Recursive Identification. Estimation and Forecasting of Multivariate Time-series (original) (raw)

Recursive prediction for long term time series forecasting using advanced models

Neurocomputing, 2007

There exists a wide range of paradigms, and a high number of different methodologies that are applied to the problem of time series prediction. Most of them are presented as a modified function approximation problem using input/output data, in which the input data are expanded using values of the series at previous steps. Thus, the model obtained normally predicts the value of the series at a time ðt þ hÞ using previous time steps ðt À t 1 Þ; ðt À t 2 Þ; . . . ; ðt À t n Þ. Nevertheless, learning a model for long term time series prediction might be seen as a more complicated task, since it might use its own outputs as inputs for long term prediction (recursive prediction). This paper presents the utility of two different methodologies, the TaSe fuzzy TSK model and the least-squares SVMs, to solve the problem of long term time series prediction using recursive prediction. This work also introduces some techniques that upgrade the performance of those advanced one-step-ahead models (and in general of any one-step-ahead model), where they are used recursively for long term time series prediction. r

Recursive and direct multi-step forecasting: the best of both worlds

2012

Abstract We propose a new forecasting strategy, called rectify, that seeks to combine the best properties of both the recursive and direct forecasting strategies. The rationale behind the rectify strategy is to begin with biased recursive forecasts and adjust them so they are unbiased and have smaller error. We use linear and nonlinear simulated time series to investigate the performance of the rectify strategy and compare the results with those from the recursive and the direct strategies.

Recursive multi-step time series forecasting by perturbing data

2011

Abstract The Recursive strategy is the oldest and most intuitive strategy to forecast a time series multiple steps ahead. At the same time, it is well-known that this strategy suffers from the accumulation of errors as long as the forecasting horizon increases.

The vector innovations structural time series framework: A simple approach to multivariate forecasting

Statistical Modelling, 2010

The vector innovations structural time series framework is proposed as a way of modelling a set of related time series. As with all multivariate approaches, the aim is to exploit potential inter-series dependencies to improve the fit and forecasts. The model is based around an unobserved vector of components representing features such as the level and slope of each time series. Equations that describe the evolution of these components through time are used to represent the inter-temporal dependencies. The approach is illustrated on a bivariate data set comprising Australian exchange rates of the UK pound and US dollar. The forecasting accuracy of the new modelling framework is compared to other common uni-and multivariate approaches in an experiment using time series from a large macroeconomic database.

Forecasting With Nonlinear Time Series Models

Oxford Handbooks Online, 2011

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econometrics are presented and some of their properties discussed. This includes two models based on universal approximators: the Kolmogorov-Gabor polynomial model and two versions of a simple arti…cial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with complex dynamic systems, albeit less frequently applied to economic forecasting problems, is brie ‡y highlighted. A number of large published studies comparing macroeconomic forecasts obtained using di¤erent time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a particular case where the data-generating process is a simple arti…cial neural network model. Suggestions for further reading conclude the paper.

Forecasting Time Series:A Comparative Analysis of Alternative Classes of Time Series Models

Journal of Time Series Analysis, 1985

Performance of the state dependent model developed by Priestley is evaluated relative to that of bilinear and standard linear models using two well-known time series. The results indicate the use of broader classes of time series models beyond the conventional ARMA class is likely to lead to significant reductions in forecasting error. However, there are difficult problems relating to the identification of the order of the model, estimation of the parameters, and determination of the correct nonlinear model.

Representation, Estimation and Forecasting of the Multivariate Index-Augmented Autoregressive Model

We examine the conditions under which each individual series that is generated by a vector autoregressive model can be represented as an autoregressive model that is augmented with the lags of few linear combinations of all the variables in the system. We call this modelling Multivariate Index-Augmented Autoregression (MIAAR). We show that the parameters of the MIAAR can be estimated by a switching algorithm that increases the Gaussian likelihood at each iteration. Since maximum likelihood estimation may perform poorly when the number of parameters gets larger, we propose a regularized version of our algorithm to handle a medium-large number of time series. We illustrate the usefulness of the MIAAR modelling both by empirical applications and simulations.

The Prominence of Vector Autoregressive Model in Multivariate Time Series Forecasting Models with Stationary Problems

BAREKENG: Jurnal Ilmu Matematika dan Terapan

One of the problems in modelling multivariate time series is stationary. Stationary test results do not always produce all stationary variables; mixed stationary and non-stationary variables are possible. When stationary problems are found in multivariate time series modelling, it is necessary to evaluate the model's performance in various stationary conditions to obtain the best forecasting model. This study aims to get a superior multivariate time series forecasting model based on the goodness of the model in various stationary conditions. In this study, the evaluation of the model's performance through simulation data modelling is then applied to the actual data with a stationary problem, namely Bogor City inflation data. The best model in simulation modelling is based on the stability of RMSE and MAD in 100 replications. The results are that the VAR model is the best in various stationary conditions. Meanwhile, the best model on actual data modelling is based on evaluati...