68,970 research outputs found
Noncausal autoregressions for economic time series
This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. In these models, future errors are predictable, indicating that they can be used to empirically approach rational expectations models with nonfundamental solutions. In the previous theoretical literature, nonfundamental solutions have typically been represented by noninvertible moving average models. However, noncausal autoregressive and noninvertible moving average models closely approximate each other, and therefore,the former provide a viable and practically convenient alternative. We show how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and derive related test procedures. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a model selection procedure is proposed. As an empirical application, we consider modeling the U.S. inflation which, according to our results, exhibits purely forward-looking dynamics
Noncausal autoregressions for economic time series
This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. In these models, future errors are predictable, indicating that they can be used to empirically approach rational expectations models with nonfundamental solutions. In the previous theoretical literature, nonfundamental solutions have typically been represented by noninvertible moving average models. However, noncausal autoregressive and noninvertible moving average models closely approximate each other, and therefore,the former provide a viable and practically convenient alternative. We show how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and derive related test procedures. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a model selection procedure is proposed. As an empirical application, we consider modeling the U.S. inflation which, according to our results, exhibits purely forward-looking dynamics.Noncausal autoregression; expectations; inflation persistence
Improved Subset Autoregression: With R Package
The FitAR R (R Development Core Team 2008) package that is available on the Comprehensive R Archive Network is described. This package provides a comprehensive approach to fitting autoregressive and subset autoregressive time series. For long time series with complicated autocorrelation behavior, such as the monthly sunspot numbers, subset autoregression may prove more feasible and/or parsimonious than using AR or ARMA models. The two principal functions in this package are SelectModel and FitAR for automatic model selection and model fitting respectively. In addition to the regular autoregressive model and the usual subset autoregressive models (Tong'77), these functions implement a new family of models. This new family of subset autoregressive models is obtained by using the partial autocorrelations as parameters and then selecting a subset of these parameters. Further properties and results for these models are discussed in McLeod and Zhang (2006). The advantages of this approach are that not only is an efficient algorithm for exact maximum likelihood implemented but that efficient methods are derived for selecting high-order subset models that may occur in massive datasets containing long time series. A new improved extended {BIC} criterion, {UBIC}, developed by Chen and Chen (2008) is implemented for subset model selection. A complete suite of model building functions for each of the three types of autoregressive models described above are included in the package. The package includes functions for time series plots, diagnostic testing and plotting, bootstrapping, simulation, forecasting, Box-Cox analysis, spectral density estimation and other useful time series procedures. As well as methods for standard generic functions including print, plot, predict and others, some new generic functions and methods are supplied that make it easier to work with the output from FitAR for bootstrapping, simulation, spectral density estimation and Box-Cox analysis.
ACCUMULATED PREDICTION ERRORS, INFORMATION CRITERIA AND OPTIMAL FORECASTING FOR AUTOREGRESSIVE TIME SERIES
The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APE,is investigated in infinite-order autoregressive (AR()) models. Instead of accumulating squares of sequential prediction errors from the beginning, APE is obtained by summing these squared errors from stage , where is the sample size and $0Accumulated prediction errors, Asymptotic equivalence, Asymptotic efficiency, Information criterion, Order selection, Optimal forecasting
Determining the Number of Regimes in a Threshold Autoregressive Model Using Smooth Transition Autoregressions
In this paper we propose a method for determining the number of regimes in threshold autoregressive models using smooth transition autoregression as a tool. As the smooth transition model is just an approximation to the threshold autoregressive one, no asymptotic properties are claimed for the proposed method. Tests available for testing the adequacy of a smooth transition autoregressive model are applied sequentially to determine the number of regimes. A simulation study is performed in order to find out the finite-sample properties of the procedure and to compare it with two other procedures available in the literature. We find that our method works reasonably well for both single and multiple threshold models.Model specification; model selection criterion; nonlinear modelling; sequential testing; switching regression
Computational problems in autoregressive moving average (ARMA) models
The choice of the sampling interval and the selection of the order of the model in time series analysis are considered. Band limited (up to 15 Hz) random torque perturbations are applied to the human ankle joint. The applied torque input, the angular rotation output, and the electromyographic activity using surface electrodes from the extensor and flexor muscles of the ankle joint are recorded. Autoregressive moving average models are developed. A parameter constraining technique is applied to develop more reliable models. The asymptotic behavior of the system must be taken into account during parameter optimization to develop predictive models
Are you sure you are using the correct model? Model Selection and Averaging of Impulse Responses
Impulse responses can be estimated to analyze the effects of a shock to a variable over time. Typically, (vector) autoregressive models are estimated and the impulse responses implied by the coefficients calculated. In general, however, there is no knowledge of the correct autoregressive order. In fact, when models are seen as approximations to the data generating process (DGP), all models are imperfect and there is no a priori difference in their validity. Hence, a lag length should be chosen by a sensible method, for instance an information criterion. In Monte Carlo simulations, this paper studies what characteristics influence the optimal autoregressive order when all models are only approximations to the DGP. It finds that the precise coefficients in the DGP, the sample size, and the impulse response horizon to be estimated all influence the mean squared error-minimizing lag length. Furthermore, it evaluates the performance of model selection and averaging methods for estimating impulse responses. Across the characteristics found to be relevant, averaging outperforms model selection, and in particular Mallows' Model Averaging and a smoothed Hannan-Quinn Information Criterion perform best. Finally, the study is extended to vector autoregressive models. In addition to the characteristics relevant in the univariate case, the optimal lag length also depends on which (cross) impulse response is to be estimated. Many issues remain for vector autoregressive models, however, and more work is necessary
Order Selection of Spatial and Temporal Autoregressive Models with Errors in Variables
In this paper we consider the issues involved in model order selection for processes observed with additive Gaussian noise. In particular, we discuss conditional maximum likelihood estimation of noisy autoregressive models and provide an estimator that takes care of the observational noise. The estimator is weakly consistent, can be computed in only O(n) steps and can be used in the automatic model identification phase. Using information criteria, an extensive simulation study shows the results of order selection in the context of time and spatial series analysis
- …