Class Of Time Series Models Research Articles

Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

Rank-Based Extensions of the Brock, Dechert, and Scheinkman Test

This article proposes new tests of randomness for innovations in a large class of time series models. These tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks. The asymptotic behavior of these processes is determined under the null hypothesis of randomness. The limiting distributions are seen to be independent of estimation errors under appropriate regularity conditions. Several test statistics are derived from these processes; the classical Brock, Dechert, and Scheinkman statistic and a rank-based analog are included as special cases. Because the limiting distributions of the rank-based test statistics are margin-free, their finite-sample p values can be easily calculated by simulation. Monte Carlo experiments show that these statistics are quite powerful against several classes of alternatives.

Mechanical refrigeration, seasonality, and the hog–corn cycle in the United States: 1870–1940

This paper examines the role of mechanical refrigeration in seasonality and structural change in the U.S. hog–corn cycle, 1870–1940. This period covers an era in which the widespread adoption of mechanical refrigeration greatly affected the ability to store and transport perishable commodities. These developments in turn altered the seasonal production and price structure for many commodities, including pork. We use a new class of time series models, time-varying smooth transition autoregressions (TV-STARs), to document both the structural change and the nonlinear features observed in seasonal patterns for the U.S. hog–corn price relationship during the late nineteenth and early twentieth centuries.

Testing for change points in time series models and limiting theorems for NED sequences

This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald test for change points in a general class of time series models under the no change-point hypothesis. As an application, we verify our assumptions for the long-memory fractional ARIMA model.

Electricity Pool Prices: Long-Term Uncertainty Characterization for Futures-Market Trading and Risk Management

This paper provides a procedure to forecast electricity pool prices one year ahead. A technique to generate pool price scenarios spanning one year into the future is also provided. The information obtained through the above methodology is crucial to make informed decisions in financial markets by electricity producers, retailers and consumers. The proposed forecasting procedure is based on classical time series models and in a novel manner uses as explicative variables the prices of financial market products. A realistic case study is analyzed and results are reported to show the efficaciousness of the methodology proposed. Finally, several relevant conclusions are duly drawn.

Real-time prediction of order flowtimes using support vector regression

In a make-to-order production system, a due date must be assigned to new orders that arrive dynamically, which requires predicting the order flowtime in real-time. This study develops a support vector regression model for real-time flowtime prediction in multi-resource, multi-product systems. Several combinations of kernel and loss functions are examined, and results indicate that the linear kernel and the ε -insensitive loss function yield the best generalization performance. The prediction error of the support vector regression model for three different multi-resource systems of varying complexity is compared to that of classic time series models (exponential smoothing and moving average) and to a feedforward artificial neural network. Results show that the support vector regression model has lower flowtime prediction error and is more robust. More accurately predicting flowtime using support vector regression will improve due-date performance and reduce expenses in make-to-order production environments.

THE EFFECT OF DECOMPOSITION METHOD AS DATA PREPROCESSING ON NEURAL NETWORKS MODEL FOR FORECASTING TREND AND SEASONAL TIME SERIES

Recently, one of the central topics for the neural networks (NN) community is the issue of data preprocessing on the use of NN. In this paper, we will investigate this topic particularly on the effect of Decomposition method as data processing and the use of NN for modeling effectively time series with both trend and seasonal patterns. Limited empirical studies on seasonal time series forecasting with neural networks show that some find neural networks are able to model seasonality directly and prior deseasonalization is not necessary, and others conclude just the opposite. In this research, we study particularly on the effectiveness of data preprocessing, including detrending and deseasonalization by applying Decomposition method on NN modeling and forecasting performance. We use two kinds of data, simulation and real data. Simulation data are examined on multiplicative of trend and seasonality patterns. The results are compared to those obtained from the classical time series model. Our result shows that a combination of detrending and deseasonalization by applying Decomposition method is the effective data preprocessing on the use of NN for forecasting trend and seasonal time series.

Quantile Autoregression

We consider quantile autoregression (QAR) models in which the autoregressive coefficients can be expressed as monotone functions of a single, scalar random variable. The models can capture systematic influences of conditioning variables on the location, scale, and shape of the conditional distribution of the response, and thus constitute a significant extension of classical constant coefficient linear time series models in which the effect of conditioning is confined to a location shift. The models may be interpreted as a special case of the general random-coefficient autoregression model with strongly dependent coefficients. Statistical properties of the proposed model and associated estimators are studied. The limiting distributions of the autoregression quantile process are derived. QAR inference methods are also investigated. Empirical applications of the model to the U.S. unemployment rate, short-term interest rate, and gasoline prices highlight the model's potential.

Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning

Abstract. We obtain new models and results for count data time series based on binomial thinning. Count data time series may have non‐stationarity from trends or covariates, so we propose an extension of stationary time series based on binomial thinning such that the univariate marginal distributions are always in the same parametric family, such as negative binomial. We propose a recursive algorithm to calculate the probability mass functions for the innovation random variable associated with binomial thinning. This simplifies numerical calculations and estimation for the classes of time series models that we consider. An application with real data is used to illustrate the models.

An Examination of the Role of Time and its Impact on Price Revision

We consider a new class of time series models (introduced by Engle & Russell 1998) used in statistical applications in finance. These models treat the time between events (durations) as a stochastic process and the corresponding durations are modelled using a theory similar to that of autoregressive processes On a sample of six stocks listed on the ASX, we find evidence in support of the important role that both the deterministic and stochastic components of time play in both our quote revision and signed trade equations, and it is the stochastic indicator of time that has a greater influence than the time-of day periodicities.

Periodic Transfer Function-Noise Model for Forecasting

A new class of time series models, referred to in this paper as the “periodic transfer function-noise (PTFN) model,” has been developed through an extension of conventional nonperiodic (or constant parameter) transfer function-noise (TFN) models. The proposed PTFN model is very flexible, as its form or order and parameter values of both the dynamic and noise components may vary depending on the season of the year. It is shown that Box et al.’s modeling techniques for TFN models can be applied to PTFN models as well. The model has been applied for monthly forecasting of the Ganges River flow using monthly rainfall data of northern India as the predictor. The results are encouraging and suggest that the PTFN class of models has the potential to be useful in capturing the seasonally varying dynamic relationship between a dependent time series and one or more independent time series where each series is interyear stationary but within-year nonstationary.

Some statistical models for durations and an application to News Corporation stock prices

This paper considers a new class of time series models called autoregressive conditional duration (ACD) models. These models have been developed and applied to investigate the price discovery process in the context of financial markets. The various statistical properties of this class of ACD models are examined. A minimum mean square error (MMSE) forecast function is obtained as it plays an important role in many practical applications. The theory and utilisation of these models are illustrated using a potential application based on a sample of high frequency transactions based stock price data for News Corporation.

Semiparametric Duration Models

In this article we consider semiparametric duration models and efficient estimation of the parameters in a non-iid environment. In contrast to classical time series models where innovations are assumed to be iid we show that in, for example, the often-used autoregressive conditional duration (ACD) model, the assumption of independent innovations is too restrictive to describe financial durations accurately. Therefore, we consider semiparametric extensions of the standard specification that allow for arbitrary kinds of dependencies between the innovations. The exact nonparametric specification of these dependencies determines the flexibility of the semiparametric model. We calculate semiparametric efficiency bounds for the ACD parameters, discuss the construction of efficient estimators, and study the efficiency loss of the exponential pseudolikelihood procedure. This efficiency loss proves to be sizeable in applications. For durations observed on the Paris Bourse for the Alcatel stock in July and August 1996, the proposed semiparametric procedures clearly outperform pseudolikelihood procedures. We analyze these efficiency gains using a simulation study confirming that, at least at the Paris Bourse, dependencies among rescaled durations can be exploited.

An Examination of the Role of Time in Ultra-High Frequency Data and its Impact on Price Revisions in News Corporation Stock

We consider a new class of time series models (introduced by Engle and Russell (1998)) used in statistical applications in finance. These models treat the time between events (durations) as a stochastic process and the corresponding durations are modelled using a theory similar to that of autoregressive processes. This new class of time series models is called Autoregressive Conditional Duration (ACD) models. We apply the theory to analyse the behaviour of an Australian Stock: News Corporation, using a high-frequency data set obtained from SIRCA.

DIAGNOSTIC CHECKING FOR THE ADEQUACY OF NONLINEAR TIME SERIES MODELS

We propose a new diagnostic test for linear and nonlinear time series models, using a generalized spectral approach. Under a wide class of time series models that includes autoregressive conditional heteroskedasticity (ARCH) and autoregressive conditional duration (ACD) models, the proposed test enjoys the appealing “nuisance-parameter-free” property in the sense that model parameter estimation uncertainty has no impact on the limit distribution of the test statistic. It is consistent against any type of pairwise serial dependence in the model standardized residuals and allows the choice of a proper lag order via data-driven methods. Moreover, the new test is asymptotically more efficient than the correlation integral–based test of Brock, Hsieh, and LeBaron (1991, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence) and Brock, Dechert, Scheinkman, and LeBaron (1996, Econometric Reviews 15, 197–235), the well-known BDS test, against a class of plausible local alternatives (not including ARCH). A simulation study compares the finite-sample performance of the proposed test and the tests of BDS, Box and Pierce (1970, Journal of the American Statistical Association 65, 1509–1527), Ljung and Box (1978, Biometrika 65, 297–303), McLeod and Li (1983, Journal of Time Series Analysis 4, 269–273), and Li and Mak (1994, Journal of Time Series Analysis 15, 627–636). The new test has good power against a wide variety of stochastic and chaotic alternatives to the null models for conditional mean and conditional variance. It can play a valuable role in evaluating adequacy of linear and nonlinear time series models. An empirical application to the daily S&P 500 price index highlights the merits of our approach.We thank the co-editor (Don Andrews) and two referees for careful and constructive comments that have lead to significant improvement over an earlier version. We also thank C.W.J. Granger, D. Tjostheim, and Z. Xiao for helpful comments. Hong's participation is supported by the National Science Foundation via NSF grant SES–0111769. Lee thanks the UCR Academic Senate for research support.

General Data Analysis Supported SPC

The issue of autocorrelation in statistical process control (SPC) data has been and continues to be a much discussed and researched topic. In nearly all published studies and in SPC training modules, the predominate models for autocorrelation come from a class of time-series models known as autoregressive-integrated moving average (ARIMA) models. However, little attention is given to a variety of systematic patterns pervasive in SPC applications that are not adequately modeled by the ARIMA framework. In this paper, we suggest the need for an even broader perspective than defined by ARIMA models. Furthermore, we argue that effective SPC training not only requires attention to data analysis tools for modeling systematic patterns but also to tools for diagnostically checking the distributional assumptions of variable and attribute charts.

A Statistical Method for the Determination of the Appropriate Order in a General Class of Time Series Models

We propose a method to determine the order q of a model in a general class of time series models. For the subset of linear moving average models (MA(q)), our method is compared with that of the sample autocorrelations. Since the sample autocorrelation is meant to detect a linear structure of dependence between random variables, it turns out to be more suitable for the linear case. However, our method presents a competitive option in that case, and for nonlinear models (NLMA(q)) it is shown to work better. The main advantages of our approach are that it does not make assumptions on the existence of moments and on the distribution of the noise involved in the moving average models. We also include an example with real data corresponding to the daily returns of the exchange rate process of mexican pesos and american dollars.

Padé Approximation in Economics

In economics, the systematic treatment of data to obtain specific properties from long (or short) data series is a main objective. The use of rational models and related numerical methods can be useful to help to predict the behaviour of relevant economic variables with a certain degree of certainty. This paper is concerned with illustrating the application of several numerical methods, in particular, the corner method, epsilon-algorithm, rs-algorithm and qd-algorithm, to the problem of model identification in time series analysis. These methods, closely related to theoretical research in Pade Approximation, are proposed to identify some type of rational structure associated with economic data in different contexts (financial, marketing, farming). Moreover, they incorporate the expectations of exogenous economic variables to improve the fit and forecasting of classic time series models.

Some Statistical Models for Durations and Their Applications in Finance

We consider a new class of time series models (introduced by Engle and Russell (1998)) used in statistical applications in finance. These models treat the time between events (durations) as a stochastic process and the corresponding durations are modelled using a theory similar to that of autoregressive processes. On a sample of six stocks listed on the ASX, We find evidence in support of the important role that both the deterministic and stochastic components of time play in both our quote revision and signed trade equations, and it is the stochastic indicator of time that has a greater influence than the time-of-day periodicities.

Spectral Analysis of Overseas Tourists’ Expenditures in the United Kingdom

This article introduces univariate and bivariate spectral analysis as methods of modeling overseas tourists’ expenditures in the United Kingdom. In general, these two methods detect cyclical behavior within and between time-series data, respectively. The univariate spectrum refutes any long-term “business cycle”-type oscillations in the expenditure data. Only a significant annual cycle is revealed. The univariate spectrum is shown to assist greatly in the difficult problem of parameter determination in the more conventional autoregressive integrated moving average (ARIMA) class of time-series models. The bivariate spectrum reveals significant lead relationships between cycles in pound sterling exchange rates against the U.S. dollar and French franc and cycles in tourists’ expenditures. Such relationships would be difficult to detect via more commonly used time-series procedures.