Forecasting with Vector Nonlinear Time Series Models

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

Common Features in Vector Nonlinear Time Series Models

This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting nonlinear common features. The aim of this thesis is to develop new econometric contributions for hypothesis testing and forecasting in these area. Both stationary and nonstationary time series are concerned. A definition of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with common features is set up for testing for common features. The proposed models are available for forecasting as well after being well specified. The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointegration, is examined. The ST cointegration nests the previously developed linear and threshold cointegration. An Ftypetest for examining the ST cointegration is derived when stationary transition variables are imposed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for common nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper considers forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail,and thereafter illustrated within two corresponding macroeconomic data sets.

Aerobic power and lean mass are indicators of competitive sprint performance among elite female cross-country skiers

The purpose of this study was to establish the optimal allometric models to predict International Ski Federation’s ski-ranking points for sprint competitions (FISsprint) among elite female cross-country skiers based on maximal oxygen uptake (V̇O2max) and lean mass (LM). Ten elite female cross-country skiers (age: 24.5±2.8 years [mean ± SD]) completed a treadmill roller-skiing test to determine V̇O2max (ie, aerobic power) using the diagonal stride technique, whereas LM (ie, a surrogate indicator of anaerobic capacity) was determined by dual-emission X-ray anthropometry. The subjects’ FISsprint were used as competitive performance measures. Power function modeling was used to predict the skiers’ FISsprint based on V̇O2max, LM, and body mass. The subjects’ test and performance data were as follows: V̇O2max, 4.0±0.3 L min-1; LM, 48.9±4.4 kg; body mass, 64.0±5.2 kg; and FISsprint, 116.4±59.6 points. The following power function models were established for the prediction of FISsprint: 3.91×105 ∙ VO -6.002maxand 6.95×1010 ∙ LM-5.25; these models explained 66% (P=0.0043) and 52% (P=0.019), respectively, of the variance in the FISsprint. Body mass failed to contribute to both models; hence, the models are based on V̇O2max and LM expressed absolutely. The results demonstrate that the physiological variables that reflect aerobic power and anaerobic capacity are important indicators of competitive sprint performance among elite female skiers. To accurately indicate performance capability among elite female skiers, the presented power function models should be used. Skiers whose V̇O2max differs by 1% will differ in their FISsprint by 5.8%, whereas the corresponding 1% difference in LM is related to an FISsprint difference of 5.1%, where both differences are in favor of the skier with higher V̇O2max or LM. It is recommended that coaches use the absolute expression of these variables to monitor skiers’ performance-related training adaptations linked to changes in aerobic power and anaerobic capacity.

Daily Calls Volume Forecasting

A massive amount has been written about forecasting but few articles are written about the development of time series models of call volumes for emergency services. In this study, we use different techniques for forecasting and make the comparison of the techniques for the call volume of the emergency service Rescue 1122 Lahore, Pakistan. For the purpose of this study data is taken from emergency calls of Rescue 1122 from 1st January 2008 to 31 December 2009 and 731 observations are used. Our goal is to develop a simple model that could be used for forecasting the daily call volume. Two different approaches are used for forecasting the daily call volume Box and Jenkins (ARIMA) methodology and Smoothing methodology. We generate the models for forecasting of call volume and present a comparison of the two different techniques.

The importance of body-mass exponent optimization for evaluation of performance capability in cross-country skiing

Introduction Performance in cross-country skiing is influenced by the skier’s ability to continuously produce propelling forces and force magnitude in relation to the net external forces. A surrogate indicator of the “power supply” in cross-country skiing would be a physiological variable that reflects an important performance-related capability, whereas the body mass itself is an indicator of the “power demand” experienced by the skier. To adequately evaluate an elite skier’s performance capability, it is essential to establish the optimal ratio between the physiological variable and body mass. The overall aim of this doctoral thesis was to investigate the importance of body-mass exponent optimization for the evaluation of performance capability in cross-country skiing. Methods In total, 83 elite cross-country skiers (56 men and 27 women) volunteered to participate in the four studies. The physiological variables of maximal oxygen uptake (V̇O2max) and oxygen uptake corresponding to a blood-lactate concentration of 4 mmol∙l-1 (V̇O2obla) were determined while treadmill roller skiing using the diagonal-stride technique; mean oxygen uptake (V̇O2dp) and upper-body power output (Ẇ) were determined during double-poling tests using a ski-ergometer. Competitive performance data for elite male skiers were collected from two 15-km classical-technique skiing competitions and a 1.25-km sprint prologue; additionally, a 2-km double-poling roller-skiing time trial using the double-poling technique was used as an indicator of upper-body performance capability among elite male and female junior skiers. Power-function modelling was used to explain the race and time-trial speeds based on the physiological variables and body mass. Results The optimal V̇O2max-to-mass ratios to explain 15-km race speed were V̇O2max divided by body mass raised to the 0.48 and 0.53 power, and these models explained 68% and 69% of the variance in mean skiing speed, respectively; moreover, the 95% confidence intervals (CI) for the body-mass exponents did not include either 0 or 1. For the modelling of race speed in the sprint prologue, body mass failed to contribute to the models based on V̇O2max, V̇O2obla, and V̇O2dp. The upper-body power output-to-body mass ratio that optimally explained time-trial speed was Ẇ ∙ m-0.57 and the model explained 63% of the variance in speed. Conclusions The results in this thesis suggest that V̇O2max divided by the square root of body mass should be used as an indicator of performance in 15-km classical-technique races among elite male skiers rather than the absolute or simple ratio-standard scaled expression. To optimally explain an elite male skier’s performance capability in sprint prologues, power-function models based on oxygen-uptake variables expressed absolutely are recommended. Moreover, to evaluate elite junior skiers’ performance capabilities in 2-km double-poling roller-skiing time trials, it is recommended that Ẇ divided by the square root of body mass should be used rather than absolute or simple ratio-standard scaled expression of power output.

Optimal V. O2max-to-mass ratio for predicting 15 km performance among elite male cross-country skiers

The aim of this study was 1) to validate the 0.5 body-mass exponent for maximal oxygen uptake (V. O2max) as the optimal predictor of performance in a 15 km classical-technique skiing competition among elite male cross-country skiers and 2) to evaluate the influence of distance covered on the body-mass exponent for V. O2max among elite male skiers. Twenty-four elite male skiers (age: 21.4±3.3 years [mean ± standard deviation]) completed an incremental treadmill roller-skiing test to determine their V. O2max. Performance data were collected from a 15 km classicaltechnique cross-country skiing competition performed on a 5 km course. Power-function modeling (ie, an allometric scaling approach) was used to establish the optimal body-mass exponent for V . O2max to predict the skiing performance. The optimal power-function models were found to be race speed = 8.83⋅(V . O2max m-0.53) 0.66 and lap speed = 5.89⋅(V . O2max m-(0.49+0.018lap)) 0.43e0.010age, which explained 69% and 81% of the variance in skiing speed, respectively. All the variables contributed to the models. Based on the validation results, it may be recommended that V. O2max divided by the square root of body mass (mL⋅min−1 ⋅kg−0.5) should be used when elite male skiers’ performance capability in 15 km classical-technique races is evaluated. Moreover, the body-mass exponent for V . O2max was demonstrated to be influenced by the distance covered, indicating that heavier skiers have a more pronounced positive pacing profile (ie, race speed gradually decreasing throughout the race) compared to that of lighter skiers.

Testing common nonlinear features in vector nonlinear autoregressive models

This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).

Pedal : identification of models for duodenal administration of levodopa

Backgound and aims: The main purpose of the PEDAL study is to identify and estimate sample individual pharmacokinetic- pharmacodynamic (PK/PD) models for duodenal infusion of levodopa/carbidopa (Duodopa®) that can be used for in numero simulation of treatment strategies. Other objectives are to study the absorption of Duodopa® and to form a basis for power calculation for a future larger study. PK/PD based on oral levodopa is problematic because of irregular gastric emptying. Preliminary work with data from [Gundert-Remy U et al. Eur J Clin Pharmacol 1983;25:69-72] suggested that levodopa infusion pharmacokinetics can be described by a two-compartment model. Background research led to a hypothesis for an effect model incorporating concentration-unrelated fluctuations, more complex than standard E-max models. Methods: PEDAL involved a few patients already on Duodopa®. A bolus dose (normal morning dose plus 50%) was given after a washout during night. Data collection continued until the clinical effect was back at baseline. The procedure was repeated on two non-consecutive days per patient. The following data were collected in 5 to 15 minutes intervals: i) Accelerometer data. ii) Three e-diary questions about ability to walk, feelings of “off” and “dyskinesia”. iii) Clinical assessment of motor function by a physician. iv) Plasma concentrations of levodopa, carbidopa and the metabolite 3-O-methyldopa. The main effect variable will be the clinical assessment. Results: At date of abstract submission, lab analyses were currently being performed. Modelling results, simulation experiments and conclusions will be presented in our poster.

Likelihood prediction for generalized linear mixed models under covariate uncertainty

This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable generalized linear model, it has been shown that in complicated cases LP produces better results than already know methods.