From general State-Space to VARMAX models

Fixed coecients State-Space and VARMAX models are equivalent, meaning that they are able to represent the same linear dynamics, being indistinguishable in terms of overall fit. However, each representation can be specifically adequate for certain uses, so it is relevant to be able to choose between them. To this end, we propose two algorithms to go from general State-Space models to VARMAX forms. The first one computes the coeficients of a standard VARMAX model under some assumptions while the second, which is more general, returns the coeficients of a VARMAX echelon. These procedures supplement the results already available in the literature allowing one to obtain the State-Space model matrices corresponding to any VARMAX. The paper also discusses some applications of these procedures by solving several theoretical and practical problems.State-Space, VARMAX models, Canonical forms, Echelon.

RICE PRICE MODELING IN SIX PROVINCE OF JAVA ISLAND USING VARMAX MODEL

Rice is an important food commodity in Indonesia because it is not only a main food but also social commodity, and has influence in politic stabilities and economic growth in Indonesia. Based on this condition is showed that everything about rice especially rice price has social economic impact in Indonesia. Factors that influence the domestic rice price in Indonesia are real exchange value, domestic corn price, and basic rice price This research aims to create models of rice price monthly data from six province in Java to real exchange value from 2007 until 2014 by using multivariate time series modeling approach with covariate, that is VARMAX (Vector ARIMAX) model. The results show that rice price in West Java, DI Yogyakarta, and Banten are influenced by rice price in DKI Jakarta, Central Java, and East Java, and real exchange value. Based on RMSE value, the best model is using VECMX(2,1) model. Keywords : ARIMA, VARMA, VARMA

Estimation of Continuous Time Models in Economics: an Overview

The dynamics of economic behaviour is often developed in theory as a continuous time system. Rigorous estimation and testing of such systems, and the analysis of some aspects of their properties, is of particular importance in distinguishing between competing hypotheses and the resulting models. The consequences for the international economy during the past eighteen months of failures in the financial sector, and particularly the banking sector, make it essential that the dynamics of financial and commodity markets and of macro-economic policy are well understood. The nonlinearity of the economic system means that it’s properties are heavily dependent on it’s parameter values. The estimators discussed here are tools to provide those parameter estimates.

The nature and causes of the Norwegian interbank offered rate

The importance of interbank rates for unsecured funding has increased vastly the last decades with the expansion of nancial instruments. Today's interbank rates are arguably the most in uential benchmarks in pricing of assets and an important indicator on the state an economy. In the aftermath of the nancial crisis, the awareness of weaknesses of interbank rates surfaced. The awareness has led to a tightening of the regulations regarding the Norwegian Interbank O ered Rate (NIBOR). The purpose of this paper is to identify the nature of NIBOR in both a domestic and international context, and expand on NIBOR's ability to accurately re ect the lending cost between Norwegian prime banks. The rst part of the paper uses the Nelson-Siegel and Vasicek models to compare o ered rates against observable nancing cost using unsecured corporate bonds. NIBOR has historically been quoted higher than both STIBOR and EURIBOR, and we nd that Norwegian banks contributing to NIBOR and STIBOR face the same nancing costs as European banks contributing to EURIBOR. This implies that the di erences between interbank rates cannot be justi ed by higher nancing costs. When comparing the interbank rates to domestic nancing costs, we are unable to determine if banks contributing to NIBOR are more or less accurate in the Norwegian interbank market compared to other interbank markets where these banks are present. In the second part of the paper, we compare individual interest rate quotes to credit default swaps, and observe an inconsistent relationship between panel banks' quotes and their market priced risk over time. By applying a hidden markov model, we examine individual short term behavioral dynamics during the opening of the day, and preceding the xing. Our results indicate that interpretation of information varies across participants, which is a possible weakness of the governance structure.nhhma

Fitting replicated multiple time series models

This paper shows that the interleaving of replicated multiple time series allows the estimation methods available in standard multiple time series packages to be applied simultaneously to each of the replicated series without loss of information. The methodology employs a non-trivial multivariate extension of an earlier univariate result involving interleaving. The interleaving approach is used to model more than sixty years of daily maximum and minimum temperatures for Perth, Western Australia

Gaussian process autoregression for simultaneous proportional multi-modal prosthetic control with natural hand kinematics

Matching the dexterity, versatility, and robustness of the human hand is still an unachieved goal in bionics, robotics, and neural engineering. A major limitation for hand prosthetics lies in the challenges of reliably decoding user intention from muscle signals when controlling complex robotic hands. Most of the commercially available prosthetic hands use muscle-related signals to decode a finite number of predefined motions and some offer proportional control of open/close movements of the whole hand. Here, in contrast, we aim to offer users flexible control of individual joints of their artificial hand. We propose a novel framework for decoding neural information that enables a user to independently control 11 joints of the hand in a continuous manner-much like we control our natural hands. Toward this end, we instructed six able-bodied subjects to perform everyday object manipulation tasks combining both dynamic, free movements (e.g., grasping) and isometric force tasks (e.g., squeezing). We recorded the electromyographic and mechanomyographic activities of five extrinsic muscles of the hand in the forearm, while simultaneously monitoring 11 joints of hand and fingers using a sensorized data glove that tracked the joints of the hand. Instead of learning just a direct mapping from current muscle activity to intended hand movement, we formulated a novel autoregressive approach that combines the context of previous hand movements with instantaneous muscle activity to predict future hand movements. Specifically, we evaluated a linear vector autoregressive moving average model with exogenous inputs and a novel Gaussian process (gP) autoregressive framework to learn the continuous mapping from hand joint dynamics and muscle activity to decode intended hand movement. Our gP approach achieves high levels of performance (RMSE of 8°/s and ρ = 0.79). Crucially, we use a small set of sensors that allows us to control a larger set of independently actuated degrees of freedom of a hand. This novel undersensored control is enabled through the combination of nonlinear autoregressive continuous mapping between muscle activity and joint angles. The system evaluates the muscle signals in the context of previous natural hand movements. This enables us to resolve ambiguities in situations, where muscle signals alone cannot determine the correct action as we evaluate the muscle signals in their context of natural hand movements. gP autoregression is a particularly powerful approach which makes not only a prediction based on the context but also represents the associated uncertainty of its predictions, thus enabling the novel notion of risk-based control in neuroprosthetics. Our results suggest that gP autoregressive approaches with exogenous inputs lend themselves for natural, intuitive, and continuous control in neurotechnology, with the particular focus on prosthetic restoration of natural limb function, where high dexterity is required for complex movements

VARX Granger Analysis: Modeling, Inference, and Applications

Complex systems, such as brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often challenging. We propose using a Vector Autoregressive model with eXogenous input (VARX) to capture delayed interactions between internal and external variables. While this model aligns with Granger's statistical formalism for testing "causal relations", the connection between the two is not widely understood. Here, we bridge this gap by providing fundamental equations, user-friendly code, and demonstrations using simulated and real-world data from neuroscience, physiology, sociology, and economics. Our examples illustrate how the model avoids spurious correlation by factoring out external influences from internal dynamics, leading to more parsimonious explanations of the systems. We also provide methods for enhancing model efficiency, such as L2 regularization for limited data and basis functions to cope with extended delays. Additionally, we analyze model performance under various scenarios where model assumptions are violated. MATLAB, Python, and R code are provided for easy adoption: https://github.com/lcparra/var

A Pipeline for Multivariate Time Series Forecasting of Gas Consumption in Pelletization Process

Gas consumption is a critical aspect of the pelletizing process, directly influencing operational costs and environmental impact. This study investigates the application of a multivariate time series forecasting pipeline for predicting gas consumption in pelletizing plants. The pipeline comprises: (i) data preprocessing, (ii) converting the dataset into a tabular format using a sliding window technique, (iii) applying feature selection methods, and (iv) employing machine learning tuned via AutoML. The methodology was tested on a dataset with 45 operational parameters collected over 90 days from an industrial plant, with predictions evaluated using Root Mean Squared Error (RMSE). In step (iii), twelve features were identified as the most relevant based on the Random Forest importance index. In the final stage, two AutoML approaches were employed: neural architecture search using AutoKeras and the DEAP (Distributed Evolutionary Algorithm) framework. The neural network architectures tested included MLP, RNN, LSTM, and Conv1D. The best performance was achieved by the DEAP framework combined with LSTM networks, which yielded an RMSE of 0.33. Although AutoML did not outperform the statistical model in terms of RMSE values, regarding training time, AutoML models were significantly more efficient than the statistical approach, optimizing computational resource usage and enabling faster model adjustments. These findings confirm the generalization capability of the pipeline, demonstrating its applicability across different industrial environments