Threshold Autoregressive Model for a Time Series Data

In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.

Stochastic processes and their applications time dependent solutions for some queueing and inventory models

The objective of this thesis is to study the time dependent behaviour of some complex queueing and inventory models. It contains a detailed analysis of the basic stochastic processes underlying these models. In the theory of queues, analysis of time dependent behaviour is an area.very little developed compared to steady state theory. Tine dependence seems certainly worth studying from an application point of view but unfortunately, the analytic difficulties are considerable. Glosod form solutions are complicated even for such simple models as M/M /1. Outside M/>M/1, time dependent solutions have been found only in special cases and involve most often double transforms which provide very little insight into the behaviour of the queueing systems themselves. In inventory theory also There is not much results available giving the time dependent solution of the system size probabilities. Our emphasis is on explicit results free from all types of transforms and the method used may be of special interest to a wide variety of problems having regenerative structure.

Significance of Time Scales in Nonlinear Dynamical Analysis of Electroencephalogram Signals

We propose to show in this paper, that the time series obtained from biological systems such as human brain are invariably nonstationary because of different time scales involved in the dynamical process. This makes the invariant parameters time dependent. We made a global analysis of the EEG data obtained from the eight locations on the skull space and studied simultaneously the dynamical characteristics from various parts of the brain. We have proved that the dynamical parameters are sensitive to the time scales and hence in the study of brain one must identify all relevant time scales involved in the process to get an insight in the working of brain.

Modelling and Analysis of Some Time Series

The thesis deals with some of the non-linear Gaussian and non-Gaussian time models and mainly concentrated in studying the properties and application of a first order autoregressive process with Cauchy marginal distribution. In this thesis some of the non-linear Gaussian and non-Gaussian time series models and mainly concentrated in studying the properties and application of a order autoregressive process with Cauchy marginal distribution. Time series relating to prices, consumptions, money in circulation, bank deposits and bank clearing, sales and profit in a departmental store, national income and foreign exchange reserves, prices and dividend of shares in a stock exchange etc. are examples of economic and business time series. The thesis discuses the application of a threshold autoregressive(TAR) model, try to fit this model to a time series data. Another important non-linear model is the ARCH model, and the third model is the TARCH model. The main objective here is to identify an appropriate model to a given set of data. The data considered are the daily coconut oil prices for a period of three years. Since it is a price data the consecutive prices may not be independent and hence a time series based model is more appropriate. In this study the properties like ergodicity, mixing property and time reversibility and also various estimation procedures used to estimate the unknown parameters of the process.

Modeling of Suspended Sediment Dynamics in Tropical River Basins

It is proposed to study the suspended sediment transport characteristics of river basins of Kerala and to model suspended sediment discharge mechanism for typical micro-watersheds. The Pamba river basin is selected as a representative hydrologic regime for detailed studies of suspended sediment characteristics and its seasonal variation. The applicability of various erosion models would be tested by comparing with the observed event data (by continuous monitoring of rainfall, discharge, and suspended sediment concentration for lower order streams). Empirical, conceptual and physically distributed models were used for making the comparison of performance of the models. Large variations in the discharge and sediment quantities were noticed during a particular year between the river basins investigated and for an individual river basin during the years for which the data was available. In general, the sediment yield pattern follows the seasonal distribution of rainfall, discharge and physiography of the land. This confirms with similar studies made for other Indian rivers. It was observed from this study, that the quantity of sediment transported downstream shows a decreasing trend over the years corresponding to increase in discharge. For sound and sustainable management of coastal zones, it is important to understand the balance between erosion and retention and to quantify the exact amount of the sediments reaching this eco-system. This, of course, necessitates a good length of time series data and more focused research on the behaviour of each river system, both present and past. In this realm of river inputs to ocean system, each of the 41 rivers of Kerala may have dominant yet diversified roles to influence the coastal ecosystem as reflected from this study on the major fraction of transport, namely the suspended sediments

Activation of Progesterone Receptor by ATP

Progesterone-receptor complex from freshly prepared hen oviduct cytosol acquired the ability to bind to isolated nuclei, DNA-cellulose and ATP-Sepharose when incubated with 5-10 mM ATP at 4°C. The extent of this ATP-dependent activation was higher when compared with heat-activation achieved by warming the progesterone- receptor complex at 23 °C. The transformation of progesterone-receptor complex which occurred in a time-dependent manner was only partially dependent on hormone presence. The ATP effect was selective in causing this transformation whereas ADP, AMP and cAMP failed to show any such effect. The non-hydrolizable analogs of ATP, adenosine 5'-[a,/3-methylene]triphosphate and adenosine 5-[/l,y-imido]triphosphate were also found to be ineffective. Presence of 10 mM sodium molybdate blocked both the ATP and the heat-activation of progesterone-receptor complex. Mn" or Mg` had no detectable effect on the receptor activation but the presence of Ca" increased the extent of ATP-activation slightly. EDTA presence (> 5 mM) decreased the extent of receptor activation by about 40 % and was, therefore, not included in the buffers used for activation studies. Divalent cations were also ineffective when tested in the presence of 1- 5 mM EDTA. The properties of progesterone-receptor complex remained intact under the above conditions when analyzed for steroid-binding specificity and Scatchard analysis. However, the ATP-activated progesterone-receptor complex lost the ability to aggregate when tested on low-salt sucrose gradients. ATP was equally effective in activating the rat-uterine estradiol-receptor complex at 4 "C and influenced the transformation of 4-S receptor form into a 5-S form when analyzed on sucrose gradients containing 0.3 M KCI. The presence of ATP also increased the rate of activation of progesterone-receptor complex at 23 °C. These findings suggest a role for ATP in receptor function and offer a convenient method of studying the process of receptor activation at low temperature and mild assay conditions.

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

Cellular and humoral factors involved in defense mechanisms of Fenneropenaeus indicus (H. Milne Edwards, 1837)

The present investigation revealed three types of circulating haemocytes in the haemolymph of F. indicus: hyalinocytes, small-granule haemocytes, and large-granule haemocytes. Intermediate stages indicate the maturing process of a single cell. The presence of enzymes such as peroxidase, phenoloxidase and acid phosphatase in the haemocytes, and the substantial production of oxygen radicals during phagocytosis show that the haemocytes are capable of mounting a fme cellular defense mechanism. The enzyme activities of the serum and the presence of agglutinins in the serum, which may act as opsonins, agglutinate foreign particles and augment phagocytosis, confirm the presence of a superior humoral immune system in F. indicus.Bacterial infection caused considerable variations in the cellular and humoral factors, such as the number of circulating cells and haemagglutinating activity, especially in the initial hours of infection. The total haemocyte count, haemagglutination titer and phenoloxidase enzyme showed significant reductions on bacterial presence and could be used as indicators of bacterial infection.The number of circulating cells showed drastic fluctuation on exposure to pollutants. Nuvan at low concentrations was able to produce changes in the haemolymph factors and in the tissue organization, which implies that the animal is under stress and is easily prone to infections. Exposure to nuvan resulted in significant variation in all of the cellular and humoral factors, especially, the total haemocyte count, percentage of small granule haemocytes, phagocytic activity and the haemagglutinating activity, which might be good indicators of pesticide pollution. Heavy metal exposure caused significant increase in total haemocyte count and reduction in phenoloxidase enzyme activity Even changes in the physio-chemical parameters, such as salinity caused fluctuations in the defense factors, indicating stress in this euryhaline species. The dietary incorporation of a commercial immunostimulant containing P-l,3 glucan resulted in stimulation of some of the humoral defense factors of F indicus, but was time dependent. The modulations, on exposure to various external factors, in the cellular and humoral factors, especially, total haemocyte count, phagocytic activity, haemagglutinating activity and the phenoloxidase and acid phosphatase enzymes suggest that these parameters could be used as indicators of the health status of F indicus, which assist in better monitoring and effective health management of this important cultured species.

Numerical Investigations on Soil Structure Interaction of Multistorey Frames

Frames are the most widely used structural system for multistorey buildings. A building frame is a three dimensional discrete structure consisting of a number of high rise bays in two directions at right angles to each other in the vertical plane. Multistorey frames are a three dimensional lattice structure which are statically indeterminate. Frames sustain gravity loads and resist lateral forces acting on it. India lies at the north westem end of the Indo-Australian tectonic plate and is identified as an active tectonic area. Under horizontal shaking of the ground, horizontal inertial forces are generated at the floor levels of a multistorey frame. These lateral inertia forces are transferred by the floor slab to the beams, subsequently to the columns and finally to the soil through the foundation system. There are many parameters that affect the response of a structure to ground excitations such as, shape, size and geometry of the structure, type of foundation, soil characteristics etc. The Soil Structure Interaction (SS1) effects refer to the influence of the supporting soil medium on the behavior of the structure when it is subjected to different types of loads. Interaction between the structure and its supporting foundation and soil, which is a complete system, has been modeled with finite elements. Numerical investigations have been carried out on a four bay, twelve storeyed regular multistorey frame considering depth of fixity at ground level, at characteristic depth of pile and at full depth. Soil structure interaction effects have been studied by considering two models for soil viz., discrete and continuum. Linear static analysis has been conducted to study the interaction effects under static load. Free vibration analysis and further shock spectrum analysis has been conducted to study the interaction effects under time dependent loads. The study has been extended to four types of soil viz., laterite, sand, alluvium and layered.The structural responses evaluated in the finite element analysis are bending moment, shear force and axial force for columns, and bending moment and shear force for beams. These responses increase with increase in the founding depth; however these responses show minimal increase beyond the characteristic length of pile. When the soil structure interaction effects are incorporated in the analysis, the aforesaid responses of the frame increases upto the characteristic depth and decreases when the frame has been analysed for the full depth. It has been observed that shock spectrum analysis gives wide variation of responses in the frame compared to linear elastic analysis. Both increase and decrease in responses have been observed in the interior storeys. The good congruence shown by the two finite element models viz., discrete and continuum in linear static analysis has been absent in shock spectrum analysis.

Studies on Thermal structure in the seas around in India

The thesis entitled Studies on Thermal Structure in the Seas Around India. An attempt is made in this study to document the observed variability of thermal structure, both on seasonal and short-term scales, in the eastern Arabian Sea and southwestern Bay of Bengal, from the spatial and time series data sets from a reasonably strong data base. The present study has certain limitations. The mean temperatures are based on an uneven distribution of data in space and time. Some of the areas, although having a ‘full annual coverage, do not have adequate data for some months. Some portions in the area under study are having data gaps. The consistency and the coherence in the internal wave characteristics could not be examined due to non-availability of adequate data sets. The influence of generating mechanisms; other than winds and tides on the observed internal wave fields could not be ascertained due to lack of data. However, a comprehensive and intensive data collection can overcome these limitations. The deployment of moored buoys with arrays of sensors at different depths at some important locations for about 5 to 10 years can provide intensive and extensive data sets. This strong data base can afford to address the short-term and seasonal variability of thermal field and understand in detail the individual and collective influences of various physical and dynamical mechanisms responsible for such variability.

Studies On Mixed Layer Depth In The Arabian Sea

This thesis is the result of an elaborate study on the mixed layer depth (MLD) and the various oceanic environmental factors controlling it in the Arabian Sea examining its predictability on annual and short term basis. To accomplish this, the study area between 100 — 250 N latitudes and 600 — 750 E longitudes in the Arabian Sea is divided into 8 subareas of 50 quadrangles. The distribution of monthly means of the surface wind field, net heat exchange mKi868€%WTmN¥tWMWF3UH9 (SST) over each subarea in the annual cycle is examined. The corresponding wind (mechanical) and convective mixing values are computed and presented along with the observed mean MLD for the subareas in the annual cycle. Effects of advection due to surface currents and surface divergence (convergence and divergence) for these subareas are examined for correlating the MLD variations. A representative time series data from typical deep water station under southwest monsoonal forcing is analysed for the spectral components to estimate the amplitude perturbations on the mean MLD variation

Econometrics as an Academic Discipline in Higher Education: An Exploratory Study of the Need, Relevance and Significance

Econometrics is a young science. It developed during the twentieth century in the mid-1930’s, primarily after the World War II. Econometrics is the unification of statistical analysis, economic theory and mathematics. The history of econometrics can be traced to the use of statistical and mathematics analysis in economics. The most prominent contributions during the initial period can be seen in the works of Tinbergen and Frisch, and also that of Haavelmo in the 1940's through the mid 1950's. Right from the rudimentary application of statistics to economic data, like the use of laws of error through the development of least squares by Legendre, Laplace, and Gauss, the discipline of econometrics has later on witnessed the applied works done by Edge worth and Mitchell. A very significant mile stone in its evolution has been the work of Tinbergen, Frisch, and Haavelmo in their development of multiple regression and correlation analysis. They used these techniques to test different economic theories using time series data. In spite of the fact that some predictions based on econometric methodology might have gone wrong, the sound scientific nature of the discipline cannot be ignored by anyone. This is reflected in the economic rationale underlying any econometric model, statistical and mathematical reasoning for the various inferences drawn etc. The relevance of econometrics as an academic discipline assumes high significance in the above context. Because of the inter-disciplinary nature of econometrics (which is a unification of Economics, Statistics and Mathematics), the subject can be taught at all these broad areas, not-withstanding the fact that most often Economics students alone are offered this subject as those of other disciplines might not have adequate Economics background to understand the subject. In fact, even for technical courses (like Engineering), business management courses (like MBA), professional accountancy courses etc. econometrics is quite relevant. More relevant is the case of research students of various social sciences, commerce and management. In the ongoing scenario of globalization and economic deregulation, there is the need to give added thrust to the academic discipline of econometrics in higher education, across various social science streams, commerce, management, professional accountancy etc. Accordingly, the analytical ability of the students can be sharpened and their ability to look into the socio-economic problems with a mathematical approach can be improved, and enabling them to derive scientific inferences and solutions to such problems. The utmost significance of hands-own practical training on the use of computer-based econometric packages, especially at the post-graduate and research levels need to be pointed out here. Mere learning of the econometric methodology or the underlying theories alone would not have much practical utility for the students in their future career, whether in academics, industry, or in practice This paper seeks to trace the historical development of econometrics and study the current status of econometrics as an academic discipline in higher education. Besides, the paper looks into the problems faced by the teachers in teaching econometrics, and those of students in learning the subject including effective application of the methodology in real life situations. Accordingly, the paper offers some meaningful suggestions for effective teaching of econometrics in higher education

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis

Study on period search methods of variable stars: Application to ASAS and CRTS databases

Study on variable stars is an important topic of modern astrophysics. After the invention of powerful telescopes and high resolving powered CCD’s, the variable star data is accumulating in the order of peta-bytes. The huge amount of data need lot of automated methods as well as human experts. This thesis is devoted to the data analysis on variable star’s astronomical time series data and hence belong to the inter-disciplinary topic, Astrostatistics. For an observer on earth, stars that have a change in apparent brightness over time are called variable stars. The variation in brightness may be regular (periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and are caused by various reasons. In some cases, the variation is due to some internal thermo-nuclear processes, which are generally known as intrinsic vari- ables and in some other cases, it is due to some external processes, like eclipse or rotation, which are known as extrinsic variables. Intrinsic variables can be further grouped into pulsating variables, eruptive variables and flare stars. Extrinsic variables are grouped into eclipsing binary stars and chromospheri- cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae, supernovae, etc., which rarely occurs and are not periodic phenomena. Most of the other variations are periodic in nature. Variable stars can be observed through many ways such as photometry, spectrophotometry and spectroscopy. The sequence of photometric observa- xiv tions on variable stars produces time series data, which contains time, magni- tude and error. The plot between variable star’s apparent magnitude and time are known as light curve. If the time series data is folded on a period, the plot between apparent magnitude and phase is known as phased light curve. The unique shape of phased light curve is a characteristic of each type of variable star. One way to identify the type of variable star and to classify them is by visually looking at the phased light curve by an expert. For last several years, automated algorithms are used to classify a group of variable stars, with the help of computers. Research on variable stars can be divided into different stages like observa- tion, data reduction, data analysis, modeling and classification. The modeling on variable stars helps to determine the short-term and long-term behaviour and to construct theoretical models (for eg:- Wilson-Devinney model for eclips- ing binaries) and to derive stellar properties like mass, radius, luminosity, tem- perature, internal and external structure, chemical composition and evolution. The classification requires the determination of the basic parameters like pe- riod, amplitude and phase and also some other derived parameters. Out of these, period is the most important parameter since the wrong periods can lead to sparse light curves and misleading information. Time series analysis is a method of applying mathematical and statistical tests to data, to quantify the variation, understand the nature of time-varying phenomena, to gain physical understanding of the system and to predict future behavior of the system. Astronomical time series usually suffer from unevenly spaced time instants, varying error conditions and possibility of big gaps. This is due to daily varying daylight and the weather conditions for ground based observations and observations from space may suffer from the impact of cosmic ray particles. Many large scale astronomical surveys such as MACHO, OGLE, EROS, xv ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke- pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even though their primary intention is not variable star observation. Center for Astrostatistics, Pennsylvania State University is established to help the astro- nomical community with the aid of statistical tools for harvesting and analysing archival data. Most of these surveys releases the data to the public for further analysis. There exist many period search algorithms through astronomical time se- ries analysis, which can be classified into parametric (assume some underlying distribution for data) and non-parametric (do not assume any statistical model like Gaussian etc.,) methods. Many of the parametric methods are based on variations of discrete Fourier transforms like Generalised Lomb-Scargle peri- odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi- sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994) etc. Even though most of the methods can be brought under automation, any of the method stated above could not fully recover the true periods. The wrong detection of period can be due to several reasons such as power leakage to other frequencies which is due to finite total interval, finite sampling interval and finite amount of data. Another problem is aliasing, which is due to the influence of regular sampling. Also spurious periods appear due to long gaps and power flow to harmonic frequencies is an inherent problem of Fourier methods. Hence obtaining the exact period of variable star from it’s time series data is still a difficult problem, in case of huge databases, when subjected to automation. As Matthew Templeton, AAVSO, states “Variable star data analysis is not always straightforward; large-scale, automated analysis design is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of xvi huge amount of data in these databases is quite challenging, even when looking at seemingly small issues such as period determination and classification”. It will be beneficial for the variable star astronomical community, if basic parameters, such as period, amplitude and phase are obtained more accurately, when huge time series databases are subjected to automation. In the present thesis work, the theories of four popular period search methods are studied, the strength and weakness of these methods are evaluated by applying it on two survey databases and finally a modified form of cubic spline method is intro- duced to confirm the exact period of variable star. For the classification of new variable stars discovered and entering them in the “General Catalogue of Vari- able Stars” or other databases like “Variable Star Index“, the characteristics of the variability has to be quantified in term of variable star parameters.