Showing papers on "Moving-average model published in 2004"
01 Aug 2004
TL;DR: In this article, a model for the DGP of a set of economic time series variables can be constructed, which can be used for analyzing the dynamic interactions between the variables when such a model is available, usually done by tracing the effect of an impulse in one of the variables through the system.
Abstract: Introduction In the previous chapter we have seen how a model for the DGP of a set of economic time series variables can be constructed. When such a model is available, it can be used for analyzing the dynamic interactions between the variables. This kind of analysis is usually done by tracing the effect of an impulse in one of the variables through the system. In other words, an impulse response analysis is performed. Although this is technically straightforward, some problems related to impulse response analysis exist that have been the subject of considerable discussion in the literature. As argued forcefully by Cooley & LeRoy (1985), vector autoregressions have the status of “reduced form” models and therefore are merely vehicles to summarize the dynamic properties of the data. Without reference to a specific economic structure, such reduced-formVAR models are difficult to understand. For example, it is often difficult to draw any conclusion from the large number of coefficient estimates in a VAR system. As long as such parameters are not related to “deep” structural parameters characterizing preferences, technologies, and optimization behavior, the parameters do not have an economic meaning and are subject to the so-called Lucas critique. Sims (1981, 1986), Bernanke (1986), and Shapiro & Watson (1988) put forward a new class of econometric models that is now known as structural vector autoregression (SVAR) or identified VAR . Instead of identifying the (autoregressive) coefficients, identification focuses on the errors of the system, which are interpreted as (linear combinations of) exogenous shocks. In the early applications of Sargent (1978) and Sims (1980), the innovations of the VAR were orthogonalized using a Choleski decomposition of the covariance matrix.
186 citations
01 Aug 2004
TL;DR: The first step in building dynamic econometric models entails a detailed analysis of the characteristics of the individual time series variables involved as mentioned in this paper, which is important because the properties of individual series have to be taken into account in modeling the data generation process (DGP) of a system of potentially related variables.
Abstract: Characteristics of Time Series The first step in building dynamic econometric models entails a detailed analysis of the characteristics of the individual time series variables involved. Such an analysis is important because the properties of the individual series have to be taken into account in modeling the data generation process (DGP) of a system of potentially related variables. Some important characteristics of time series can be seen in the example series plotted in Figure 2.1. The first series consists of changes in seasonally adjusted U.S. fixed investment. It appears to fluctuate randomly around a constant mean, and its variability is homogeneous during the observation period. Some correlation between consecutive values seems possible. In contrast, the second series, representing a German long-term interest rate, evolves more slowly, although its variability is also fairly regular. The sluggish, longer term movements are often thought of as a stochastic trend. The third series represents German gross national product (GNP). It appears to evolve around a deterministic polynomial trend, and, moreover, it has a distinct seasonal movement. In addition there is a level shift in the third quarter of 1990. This shift is due to a redefinition of the series, which refers to West Germany only until the second quarter of 1990 and to the unified Germany afterwards. Although German reunification took place officially in October 1990, many economic time series were adjusted already on 1 July of that year, the date of the monetary unification. Finally, the last series in Figure 2.1 represents the daily DAFOX returns from 1985 to 1996. The DAFOX is a German stock index.
73 citations
TL;DR: A nonlinear version of the threshold autoregressive model for time series is introduced, which brings together the genetic algorithm, in its simplest binary form, and some basic features from spline theory, and results in a powerful 8exible tool which is shown to be able to approximate a wide class of nonlinear time series models.
48 citations
TL;DR: In this article, the authors proposed some tests for fitting a regression model with a long memory covariate process and with errors that form either a martingale difference sequence or a long-memory moving average process, independent of the covariate.
Abstract: This paper proposes some tests for fitting a regression model with a long memory covariate process and with errors that form either a martingale difference sequence or a long memory moving average process, independent of the covariate. The tests are based on a partial sum process of the residuals from the fitted regression. The asymptotic null distribution of this process is discussed in some detail under each set of these assumptions. The proposed tests are shown to have known asymptotic null distributions in the case of martingale difference errors and also in the case of fitting a polynomial of a known degree through the origin when the errors have long memory. The theory is then illustrated with some examples based on the forward premium anomaly where a squared interest rate differential proxies a time dependent risk premium. The paper also shows that the proposed test statistic converges weakly to nonstandard distributions in some cases.The authors gratefully acknowledge the helpful comments of the co-editor Don Andrews and two anonymous referees. The research of the first two authors was partly supported by NSF grant DMS 00-71619.
24 citations
TL;DR: In this paper, an estimation theory is provided for the fitting of possibly incorrect, invertible, short-memory models to (short or long-memory) time series or time series arrays by multistep prediction error minimization or Gaussian likelihood maximization.
17 citations
27 Jun 2004
TL;DR: The proposed model is an application of the Takagi-Sugeno's fuzzy system and is a generalization of the threshold autoregressive model for time series, and the applicability is considered by applying to real time series.
Abstract: A time series model based on fuzzy if-then rules is introduced and its estimation problem is considered. The proposed model is an application of the Takagi-Sugeno's fuzzy system and is a generalization of the threshold autoregressive model for time series. The applicability of the proposed model is considered by applying to real time series.
15 citations
TL;DR: In this paper, it was shown that the behavior of the periodogram and other tapered estimators cannot be simply extended from the work of Kunsch (1986) and Hurvich & Beltrao (1993) on long memory induced by a pole at the origin, and potentially large both positive and negative bias can be found from the same value of the long-memory parameter.
Abstract: Seasonally persistent models were first introduced by Andel (1986) and Gray et al. (1989) to extend autoregressive moving-average and fractionally differenced models and to encompass long-memory quasi-periodic behaviour. These models are, for certain ranges of parameters, stationary, and we prove here that the behaviour of the periodogram and other tapered estimators cannot be simply extended from the work of Kunsch (1986) and Hurvich & Beltrao (1993) on long memory induced by a pole at the origin. We demonstrate that potentially large both positive and negative bias can be found from the same value of the long-memory parameter, and that the new distribution can be easily written down in the case of Gaussian processes. We also consider using both the cosine taper and the sine taper. The extended least squares estimator is also considered in this context.
13 citations
TL;DR: A general class of matricial measures of dependence is proposed, that corresponds to sample autocovariance matrices of the vector time series of squared residuals and cross products of (standardized) residuals, that derive the asymptotic distribution of these residual autocorrelations.
12 citations
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TL;DR: In this article, the integer-valued moving average model is used to model the number of transactions in intra-day data of stocks and the conditional mean and variance properties are discussed and model extensions to include explanatory variables are offered.
Abstract: The integer-valued moving average model is advanced to model the number of transactions in intra-day data of stocks The conditional mean and variance properties are discussed and model extensions to include, eg, explanatory variables are offered Least squares and generalized method of moment estimators are presented In a small Monte Carlo study the least squares estimator comes out as the best choice Empirically we find support for the use of long-lag moving average models in a Swedish stock series News about prices are found to exert a symmetric and positive effect on the number of transactions
11 citations
TL;DR: In this article, a new identification method based on the residual white noise autoregressive criterion (Pukkila et al., 1990) was proposed to select the order of VARMA structures.
Abstract: In this paper we propose a new identification method based on the residual white noise autoregressive criterion (Pukkila et al., 1990) to select the order of VARMA structures. Results from extensive simulation experiments based on different model structures with varying number of observations and number of component series are used to demonstrate the performance of this new procedure. We also use economic and business data to compare the model structures selected by this order selection method with those identified in other published studies.
10 citations
01 Jan 2004
TL;DR: In this article, the autocorrelation in a regression model is considered and the generalized least-squares technique is used to estimate the regression coefficients, assuming that the disturbances follow a first-order autoregressive process.
Abstract: The presence of autocorrelation in a regression model requires the use of the generalized least-squares technique in estimating the regression coefficients. To study the diagnostics of such a model it is therefore necessary to take account of the autocorrelation while re-estimating the parameters after the deletion of an observation. In this paper we look into this problem assuming that the disturbances follow a first-order autoregressive process.
TL;DR: In this article, a Cautious Minimum Variance (CMV) control approach is proposed for controlling industrial process variability when the model parameters are estimated from data and subject to uncertainty.
Abstract: This article investigates a Cautious Minimum Variance (CMV) control approach for controlling industrial process variability when the model parameters are estimated from data and subject to uncertainty. CMV control has a number of advantages over traditional robust control methods. It incorporates probabilistic, as opposed to deterministic, measures of parameter uncertainty, which are more consistent with the statistical methods typically used to estimate industrial process models. CMV control is also more consistent with the objective of minimizing process variability, since parameter uncertainty is treated simply as an additional source of variation. CMV results have previously been derived for the case where the process disturbance follows a first-order integrated moving average model. This work extends the results to autoregressive moving average and autoregressive integrated moving average disturbances.
TL;DR: In this article, the authors study the application of the quasi-least squares method to estimate the parameters in a replicated time series model with errors that follow an autoregressive process of order p.
Abstract: Time series regression models have been widely studied in the literature by several authors. However, statistical analysis of replicated time series regression models has received little attention. In this paper, we study the application of the quasi-least squares method to estimate the parameters in a replicated time series model with errors that follow an autoregressive process of order p. We also discuss two other established methods for estimating the parameters: maximum likelihood assuming normality and the Yule-Walker method. When the number of repeated measurements is bounded and the number of replications n goes to infinity, the regression and the autocorrelation parameters are consistent and asymptotically normal for all three methods of estimation. Basically, the three methods estimate the regression parameter efficiently and differ in how they estimate the autocorrelation. When p=2, for normal data we use simulations to show that the quasi-least squares estimate of the autocorrelation is undoub...
25 Jul 2004
TL;DR: In this paper, an autoregressive model is fitted to the first differences of the data by minimising the residual sum of squared, subject certain restrictions that enable the gaps left by the missing observations to be bridged.
Abstract: This paper predicts the 100 missing values in CATS Benchmark. The SVCA model is an autoregressive model in which the coefficients vary smoothly with time. The model is fitted to the first differences of the data by minimising the residual sum of squared, subject certain restrictions that enable the gaps left by the missing observations to be bridged. The path of each time-varying coefficient is described by a combination of a sine and cosine function. The latter are specified via their amplitudes, phases and periods.
TL;DR: In this paper, the authors make a Bayesian analysis of a first-order autoregressive process subject to one change in both the variance of the error terms and the autocorrelation coefficients at an unknown time point.
Abstract: The purpose of this paper is to make a Bayesian analysis of a first-order autoregressive process subject to one change in both the variance of the error terms and the autocorrelation coefficients at an unknown time point. The main emphasis is to derive the posterior distributions of the change point, the autocorrelation parameter and the variance ratio. A numerical illustration is provided using the Gibbs sampler.
TL;DR: In this paper, the integer-valued moving average model is used to model the number of transactions in intra-day data of stocks and the conditional mean and variance properties are discussed and model extensions to include explanatory variables are offered.
Abstract: The integer-valued moving average model is advanced to model the number of transactions in intra-day data of stocks. The conditional mean and variance properties are discussed and model extensions to include, e.g., explanatory variables are offered. Least squares and generalized method of moment estimators are presented. In a small Monte Carlo study the least squares estimator comes out as the best choice. Empirically we find support for the use of long-lag moving average models in a Swedish stock series. News about prices are found to exert a symmetric and positive effect on the number of transactions.
TL;DR: For estimating spectral densities of stationary seasonal time series processes, a new kernel is proposed in this paper, which is of the shape which is in harmony with oscillating patterns of the autocorrelation functions of typical seasonal time-series process.
TL;DR: In this paper, the authors studied the limit behavior of the partial sums, sample variance, and periodogram of the stable moving average process explored in Resnick, S., Samorodnitsky, G., and Xue, F.
Abstract: We study the limit behavior of the partial sums, sample variance, and periodogram of the stable moving average process explored in Resnick, S., Samorodnitsky, G., and Xue, F. (1999). How misleading can sample ACF's of stable MA's be? (Very!). Annals of Applied Probability, 9 (3), 797–817. Each of these statistics has a rate of convergence involving the “characteristic exponent” α, which is an unknown parameter of the model. Through the employment of self-normalization, this number α can be removed from the rate of convergence; the various limit distributions can then be approximated via subsampling. As a result, statistical inference for the mean can be conducted without knowledge (or explicit estimation) of α. New techniques, which are easily generalizable to a random field model, are presented to prove these results.
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TL;DR: In this paper, the authors introduce a smooth transition model whose parameters can change in a smooth fashion between regimes as a function of an exogenous variable, which is useful in situations in which it is suspected that the behaviour of the dependent variable may vary between regimes.
Abstract: During the last few years nonlinear models have been a very active area of econometric research: new models have been introduced and existing ones generalized. To a large extent, these developments have concerned models in which the conditional moments are regime-dependent. In such models, the different regimes are usually linear and the change between them is governed by an observable or unobservable variable. These specifications can be useful in situations in which it is suspected that the behaviour of the dependent variable may vary between regimes. A classical example can be found the business cycle literature where it is argued that contractions in the economy are not only more violent but also short-lived than expansions. Unemployment, which tends to rise faster during recessions than decline during booms, constitutes another example. Two of the most popular regime-dependent models are the smooth transition and the threshold model. In both models cases the transition variable is observable but the specification of the way in which the model changes from one regime to the other is different. Particularly, in the smooth transition model the change is a continuous whereas in the threshold model it is abrupt. One of the factors that has influenced the development of nonlinear models are improvements in computer technology. They have not only permitted an introduction of more complex models but have also allowed the use of computer-intensive methods in hypothesis testing. This is particularly important in nonlinear models because there these methods have proved to be practical in testing statistical hypothesis such as linearity and parameter constancy. In general, these testing situation are not trivial and their solution often requires computer-intensive methods. In particular, bootstrapping and Monte Carlo testing are now commonly used. In this thesis the smooth transition model is used in different ways. In the first chapter, a vector smooth transition model is used as a device for deriving a test for parameter constancy in stationary vector autoregressive models. In the second chapter we introduce a panel model whose parameters can change in a smooth fashion between regimes as a function of an exogenous variable. The method is used to investigate whether financial constraints affect firms' \ investment decisions. The third chapter is concern with linearity testing in smooth transition models. New tests are introduced and Monte Carlo testing techniques are shown to be useful in achieving control over the size of the test. Finally, the last chapter is devoted to the Smooth Permanent Surge model. This is a nonlinear moving average model in which a shock can have transitory or permanent effects depending on its sign and magnitude. Test for linearity and random walk hypothesis are introduced.
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TL;DR: In this paper, a moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established, where the main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random variables and the continuity, or weaker, of the spectral density.
Abstract: A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random variables and the continuity, or weaker, of the spectral density of the moving average process We also obtain the moderate deviations for the empirical spectral density, exhibiting an interesting new form of the rate function, ie with a correction term compared to the Gaussian rate functionnal
TL;DR: In this article, a simple formula for the local power of second order for the likelihood ratio, the Wald and score statistics, when a Gaussian autoregressive and moving average model of first order is considered and the interest and nuisance parameter vectors are multi-dimensional.
Abstract: In this paper we extend heuristically a simple formula for the local power of second order for the likelihood ratio, the Wald and score statistics, when a Gaussian autoregressive and moving average model of first order is considered and the interest and nuisance parameter vectors are multi-dimensional. The second order local power for the three criteria mentioned here are compared using particular models and hypotheses.
TL;DR: The objective of the present paper is to simplify the simulation method for a strictly stationary non-Gaussian process with given one-dimensional marginal distribution and autocorrelation function - if by Mehler formula it is possible to find an autoc orrelation function yielding the target autocOrrelation function.
Abstract: In a first part of the paper a simulation method for a strictly stationary non-Gaussian process with given one-dimensional marginal distribution (or N-first statistical moments) and autocorrelation function is recalled. This method was already widely treated in the articles [14] and [13]. The objective of the present paper is twofold: first, to simplify this method - if by Mehler formula it is possible to find an autocorrelation function yielding the target autocorrelation function, and second, analyze the difference between the given autocorrelation function and the model one.
01 Jan 2004
TL;DR: In this paper, the estimation of the autoregressive coefficients is studied in non-parametric and semiparametric models with auto-regression time series errors, and the relationship via regression surface function nonparametrically and then use the estimated residuals to estimate the second-order characteristics of the unknown noise process.
Abstract: The estimation of the autoregressive coefficients are studied in non- parametric and semiparametric models with autoregressive time series errors. We estimate the relationship via regression surface function nonparametrically and then use the estimated residuals to estimate the second-order characteristics of the unknown noise process. It is shown that under mild assumptions theses estimator are asymptotically equivalent to the estimators based on the autoregressive error process. For real data analysis, we find that the stock data has nonlinear characteristic and the nonparametric prediction ability is better than the classical multivariate time series model.
TL;DR: The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average (ARMA) model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators.
Abstract: The polynomial matrix using the block coefficient matrix representation auto-regressive moving average (referred to as the PM-ARMA) model is constructed in this paper for actively controlled multi-degree-of-freedom (MDOF) structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization. The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average (ARMA) model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators. (The sensors and actuators are required to maintain the identical number.) under any dimensional stationary stochastic excitation.
19 Aug 2004
TL;DR: A universal method to achieve nonlinear model identification based on the theory of information entropy and its development, called as nonlinear irreducible autocorrelation is introduced.
Abstract: Although, in theory, the neural network is able to fit, model and predict any continuous determinant system, there is still an obstacle to prevent the neural network from wider and more effective applications due to the lack of complete theory of model identification. This paper addresses this issue by introducing a universal method to achieve nonlinear model identification. The proposed method is based on the theory of information entropy and its development, which is called as nonlinear irreducible autocorrelation. The latter is originally defined in the paper and could determine the optimal autoregressive order of nonlinear autoregression models by investigating the irreducible auto-dependency of the investigated time series. Following the above proposal, robust prediction of chaotic time series became realizable. Our idea is perfectly supported by computer simulations.
TL;DR: A number of algorithms generating noise sequences with precisely predicted statistical characteristics are suggested that can be used to study a response of physical systems to external noise disturbances and internal fluctuation processes.
Abstract: Properties of a modified logistic map are investigated analytically and numerically. The effect of the order parameter on the probability measure, autocorrelation function, average value, and variance of time series generated by a dynamic system with discrete time is studied. A number of algorithms generating noise sequences with precisely predicted statistical characteristics are suggested. Such sequences can be used to study a response of physical systems to external noise disturbances and internal fluctuation processes.