Bayesian Time Series Model Research Articles

Modelling long-term investment returns via Bayesian infinite mixture time series models

This paper introduces the class of Bayesian infinite mixture time series models first proposed in Lau & So (2004) for modelling long-term investment returns. It is a flexible class of time series models and provides a flexible way to incorporate full information contained in all autoregressive components with various orders by utilizing the idea of Bayesian averaging or mixing. We adopt a Bayesian sampling scheme based on a weighted Chinese restaurant process for generating partitions of investment returns to estimate the Bayesian infinite mixture time series models. Instead of using the point estimates, as in the classical or non-Bayesian approach, the estimation in this paper is performed by the full Bayesian approach, utilizing the idea of Bayesian averaging to incorporate all information contained in the posterior distributions of the random parameters. This provides a natural way to incorporate model risk or uncertainty. The proposed models can also be used to perform clustering of investment returns and detect outliers of returns. We employ the monthly data from the Toronto Stock Exchange 300 (TSE 300) indices to illustrate the implementation of our models and compare the simulated results from the estimated models with the empirical characteristics of the TSE 300 data. We apply the Bayesian predictive distribution of the logarithmic returns obtained by the Bayesian averaging or mixing to evaluate the quantile-based and conditional tail expectation risk measures for segregated fund contracts via stochastic simulation. We compare the risk measures evaluated from our models with those from some well-known and important models in the literature, and highlight some features that can be obtained from our models.

A Probability Method for Very Short-Term Steady State Analysis of a Distribution System with Wind Farms

In this paper, a probabilistic method is proposed to analyze the very short-term steady-state performance of an unbalanced distribution electrical system characterized by the presence of wind farms. This method, which can take into account the uncertainties of loads and wind productions, is based on a Monte Carlo simulation procedure applied to the non-linear three-phase load flow equations, including wind farm models. Bayesian time series models are used to predict the next hour's wind speed probability density functions, making possible a predictive evaluation of the very short-term system steady-state behavior. Numerical applications are presented and discussed with reference to the three-phase unbalanced IEEE 34-bus test distribution system in the presence of wind farms connected at different busbars.

Long-term tendencies in the MLT prevailing winds and tides over Antarctica as observed by radars at Molodezhnaya, Mawson and Davis

Long-term tendencies in horizontal neutral wind parameters in the southern polar mesosphere/lower thermosphere are presented. The wind data analyzed were obtained from meteor and MF radars situated at Molodezhnaya (45.9°E, 67.7°S), Mawson (62.9°E, 67.6°S) and Davis (78.0°E, 68.6°S). The composite dataset covers years from 1970 to 2006. A Bayesian approach in the form proposed by Wang and Zivot [2000. A Bayesian time series model of multiple structural changes in level, trend and variance. Journal of Business and Economic Statistics 8, 374–386] is used for the trend assessment. This approach allows structural breaks to be identified in the trend parameters (slope, mean or variance of residuals) or demonstrates their absence. The results of our analysis have shown persistence through such structural breaks in trends of the winter and summer prevailing winds and in meridional tidal components. It is demonstrated that the wind parameters exhibit different stable states with transitions between the states. Correlations between the southern polar MLT wind and indices of atmospheric variability (Northern annular mode, Southern annular mode, Multivariate El-Niño/Southern Oscillation Index) were then considered. The results show that statistically significant correlations exist during some periods of observations that do not exist during others.

Evaluating the Predictive Distributions of Bayesian Models of Asset Returns

Bayesian time series models provide exact, out-of-sample predictive distributions. This paper examines two approaches to the comparison and evaluation of these distributions and illustrates them using five alternative models of asset returns applied to the daily S&P 500 index from 1976 through 2005. It is shown that the first approach, using predictive likelihoods, is intimately related to Bayes factors. The illustration shows how analysis of predictive likelihoods provides insight into the relative strengths and weaknesses of alternative prediction models. The second approach, using the probability integral transform, provides absolute standards in the evaluation of the quality of predictive distributions. The illustration shows that the two approaches can be complementary, each identifying strengths and weaknesses in the model that are not evident using the other. For the S&P 500 data, the predictive distributions of the hierarchical Markov normal mixture model prove superior to those of a stochastic volatility model and several models in the ARCH family.

Probabilistic Index for Increasing Hourly Transmission Line Ratings

The steady state thermal rating of overhead transmission lines is limited by the conductor`s maximum design temperature, which is related to the maximum sag and the loss of tensile strength of the conductors. Traditionally, this overhead transmission lines rating is computed using a deterministic approach, with reference to severe weather conditions. Thus, the application of this method leads to conservative results resulting in under-utilization of conductors. In this paper, a new method based on an hourly probabilistic index is proposed to predict the line thermal rating for each hour of the day; this index is evaluated using the conductor current limit probability density function (pdf). The method uses Bayesian time series models for the weather parameters (ambient temperature, wind speed and wind direction) and calculates the conductor current limit pdf using a Monte Carlo simulation. The probabilistic index is applied by considering measured weather data of both hot and cold seasons; the corresponding lines ratings are reported and analyzed.

Structural changes in Central and Eastern European economies: breaking news or breaking the ice?

This paper extends the sparse existing literature on structural breaks in emerging markets in Central and Eastern Europe by analyzing structural breaks in the intercept, trend and variance of monthly key macroeconomic variables, such as industrial production, inflation, monetary aggregates, nominal exchange rates and series related to the labor market. Using the Bayesian procedure developed by Wang and Zivot (2000, A Bayesian time series model of multiple structural changes in level, trend and variance. J Busi Econom 18:374–386), we provide strong evidence in favor of multiple structural breaks in the series under study. As most of the existing empirical literature on European emerging markets does not sufficiently deal with structural breaks, the instability found in this paper has important implications for macro-econometric modeling as well as the ensuing recommendations for economic policy.

Bayesian Time-Series Model for Short-Term Traffic Flow Forecasting

The seasonal autoregressive integrated moving average (SARIMA) model is one of the popular univariate time-series models in the field of short-term traffic flow forecasting. The parameters of the SARIMA model are commonly estimated using classical (maximum likelihood estimate and/or least-squares estimate) methods. In this paper, instead of using classical inference the Bayesian method is employed to estimate the parameters of the SARIMA model considered for modeling. In Bayesian analysis the Markov chain Monte Carlo method is used to solve the posterior integration problem in high dimension. Each of the estimated parameters from the Bayesian method has a probability density function conditional to the observed traffic volumes. The forecasts from the Bayesian model can better match the traffic behavior of extreme peaks and rapid fluctuation. Similar to the estimated parameters, each forecast has a probability density curve with the maximum probable value as the point forecast. Individual probability density curves provide a time-varying prediction interval unlike the constant prediction interval from the classical inference. The time-series data used for fitting the SARIMA model are obtained from a certain junction in the city center of Dublin.

Advances in Bayesian Time Series Modeling and the Study of Politics: Theory Testing, Forecasting, and Policy Analysis

Bayesian approaches to the study of politics are increasingly popular. But Bayesian approaches to modeling multiple time series have not been critically evaluated. This is in spite of the potential value of these models in international relations, political economy, and other fields of our discipline. We review recent developments in Bayesian multi-equation time series modeling in theory testing, forecasting, and policy analysis. Methods for constructing Bayesian measures of uncertainty of impulse responses (Bayesian shape error bands) are explained. A reference prior for these models that has proven useful in short- and medium-term forecasting in macroeconomics is described. Once modified to incorporate our experience analyzing political data and our theories, this prior can enhance our ability to forecast over the short and medium terms complex political dynamics like those exhibited by certain international conflicts. In addition, we explain how contingent Bayesian forecasts can be constructed, contingent Bayesian forecasts that embody policy counterfactuals. The value of these new Bayesian methods is illustrated in a reanalysis of the Israeli-Palestinian conflict of the 1980s.

A Bayesian approach for short-term transmission line thermal overload risk assessment

An on-line conductor thermal overload risk assessment method is presented in this paper. Bayesian time series models are used to model weather conditions along the transmission lines. An estimate of the thermal overload risk is obtained by Monte Carlo (MC) simulation. We predict the thermal overload risk for the next hour based on the current weather conditions and power system operating conditions. The predicted risk of thermal overload is useful for on-line decision making in a stressed operational environment.

A Bayesian Approach for Short-Term Transmission Line Thermal Overload Risk Assessment

An online conductor thermal overload risk assessment method is presented. Bayesian time-series models are used to model weather conditions along the transmission lines. An estimate of the thermal overload risk is obtained by Monte Carlo simulation. We predict the thermal overload risk for the next hour based on the current weather conditions and power system operating conditions. The predicted risk of thermal overload is useful for online decision-making in a stressed operational environment.

A Multivariate Time Series Model for the Analysis and Prediction of Carbon Monoxide Atmospheric Concentrations

SUMMARY We use a Bayesian multivariate time series model for the analysis of the dynamics of carbon monoxide atmospheric concentrations. The data are observed at four sites. It is assumed that the logarithm of the observed process can be represented as the sum of unobservable components: a trend, a daily periodicity, a stationary autoregressive signal and an erratic term. Bayesian analysis is performed via Gibbs sampling. In particular, we consider the problem of joint temporal prediction when data are observed at a few sites and it is not possible to fit a complex space–time model. A retrospective analysis of the trend component is also given, which is important in that it explains the evolution of the variability in the observed process.

Forecasting demand and inventory management using Bayesian time series

Discusses the development and evaluation of a forecasting model for inventory management in an advanced technology batch production environment. Traditional forecasting and inventory management do not adequately address issues relating to a short life cycle and to non‐seasonal products with a relatively long lead time. Limited historical data (fewer than 100 observations) is also a problem in predicting short‐term dynamic or unstable time series. A Bayesian dynamic linear time series model is proposed as an alternative technique for forecasting demand in a dynamically changing environment. Provides details of the important characteristics and development process of the forecasting model. A case study is then presented to illustrate the application of the model based on data from a multinational company in Singapore. It also compares the Bayesian dynamic linear time series model with a classical forecasting model (auto‐regressive integrated moving average (ARIMA) model).

A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance

A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance

A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance

We consider a deterministically trending dynamic time series model in which multiple structural changes in level, trend, and error variance are modeled explicitly and the number, but not the timing, of the changes is known. Estimation of the model is made possible by the use of the Gibbs sampler. The determination of the number of structural breaks and the form of structural change is considered as a problem of model selection, and we compare the use of marginal likelihoods, posterior odds ratios, and Schwarz's Bayesian model-selection criterion to select the most appropriate model from the data. We evaluate the efficacy of the Bayesian approach using a small Monte Carlo experiment. As empirical examples, we investigate structural changes in the U.S. ex post real interest rate and in a long time series of U.S. real gross domestic product.

An application of the Bayesian time series model and statistical system analysis for F0 control

F0 (fundamental frequency) control of human speech production is studied by using both a stochastic time series model and a system analysis with a vector autoregressive (VAR) model. We use two-dimensional time series data of F0 ( ff0 and sf0) obtained through the transformed auditory feedback (TAF) experimentation system developed by one of the authors. sf0 is extracted from speech data that includes prolonged phonation of the vowel /a/, and the signal ff0 is extracted from frequency-modulated feedback speech by white Gaussian noise. Most of the data had mean-nonstationary characteristics. The stochastic procedure decomposes the mean-nonstationary and other components in one stage without pre-manufacturing the data. The cyclical components around the mean-nonstationary components are assumed to be generated by the VAR model. We can execute a stochastic system analysis using the estimates of the VAR model to analyze the physical characteristics of the data. We also performed a simulation study using the estimates obtained by the model to discover the role of F0 control under the situation in which we completely lost our hearing ability. The results clearly indicate the dynamic properties of F0 control for each segment which occur with each breath taken during a sustained tone.

Some Properties and Generalizations of Non-negative Bayesian Time Series Models

Summary We study the most basic Bayesian forecasting model for exponential family time series, the power steady model (PSM) of Smith, in terms of observable properties of one-step forecast distributions and sample paths. The PSM implies a constraint between location and spread of the forecast distribution. Including a scale parameter in the models does not always give an exact solution free of this problem, but it does suggest how to define related models free of the constraint. We define such a class of models which contains the PSM. We concentrate on the case where observations are non-negative. Probability theory and simulation show that under very mild conditions almost all sample paths of these models converge to some constant, making them unsuitable for modelling in many situations. The results apply more generally to non-negative models defined in terms of exponentially weighted moving averages. We use these and related results to motivate, define and apply very simple models based on directly specifying the forecast distributions.

A bayesian multivariate nonstationary time series model for estimating mutual relationships among variables

The purpose of this paper is to propose a Bayesian multivariate stochastic model with latent nonstationary trends and seasonal components and show its use to determine the relationships among the variables. The model is expressed in state space form and the parameters of the model are estimated by maximum likelihood using a numerical optimization algorithm. The Kalman filter is used to compute the likelihood of the model and the information criterion AIC is used to select the best fitting model. The relationships among variables are examined in the frequency domain using estimated components. Japanese macroeconomic series are analyzed by our procedure.

Bayesian Autoregressive Time Series Analysis

Two Bayesian autoregressive time series models for partially observable dynamic processes are presented. In the first model, a general inference procedure is developed for the situation in which k previous values of the time series plus a change error determine the next value. This general model is specialized to an example in which the observational and change errors follow a normal probability law; the results for k = 1 are given and discussed. The second general model adds the facility for simultaneously inferring an unknown and unchanging parameter of the time series. This model is specialized to the same normal example presented earlier, with the precision of the change error as the unknown process parameter.