Are nominal exchange rates and price levels co-integrated? new evidence from threshold autoregressive and momentum-threshold autoregressive models

The goal of this paper is to examine evidence for co-integration between nominal exchange rates for Canada, the UK, Japan, Germany, Italy and France (G6) vis-à-vis the US dollar, and the relative price ratios using monthly data over the period 1973:01 to 1997:04. Motivated by the fact that exchange rate adjustment may be asymmetric, we allowed for asymmetric adjustment in exchange rates by using the threshold autoregressive model and the momentum threshold autoregressive model. We do not find any evidence of a co-integrating relationship; hence, we fail to establish long-run purchasing power parity.

Application of extended multivariate modeling for information flow analysis of event related responses

Event related potential (ERP) analysis is one of the most widely used methods in cognitive neuroscience research to study the physiological correlates of sensory, perceptual and cognitive activity associated with processing information. To this end information flow or dynamic effective connectivity analysis is a vital technique to understand the higher cognitive processing under different events. In this paper we present a Granger causality (GC)-based connectivity estimation applied to ERP data analysis. In contrast to the generally used strictly causal multivariate autoregressive model, we use an extended multivariate autoregressive model (eMVAR) which also accounts for any instantaneous interaction among variables under consideration. The experimental data used in the paper is based on a single subject data set for erroneous button press response from a two-back with feedback continuous performance task (CPT). In order to demonstrate the feasibility of application of eMVAR models in source space connectivity studies, we use cortical source time series data estimated using blind source separation or independent component analysis (ICA) for this data set.

Optimal lag-length choice in stable and unstable VAR models under situations of homoscedasticity and ARCH

The performance of different information criteria - namely Akaike, corrected Akaike (AICC), Schwarz-Bayesian (SBC), and Hannan-Quinn - is investigated so as to choose the optimal lag length in stable and unstable vector autoregressive (VAR) models both when autoregressive conditional heteroscedasticity (ARCH) is present and when it is not. The investigation covers both large and small sample sizes. The Monte Carlo simulation results show that SBC has relatively better performance in lag-choice accuracy in many situations. It is also generally the least sensitive to ARCH regardless of stability or instability of the VAR model, especially in large sample sizes. These appealing properties of SBC make it the optimal criterion for choosing lag length in many situations, especially in the case of financial data, which are usually characterized by occasional periods of high volatility. SBC also has the best forecasting abilities in the majority of situations in which we vary sample size, stability, variance structure (ARCH or not), and forecast horizon (one period or five). frequently, AICC also has good lag-choosing and forecasting properties. However, when ARCH is present, the five-period forecast performance of all criteria in all situations worsens.

An extended multivariate autoregressive framework for EEG-based information flow analysis of a brain network

Recently effective connectivity studies have gained significant attention among the neuroscience community as Electroencephalography (EEG) data with a high time resolution can give us a wider understanding of the information flow within the brain. Among other tools used in effective connectivity analysis Granger Causality (GC) has found a prominent place. The GC analysis, based on strictly causal multivariate autoregressive (MVAR) models does not account for the instantaneous interactions among the sources. If instantaneous interactions are present, GC based on strictly causal MVAR will lead to erroneous conclusions on the underlying information flow. Thus, the work presented in this paper applies an extended MVAR (eMVAR) model that accounts for the zero lag interactions. We propose a constrained adaptive Kalman filter (CAKF) approach for the eMVAR model identification and demonstrate that this approach performs better than the short time windowing-based adaptive estimation when applied to information flow analysis.

Multivariate adaptive autoregressive modeling and kalman filtering for motor imagery BCI

Adaptive autoregressive (AAR) modeling of the EEG time series and the AAR parameters has been widely used in Brain computer interface (BCI) systems as input features for the classification stage. Multivariate adaptive autoregressive modeling (MVAAR) also has been used in literature. This paper revisits the use of MVAAR models and propose the use of adaptive Kalman filter (AKF) for estimating the MVAAR parameters as features in a motor imagery BCI application. The AKF approach is compared to the alternative short time moving window (STMW) MVAAR parameter estimation approach. Though the two MVAAR methods show a nearly equal classification accuracy, the AKF possess the advantage of higher estimation update rates making it easily adoptable for on-line BCI systems.

Determination of long-run and short-run dynamics in EC-VARMA models via canonical correlations

This article studies a simple, coherent approach for identifying and estimating error-correcting vector autoregressive moving average (EC-VARMA) models. Canonical correlation analysis is implemented for both determining the cointegrating rank, using a strongly consistent method, and identifying the short-run VARMA dynamics, using the scalar component methodology. Finite-sample performance is evaluated via Monte Carlo simulations and the approach is applied to modelling and forecasting US interest rates. The results reveal that EC-VARMA models generate significantly more accurate out-of-sample forecasts than vector error correction models (VECMs), especially for short horizons.