried out on 913 litter records using average information-restricted maximum likelihood method applied to single trait animal models. Estimates of heritability for most traits were small, except for ABW (0·33) and MW (0·35). Estimates of repeatability were slightly higher than those of heritability for TNB, NBA and NW, but they were almost identical for ABW, MW, GL and DFI. After 4 years of selection, the high growth line sows had significantly heavier body weight prior to mating and produced significantly more piglets born alive with heavier average birth weight than the low line sows. There were, however, no statistical differences between the selected lines in TNB or NW. The lower food intake of high relative to low line sows during lactation was not significant, indicating that daily food intake differences found between grower pigs in the high and low lines (2·71 v. 2·76 kg/day, s.e.d. 0·024) on ad libitum feeding were not fully expressed in lactating sows. It is concluded that selection for growth rate on the restricted ration resulted in beneficial effects on important measures of reproductive performance of the sows.

Genetic influences on handedness: data from 25,732 Australian and Dutch twin families

Handedness refers to a consistent asymmetry in skill or preferential use between the hands and is related to lateralization within the brain of other functions such as language. Previous twin studies of handedness have yielded inconsistent results resulting from a general lack of statistical power to find significant effects. Here we present analyses from a large international collaborative study of handedness (assessed by writing/drawing or self report) in Australian and Dutch twins and their siblings (54,270 individuals from 25,732 families). Maximum likelihood analyses incorporating the effects of known covariates (sex, year of birth and birth weight) revealed no evidence of hormonal transfer, mirror imaging or twin specific effects. There were also no differences in prevalence between zygosity groups or between twins and their singleton siblings. Consistent with previous meta-analyses, additive genetic effects accounted for about a quarter (23.64%) of the variance (95%CI 20.17, 27.09%) with the remainder accounted for by non-shared environmental influences. The implications of these findings for handedness both as a primary phenotype and as a covariate in linkage and association analyses are discussed.