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 and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

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.

De lo micro a lo macro prudencial: Un análisis de la supervisión bancaria desde la econometría espacial

La crisis que se desató en el mercado hipotecario en Estados Unidos en 2008 y que logró propagarse a lo largo de todo sistema financiero, dejó en evidencia el nivel de interconexión que actualmente existe entre las entidades del sector y sus relaciones con el sector productivo, dejando en evidencia la necesidad de identificar y caracterizar el riesgo sistémico inherente al sistema, para que de esta forma las entidades reguladoras busquen una estabilidad tanto individual, como del sistema en general. El presente documento muestra, a través de un modelo que combina el poder informativo de las redes y su adecuación a un modelo espacial auto regresivo (tipo panel), la importancia de incorporar al enfoque micro-prudencial (propuesto en Basilea II), una variable que capture el efecto de estar conectado con otras entidades, realizando así un análisis macro-prudencial (propuesto en Basilea III).

Combined Analysis of the Short-Term Effects of Photochemical Air Pollutants on Mortality within the EMECAM Project

In recent years, some epidemiologic studies have attributed adverse effects of air pollutants on health not only to particles and sulfur dioxide but also to photochemical air pollutants (nitrogen dioxide and ozone). The effects are usually small, leading to some inconsistencies in the results of the studies. Furthermore, the different methodologic approaches of the studies used has made it difficult to derive generic conclusions. We provide here a quantitative summary of the short-term effects of photochemical air pollutants on mortality in seven Spanish cities involved in the EMECAM project, using generalized additive models from analyses of single and multiple pollutants. Nitrogen dioxide and ozone data were provided by seven EMECAM cities (Barcelona, Gijón, Huelva, Madrid, Oviedo, Seville, and Valencia). Mortality indicators included daily total mortality from all causes excluding external causes, daily cardiovascular mortality, and daily respiratory mortality. Individual estimates, obtained from city-specific generalized additive Poisson autoregressive models, were combined by means of fixed effects models and, if significant heterogeneity among local estimates was found, also by random effects models. Significant positive associations were found between daily mortality (all causes and cardiovascular) and NO2, once the rest of air pollutants were taken into account. A 10 μg/m3 increase in the 24-hr average 1-day NO2 level was associated with an increase in the daily number of deaths of 0.43% [95% confidence interval(CI), –0.003–0.86%] for all causes excluding external. In the case of significant relationships, relative risks for cause-specific mortality were nearly twice as much as that for total mortality for all the photochemical pollutants. Ozone was independently related only to cardiovascular daily mortality. No independent statistically significant relationship between photochemical air pollutants and respiratory mortality was found. The results in this study suggest that, given the present levels of photochemical pollutants, people living in Spanish cities are exposed to health risks derived from air pollution

Evidence for the chaotic origin of Northern Annular Mode variability

Exponential spectra are found to characterize variability of the Northern Annular Mode (NAM) for periods less than 36 days. This corresponds to the observed rounding of the autocorrelation function at lags of a few days. The characteristic persistence timescales during winter and summer is found to be ∼5 days for these high frequencies. Beyond periods of 36 days the characteristic decorrelation timescale is ∼20 days during winter and ∼6 days in summer. We conclude that the NAM cannot be described by autoregressive models for high frequencies; the spectra are more consistent with low-order chaos. We also propose that the NAM exhibits regime behaviour, however the nature of this has yet to be identified.

Business cycle asymmetries: characterisation and testing based on Markov-switching autoregressions

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.

Bicorrelations and cross-bicorrelations as non-linearity tests and tools for exchange rate forecasting

This paper proposes and implements a new methodology for forecasting time series, based on bicorrelations and cross-bicorrelations. It is shown that the forecasting technique arises as a natural extension of, and as a complement to, existing univariate and multivariate non-linearity tests. The formulations are essentially modified autoregressive or vector autoregressive models respectively, which can be estimated using ordinary least squares. The techniques are applied to a set of high-frequency exchange rate returns, and their out-of-sample forecasting performance is compared to that of other time series models

Robust approaches to forecasting

We investigate alternative robust approaches to forecasting, using a new class of robust devices, contrasted with equilibrium-correction models. Their forecasting properties are derived facing a range of likely empirical problems at the forecast origin, including measurement errors, impulses, omitted variables, unanticipated location shifts and incorrectly included variables that experience a shift. We derive the resulting forecast biases and error variances, and indicate when the methods are likely to perform well. The robust methods are applied to forecasting US GDP using autoregressive models, and also to autoregressive models with factors extracted from a large dataset of macroeconomic variables. We consider forecasting performance over the Great Recession, and over an earlier more quiescent period.

Real-time factor model forecasting and the effects of instability

Factor forecasting models are shown to deliver real-time gains over autoregressive models for US real activity variables during the recent period, but are less successful for nominal variables. The gains are largely due to the Financial Crisis period, and are primarily at the shortest (one quarter ahead) horizon. Excluding the pre-Great Moderation years from the factor forecasting model estimation period (but not from the data used to extract factors) results in a marked fillip in factor model forecast accuracy, but does the same for the AR model forecasts. The relative performance of the factor models compared to the AR models is largely unaffected by whether the exercise is in real time or is pseudo out-of-sample.

The housing market channel of monetary policy transmission in the Euro area

Purpose – The purpose of this paper is to explore the role of the housing market in the monetary policy transmission to consumption among euro area member states. It has been argued that the housing market in one country is then important when its mortgage market is well developed. The countries in the euro area follow unitary monetary policy, however, their housing and mortgage markets show some heterogeneity, which may lead to different policy effects on aggregate consumption through the housing market. Design/methodology/approach – The housing market can act as a channel of monetary policy shocks to household consumption through changes in house prices and residential investment – the housing market channel. We estimate vector autoregressive models for each country and conduct a counterfactual analysis in order to disentangle the housing market channel and assess its importance across the euro area member states. Findings – We find little evidence for heterogeneity of the monetary policy transmission through house prices across the euro area countries. Housing market variations in the euro area seem to be better captured by changes in residential investment rather than by changes in house prices. As a result we do not find significantly large house price channels. For some of the countries however, we observe a monetary policy channel through residential investment. The existence of a housing channel may depend on institutional features of both the labour market or with institutional factors capturing the degree of household debt as is the LTV ratio. Originality/value – The study contributes to the existing literature by assessing whether a unitary monetary policy has a different impact on consumption across the euro area countries through their housing and mortgage markets. We disentangle monetary-policy-induced effects on consumption associated with variations on the housing markets due to either house price variations or residential investment changes. We show that the housing market can play a role in the monetary transmission mechanism even in countries with less developed mortgage markets through variations in residential investment.

Measuring time series predictability using support vector regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.

Stock Markets and Household Wealth: Can a Stock Market Crash Cause a Recession in The U.S. Economy?

Stock market wealth effects on the level of consumption in the United States economy have been constantly debated; there is evidence for arguments for and against its prominence and its symmetry. This paper seeks to investigate the strength of its negative effect by creating models to analyze unexpected shocks to the Standard and Poor's 500 index. First, a transmission mechanism between the stock market and GDP is established through the use of second-order vector autoregressive models. Following which, theory from the life cycle model and adaptations of previous researchers' models are used to create a structural model. This paper finds that stock market wealth effects are small, but important to consider, especially if markets are overpriced; this claim is corroborated by evidence from simulation of 'alternative scenarios' and the historical experiences of 1987 and 2001.

The importance of common cyclical features in VAR analysis: a Monte-Carlo study

Despite the commonly held belief that aggregate data display short-run comovement, there has been little discussion about the econometric consequences of this feature of the data. We use exhaustive Monte-Carlo simulations to investigate the importance of restrictions implied by common-cyclical features for estimates and forecasts based on vector autoregressive models. First, we show that the ìbestî empirical model developed without common cycle restrictions need not nest the ìbestî model developed with those restrictions. This is due to possible differences in the lag-lengths chosen by model selection criteria for the two alternative models. Second, we show that the costs of ignoring common cyclical features in vector autoregressive modelling can be high, both in terms of forecast accuracy and efficient estimation of variance decomposition coefficients. Third, we find that the Hannan-Quinn criterion performs best among model selection criteria in simultaneously selecting the lag-length and rank of vector autoregressions.

Prevendo a volatilidade realizada de ações brasileiras : evidências empíricas

Este estudo compara previsões de volatilidade de sete ações negociadas na Bovespa usando 02 diferentes modelos de volatilidade realizada e 03 de volatilidade condicional. A intenção é encontrar evidências empíricas quanto à diferença de resultados que são alcançados quando se usa modelos de volatilidade realizada e de volatilidade condicional para prever a volatilidade de ações no Brasil. O período analisado vai de 01 de Novembro de 2007 a 30 de Março de 2011. A amostra inclui dados intradiários de 5 minutos. Os estimadores de volatilidade realizada que serão considerados neste estudo são o Bi-Power Variation (BPVar), desenvolvido por Barndorff-Nielsen e Shephard (2004b), e o Realized Outlyingness Weighted Variation (ROWVar), proposto por Boudt, Croux e Laurent (2008a). Ambos são estimadores não paramétricos, e são robustos a jumps. As previsões de volatilidade realizada foram feitas através de modelos autoregressivos estimados para cada ação sobre as séries de volatilidade estimadas. Os modelos de variância condicional considerados aqui serão o GARCH(1,1), o GJR (1,1), que tem assimetrias em sua construção, e o FIGARCH-CHUNG (1,d,1), que tem memória longa. A amostra foi divida em duas; uma para o período de estimação de 01 de Novembro de 2007 a 30 de Dezembro de 2010 (779 dias de negociação) e uma para o período de validação de 03 de Janeiro de 2011 a 31 de Março de 2011 (61 dias de negociação). As previsões fora da amostra foram feitas para 1 dia a frente, e os modelos foram reestimados a cada passo, incluindo uma variável a mais na amostra depois de cada previsão. As previsões serão comparadas através do teste Diebold-Mariano e através de regressões da variância ex-post contra uma constante e a previsão. Além disto, o estudo também apresentará algumas estatísticas descritivas sobre as séries de volatilidade estimadas e sobre os erros de previsão.