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.

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.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Time-resolved studies of neutral and ionized Na_n clusters with femtosecond light pulses

The real-time dynamics of Na_n (n=3-21) cluster multiphoton ionization and fragmentation has been studied in beam experiments applying femtosecond pump-probe techniques in combination with ion and electron spectroscopy. Three dimensional wave packet motions in the trimer Na_3 ground state X and excited state B have been observed. We report the first study of cluster properties (energy, bandwidth and lifetime of intermediate resonances Na_n^*) with femtosecond laser pulses. The observation of four absorption resonances for the cluster Na_8 with different energy widths and different decay patterns is more difficult to interpret by surface plasmon like resonances than by molecular structure and dynamics. Timeresolved fragmentation of cluster ions Na_n^+ indicates that direct photo-induced fragmentation processes are more important at short times than the statistical unimolecular decay.

Time-series regression models to study the short-term effects of environmental factors on health

Time series regression models are especially suitable in epidemiology for evaluating short-term effects of time-varying exposures on health. The problem is that potential for confounding in time series regression is very high. Thus, it is important that trend and seasonality are properly accounted for. Our paper reviews the statistical models commonly used in time-series regression methods, specially allowing for serial correlation, make them potentially useful for selected epidemiological purposes. In particular, we discuss the use of time-series regression for counts using a wide range Generalised Linear Models as well as Generalised Additive Models. In addition, recently critical points in using statistical software for GAM were stressed, and reanalyses of time series data on air pollution and health were performed in order to update already published. Applications are offered through an example on the relationship between asthma emergency admissions and photochemical air pollutants

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed at different points in time. Inherently, then, a compositional time series is a multivariate time series with important constraints on the variables observed at any instance in time. Although this type of data frequently occurs in situations of real practical interest, a trawl through the statistical literature reveals that research in the field is very much in its infancy and that many theoretical and empirical issues still remain to be addressed. Any appropriate statistical methodology for the analysis of compositional time series must take into account the constraints which are not allowed for by the usual statistical techniques available for analysing multivariate time series. One general approach to analyzing compositional time series consists in the application of an initial transform to break the positive and unit sum constraints, followed by the analysis of the transformed time series using multivariate ARIMA models. In this paper we discuss the use of the additive log-ratio, centred log-ratio and isometric log-ratio transforms. We also present results from an empirical study designed to explore how the selection of the initial transform affects subsequent multivariate ARIMA modelling as well as the quality of the forecasts

Compositional Time Series: An Application

The composition of the labour force is an important economic factor for a country. Often the changes in proportions of different groups are of interest. I this paper we study a monthly compositional time series from the Swedish Labour Force Survey from 1994 to 2005. Three models are studied: the ILR-transformed series, the ILR-transformation of the compositional differenced series of order 1, and the ILRtransformation of the compositional differenced series of order 12. For each of the three models a VAR-model is fitted based on the data 1994-2003. We predict the time series 15 steps ahead and calculate 95 % prediction regions. The predictions of the three models are compared with actual values using MAD and MSE and the prediction regions are compared graphically in a ternary time series plot. We conclude that the first, and simplest, model possesses the best predictive power of the three models

Time series analysis of lava flux

We have applied time series analytical techniques to the flux of lava from an extrusive eruption. Tilt data acting as a proxy for flux are used in a case study of the May–August 1997 period of the eruption at Soufrière Hills Volcano, Montserrat. We justify the use of such a proxy by simple calibratory arguments. Three techniques of time series analysis are employed: spectral, spectrogram and wavelet methods. In addition to the well-known ~9-hour periodicity shown by these data, a previously unknown periodic flux variability is revealed by the wavelet analysis as a 3-day cycle of frequency modulation during June–July 1997, though the physical mechanism responsible is not clear. Such time series analysis has potential for other lava flux proxies at other types of volcanoes.