On the stability of nonlinear ARMA models

In the present paper we study the stability of a class of nonlinear ARMA models. We derive a sufficient condition to ensure the geometric ergodicity and we apply it to a very general threshold ARMA model imposing a mild assumption on the thresholdsNonlinear ARMA models, threshold ARMA processes, stationary processes, geometric ergodicity

An Econometric model for the evolution of the Romanian Interbank Bid Rate (ROBID) in the context of the international financial crisis

The paper presents the econometric modeling of overnight inter-banking interest rates (ROBID) in our country, the analyzed period is between 1999-2010. The international financial crises had a great impact on the level of inter-banking interest rates after 2007 and it reflects the new level of risk for the Romanian system banking. The econometric model used in modeling the interest rates is an autoregressive moving average (ARMA) model, the ARMA model is typically applied to time series data; the paper propose several ARMA models, applies econometric tests and based on them the analyzed series (the inter-banking interest rates) forecast will be made.ROBID, ARIMA model, financial crisis, forecast.

Online Learning for Time Series Prediction

In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning algorithms for the prediction problem, without assuming that the noise terms are Gaussian, identically distributed or even independent. Furthermore, we show that our algorithm's performances asymptotically approaches the performance of the best ARMA model in hindsight.Comment: 17 pages, 6 figure

Hierarchical equilibria of branching populations

In this paper we study high moment partial sum processes based on residuals of a stationary ARMA model with or without a unknown mean parameter. We show that they can be approximated in probability by the analogous processes which are obtained from the independent and identically distributed (iid) errors of the ARMA model. However, if a unknown mean parameter is used, there will be an additional term that depends on model parameters and a mean estimator. But, when properly normalized, this additional term will be cancelled out. Thus they converge weakly to the same Gaussian processes as if the residuals were iid. Applications to changepoint problems and goodness-of-fit are considered, in particular CUSUM statistics for testing ARMA model structure changes and the Jarque-Bera omnibus statistic for testing normality of the unobservable error distribution of an ARMA model.ARMA, residuals, high moment partial sum process, weak convergence, CUSUM, omnibus, skewness, kurtosis, (sqare root)n consistency.

Bayesian analysis of ARMA models using noninformative priors

Parameters in ARMA models are only locally identified. It is shown that the use of diffuse priors in these models leads to a preference for locally nonidentified parameter values. We therefore suggest to use likelihood based priors like the Jeffreys' priors which overcome these problems. An algorithm involving Importance Sampling for calculating the posteriors of ARMA parameters using Jeffreys' priors is constructed. This algorithm is based on the implied AR specification of ARMA models and shows good performance in our applications. As a byproduct the algorithm allows for the computation of the posteriors of diagnostic parameters which show the identifiability of the MA parameters. As a general to specific modeling approach to ARMA models suffers heavily from the previous mentioned identification problems, we derive posterior odds ratios which are suited for comparing (nonnested) parsimonious (low order) ARMA models. These procedures are applied to two datasets, the (extended) Nelson-Plosser data and monthly observations of US 3-month and 10 year interest rates. For approximately 50% of the series in these two datasets an ARMA model is favored above an AR model which has important consequences for especially the long run parametersARMA Models;econometrics

A Guide to Solar Power Forecasting using ARMA Models

We describe a simple and succinct methodology to develop hourly auto-regressive moving average (ARMA) models to forecast power output from a photovoltaic solar generator. We illustrate how to build an ARMA model, to use statistical tests to validate it, and construct hourly samples. The resulting model inherits nice properties for embedding it into more sophisticated operation and planning models, while at the same time showing relatively good accuracy. Additionally, it represents a good forecasting tool for sample generation for stochastic energy optimization models