On diagnostic checking of the autoregressive conditional intensity model

The autoregressive conditional intensity model proposed by Russell (1998) is a promising option for fitting multivariate high frequency irregularly spaced data. The authors acknowledge the validity of this model by showing the independence of its generalized residuals, a crucial assumption of the model formulation not readily recognized by researchers. The authors derive the large‐sample distribution of the autocorrelations of the generalized residual series and use it to construct a goodness‐of‐fit test for the model. Empirical results compare the performance of their test with other off‐the‐shelf tests such as the Ljung–Box test. They illustrate the use of their test with transaction records of the HSBC stock.     

A note on the limiting properties of the least squares estimation for the random coefficient autoregressive model

This note is concerned with the limiting properties of the least squares estimation for the random coefficient autoregressive model. In contrast with existing results, ours is applicable to a wide range of models under more general assumptions.     

On a mixture vector autoregressive model

The authors show how to extend univariate mixture autoregressive models to a multivariate time series context. Similar to the univariate case, the multivariate model consists of a mixture of stationary or nonstationary autoregressive components. The authors give the first and second order stationarity conditions for a multivariate case up to order 2. They also derive the second order stationarity condition for the univariate mixture model up to arbitrary order. They describe an EM algorithm for estimation, as well as a diagnostic checking procedure. They study the performance of their method via simulations and include a real application.     

A note on efficient simulation of multidimensional spatial autoregressive processes

In applications of spatial statistics, it is necessary to compute the product of some matrix W of spatial weights and a vector y of observations. The weighting matrix often needs to be adapted to the specific problems, such that the computation of Wy cannot necessarily be done with available R-packages. Hence, this article suggests one possibility treating such issues. The proposed technique avoids the computation of the matrix product by calculating each entry of Wy separately. Initially, a specific spatial autoregressive process is introduced. The performance of the proposed program is briefly compared to a basic program using the matrix multiplication.     

A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models

Just as frequentist hypothesis tests have been developed to check model assumptions, prior predictive p-values and other Bayesian p-values check prior distributions as well as other model assumptions. These model checks not only suffer from the usual threshold dependence of p-values, but also from the suppression of model uncertainty in subsequent inference. One solution is to transform Bayesian and frequentist p-values for model assessment into a fiducial distribution across the models. Averaging the Bayesian or frequentist posterior distributions with respect to the fiducial distribution can reproduce results from Bayesian model averaging or classical fiducial inference.     

A threshold autoregressive model for wholesale electricity prices

Summary.  We introduce a discrete time model for electricity prices which accounts for both transitory spikes and temperature effects. The model allows for different rates of mean reversion: one for weather events, one around price jumps and another for the remainder of the process. We estimate the model by using a Markov chain Monte Carlo approach with 3 years of daily data from Allegheny County, Pennsylvania. We show that our model outperforms existing stochastic jump diffusion models for this data set. Results also demonstrate the importance of model parameters corresponding to both the temperature effect and the multilevel mean reversion rate.     

On a mixture autoregressive model

We generalize the Gaussian mixture transition distribution (GMTD) model introduced by Le and co-workers to the mixture autoregressive (MAR) model for the modelling of non-linear time series. The models consist of a mixture of K stationary or non-stationary AR components. The advantages of the MAR model over the GMTD model include a more full range of shape changing predictive distributions and the ability to handle cycles and conditional heteroscedasticity in the time series. The stationarity conditions and autocorrelation function are derived. The estimation is easily done via a simple EM algorithm and the model selection problem is addressed. The shape changing feature of the conditional distributions makes these models capable of modelling time series with multimodal conditional distributions and with heteroscedasticity. The models are applied to two real data sets and compared with other competing models. The MAR models appear to capture features of the data better than other competing models do.     

An autoregressive model based on the generalized hyperbolic distribution

We define a nonlinear autoregressive time series model based on the generalized hyperbolic distribution in an attempt to model time series with non-Gaussian features such as skewness and heavy tails. We show that the resulting process has a simple condition for stationarity and it is also ergodic. An empirical example with a forecasting experiment is presented to illustrate the features of the proposed model.     

A nonparametric test of conditional autoregressive heteroscedasticity for threshold autoregressive models

Threshold autoregressive models are widely used in time‐series applications. When building or using such a model, it is important to know whether conditional heteroscedasticity exists. The authors propose a nonparametric test of this hypothesis. They develop the large‐sample theory of a test of nonlinear conditional heteroscedasticity adapted to nonlinear autoregressive models and study its finite‐sample properties through simulations. They also provide percentage points for carrying out this test, which is found to have very good power overall.     

Testing stability in a spatial unilateral autoregressive model

ABSTRACT

Least squares estimator of the stability parameter ? ? |α| + |β| for a spatial unilateral autoregressive process X_{k, ?} = αX_{k ? 1, ?} + βX_{k, ? ? 1} + ?_{k, ?} is investigated and asymptotic normality with a scaling factor n^5/4 is shown in the unstable case ? = 1. The result is in contrast to the unit root case of the AR(p) model X_k = α₁X_{k ? 1} + ??? + α_pX_{k ? p} + ?_k, where the limiting distribution of the least squares estimator of the unit root parameter ? ? α₁ + ??? + α_p is not normal.     

A note on the manova model with double linear restrictions

In this note we show how one may construct goodness-of-fit tests to test hypotheses for the restricted MANOVA and GMANOVA models using the multivariate seemingly unrelated regression (MSUR) model.     

A transitional Markov switching autoregressive model

ABSTRACT

This paper is concerned with properties of a transitional Markov switching autoregressive (TMSAR) model, together with its maximum-likelihood estimation and inference. We extend existing MSAR models by allowing dependence of AR parameters on hidden states at time points prior to the current time t. A stationary solution is given and expressions for the theoretical autocovariance function are derived. Two time series are analyzed and the new model outperforms two existing MSAR models in terms of maximized log-likelihood, residual correlations, and one-step-ahead forecasting performance. The new model also gives more regime changes in agreement with real events.     

A wavelet-based time-varying autoregressive model for non-stationary and irregular time series

In this work we propose an autoregressive model with parameters varying in time applied to irregularly spaced non-stationary time series. We expand all the functional parameters in a wavelet basis and estimate the coefficients by least squares after truncation at a suitable resolution level. We also present some simulations in order to evaluate both the estimation method and the model behavior on finite samples. Applications to silicates and nitrites irregularly observed data are provided as well.     

Conditional heteroscedasticity test for Poisson autoregressive model

In this article, the problem of interest is testing the conditional heteroscedasticity of Poisson autoregressive model. We construct a non parametric test statistic based on empirical likelihood method. The asymptotic distribution of the proposed statistic is derived and its finite-sample property is examined through Monte Carlo simulations. The simulation results show that the proposed method is good for practical use.     

Sample path properties of an explosive double autoregressive model

This article studies sample path properties of an explosive double autoregressive (DAR) model. After suitable renormalization, it is shown that the sample path converges weakly to a geometric Brownian motion. This further strengthens our understanding of sample paths of nonstationary DAR processes. The obtained results can be extended to nonstationary random coefficient autoregressive (RCA) models. Simulation studies are carried out to support our results.     

A note on a modified double stage shrinkage estimator

A modified double stage shrinkage estimator has been proposed for the single parameter θ of a distribution function _Fθ. It is shown to be locally better in comparison to the usual double stage shrinkage estimator in the sense of smaller mean squared error in a certain neighbourhood of prior estimate θ_o of θ.     

Efficient estimation for the conditional autoregressive model

Recently, spatial regression models have been attracting a great deal of attention in areas ranging from effect of traffic congestion on accident rates to the analysis of trends in gastric cancer mortality. In this paper, we propose efficient estimators for the regression coefficients of the spatial conditional autoregressive model, when uncertain auxiliary information is available about these coefficients. We provide efficiency comparisons of the proposed estimators based on asymptotic risk analysis and Monte Carlo simulations. We apply the proposed methods to real data on Boston housing prices and illustrate how a bootstrapping approach can be employed to compute prediction errors of the estimators.     

Lindley first-order autoregressive model with applications

ABSTRACT

A new stationary first-order autoregressive process with Lindley marginal distribution, denoted as LAR(1) is introduced. We derive the probability function for the innovation process. We consider many properties of this process, involving spectral density, some multi-step ahead conditional measures, run probabilities, stationary solution, uniqueness and ergodicity. We estimate the unknown parameters of the process using three methods of estimation and investigate properties of the estimators with some numerical results to illustrate them. Some applications of the process are discussed to two real data sets and it is shown that the LAR(1) model fits better than other known non Gaussian AR(1) models.     

Detection of outliers in mixed regressive-spatial autoregressive models

ABSTRACT

This article studies the outlier detection problem in mixed regressive-spatial autoregressive model. The formulae for testing outliers and their approximate distributions are derived under the mean-shift model and the variance-weight model, respectively. The simulation studies are conducted for examining the power and size of the test, as well as for the detection of outliers when a simulated data contains several outliers. A real data is analyzed to illustrate the proposed method, and modified models based on mean-shift and variance-weight models in which detected outliers are taken into account are suggested to deal with the outliers and confirm theconclusions.     

Structural vector autoregressive analysis for cointegrated variables

Summary Vector autoregressive (VAR) models are capable of capturing the dynamic structure of many time series variables. Impulse response functions are typically used to investigate the relationships between the variables included in such models. In this context the relevant impulses or innovations or shocks to be traced out in an impulse response analysis have to be specified by imposing appropriate identifying restrictions. Taking into account the cointegration structure of the variables offers interesting possibilities for imposing identifying restrictions. Therefore VAR models which explicitly take into account the cointegration structure of the variables, so-called vector error correction models, are considered. Specification, estimation and validation of reduced form vector error correction models is briefly outlined and imposing structural short- and long-run restrictions within these models is discussed. I thank an anonymous reader for comments on an earlier draft of this paper that helped me to improve the exposition.