On determination of the order of an autoregressive model

AbstractTo determine the order of an autoregressive model, a new method based on information theoretic criterion is proposed. This method is shown to be strongly consistent and the convergence rate of the probability of wrong determination is established

Full range autoregressive time series models

EnA new family of time series models, called the Full Range Autoregressive model, is introduced which avoids the difficult problem of order determination in time series analysis. Some of the basic statistical properties of the new model are studied

Microprocessor Implementation of Autoregressive Analysis of Process Sensor Signals

Automated signal analysis can help for effective system surveillance and also to analyze the dynamic behavior of the system such as impulse response, step response etc. Autoregressive analysis is a parametric technique widely used for system surveillance and diagnosis. The main aim objective of this research work is to develop an embedded system for autoregressive analysis of sensor signals in an online fashion for monitoring system parameters. This thesis presents the algorithm, data representation and performance of the optimized microprocessor implementation of autoregressive analysis. In this work an autoregressive (AR) model is generated as a solution to a linear system of equations called Yule-Walker linear equations. The generated model is then implemented on Motorola PowerPC MPC555 processor. The embedded software for autoregressive analysis is written in the C programming language using fixed point arithmetic. It includes estimation of the autoregressive parameters, estimation of the noise variance recursively using the AR parameters, determination of the optimal model order and the model validation

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space andthe rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using modelselection criteria. We consider model selection criteria which have data-dependent penalties for alack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybridof traditional criteria and criteria with data-dependant penalties. In order to compute the fit ofeach model, we propose an iterative procedure to compute the maximum likelihood estimates ofparameters of a VAR model with short-run and long-run restrictions. Our Monte Carlo simulationsmeasure the improvements in forecasting accuracy that can arise from the joint determination oflag-length and rank, relative to the commonly used procedure of selecting the lag-length only andthen testing for cointegration.

Bayesian Nonparametric Inference of Switching Linear Dynamical Systems

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hierarchical Dirichlet process prior to learn an unknown number of persistent, smooth dynamical modes. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn SLDS with varying state dimension or switching VAR processes with varying autoregressive order. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA stock index, and a maneuvering target tracking application.Comment: 50 pages, 7 figure

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties for a lack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybrid of traditional criteria with data-dependant penalties. In order to compute the fit of each model, we propose an iterative procedure to compute the maximum likelihood estimates of parameters of a VAR model with short-run and long-run restrictions. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank, relative to the commonly used procedure of selecting the lag-length only and then testing for cointegration.Reduced rank models, model selection criteria, forecasting accuracy

Vector Autoregressive Integrated (VARI) Method for Forecasting the Number of Internasional Visitor in Batam and Jakarta

Forecasting methods that are often used are time series analysis, the Autoregressive (AR) method. The AR method only carries out univariate analysis, meaning that it carries out a separate model between the number of international visitor coming to Indonesia through Batam and Jakarta. Though there is a possibility, the number of international visitor arriving through Jakarta affects the number of international visitor arriving through Batam. Therefore, in this study the Vector Autoregressive Integrated (VARI) method is used. The VARI model is used on the number of international visitor arrivals per month at Batam and Jakarta for the period Januari 2014 – December 2019. VARI model formation through several stages, namely stationarity test, autoregressive order determination, VARI model formation, and diagnostic checking of the model. With the VARI model, VARI(5,1), the two significant simultaneously equation results are obtained. The Mean Absolute Percentage Error (MAPE) in this model are as follows 1,98% and 2,48% in predicting the number of international visitor arrivals in Batam and Jakarta. In this study also forecasting the number of international visitor arrivals in Batam and Jakarta in January – December 202

Monthly sunspot number time series analysis and its modeling through autoregressive artificial neural network

This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p,q)). Based on minimization of AIC we find 3 and 1 as the best values of p and q respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott's index of second order and coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).Comment: 17 pages, 4 figure

The Performance of AlCC as an Order Selection Criterion in ARMA Time Series Models

This study is undertaken with the objective of investigating the performance of Akaike's Information Corrected Criterion (AlCC) as an order determination criterion for the selection of Autoregressive Moving-Average or ARMA (P,q) time series model. A simulation investigation was carried to determine the probability of the AlCC statistics picking up the correct model. Result obtained showed that the probability of the AlCC criterion picking up the correct model was moderately good. The problem of over parameterization existed but under parameterization was found to be minimal. Hence, for any two comparable models, it is always safe to choose the one with lower order of p and q

Data-based Parameter Estimation of Generalized Multidimensional Langevin Processes

The generalized Langevin equation is useful for modeling a wide range of physical processes. Unfortunately its parameters, especially the memory function, are difficult to determine for nontrivial processes. We establish relations between a time-discrete generalized Langevin model and discrete multivariate autoregressive (AR) or autoregressive moving average models (ARMA). This allows a wide range of discrete linear methods known from time series analysis to be applied. In particular, the determination of the memory function via the order of the respective AR or ARMA model is addressed. The method is illustrated on a one-dimensional test system and subsequently applied to the molecular dynamics time series of a biomolecule that exhibits an interesting relationship between the solvent method used, the respective molecular conformation, and the depth of the memory