Application of State Space Representation on Vector Autoregressive (Var) Models for Forecasting

A vector autoregressive (VAR) model is a widely used parametric method that captures linear interdependencies between multivariate time series data. However, conventional VAR models are frequently constrained by some assumptions of linearity and stationarity, limiting their ability to capture complex and nonlinearity dynamic observed in real life data. This research aims to develop Multivariate Random Forest Technique for VAR model. Augmented Dickey Fuller (ADF) was applied to test the stationarity of the time series data. Simulated stationary time series data and real time series dataset were applied for modeling VAR model in order to compare their forecast performance. The forecast performance for the proposed technique and existing technique for VAR models were based on Mean Absolute Error and Root Mean Square Error. The proposed multivariate Random Forest technique for VAR model has been developed. The results for unit root test for real life data indicate that all the variables are stationary at level. The result for simulated data in term of forecast performance indicated that the proposed multivariate Random Forest techniques for VAR model outperform existing technique (conventional VAR model) in long term forecasting, while the conventional VAR model outperform proposed multivariate Random Forest technique in short term forecast based on MAE and RMSE. The results for real dataset indicated that the proposed multivariate Random Forest technique for VAR model is superior in terms of forecast performance than that of conventional VAR model in short-term and long-term forecast based on MAE and RMS since the proposed technique has the least value of MAE and RMSE in short and long-term forecasting than the conventional VAR model.

In forecasting foreign currencies, or known as foreign exchange, fundamental analysis and technical analysis can be used. Fundamental analysis relies on external factors or news happening in the market. In comparison, technical analysis studies the price itself by relying on graphs and mathematical formulas. This study combines fundamental value and technical analysis to predict the Rupiah (IDR) against the Dollar (USD). In this study, the artificial neural network architecture that is compared is Backpropagation and Recurrent Neural Networks (RNN). The RNN architecture used in this research is Elman and Jordan with Backpropagation Through Time (BPTT) learning algorithm. Technical analysis is applied by entering the USD exchange rate against IDR at a certain time. At the same time, fundamental analysis is applied in the form of entering some data on the value of fundamental factors as a training data set. Fundamental data used in this research are inflation rate, interest rate, money supply, and the number of exports and imports in Rupiah. In this study, the prediction system is also compared, the prediction system uses technical data, and the prediction system uses technical and fundamental data. This research results in the prediction system using the Elman RNN algorithm, which is better than the Backpropagation and Jordan RNN algorithms. A prediction system using training data in time series and fundamental data is better than only training data. So, it means in this study that the best prediction system uses the Elman RNN Algorithm with training data in the form of time series data USD sell exchange rate against IDR and fundamental data.

Recent oil price changes have significantly influenced the macroeconomic activities of both oil importing and exporting economies. It has shifted the external balances of many economies. This study investigates the short and long run effects of oil price changes on macroeconomic activities of small open economy of Oman. The short-run changes in oil prices affect the economy via exchange rate and terms of trade channels, which in turn, affect the aggregate demand and supply aspects. While in long run, if the shocks remain persistent, the economy experiences the significant revenue windfalls and positive external balances. However, the degree of external shocks to domestic economy depends on the domestic response to external shocks. Vector Auto Regression (VAR) model is used to trace out those dynamics. VAR model is considered suitable methodological option in identifying the structural shocks through generalized innovations of impulse response functions and variance decompositions. The vector of six key macroeconomic variables is expressed in VAR framework. The framework establishes the joint behaviour of key variables through time and determines the structural dynamics of Oman economy. The variance decompositions are generated from a moving average representation of the VAR system and show the forecast error variance for each variable in the system attributable to both of its own innovations and those comes from other variables. Results suggest that changes in oil prices significantly affect the real exchange rate, output and external balances. Impulse response functions and variance decompositions results confirm positive effect of oil price changes on real effective exchange rates, real - output and consumer prices. To contain the inflationary expectations both in short and long run, the governments are usually resorting towards expansionary policies. The long run changes in oil prices is the key determining factor of output growth and subsequent changes in fiscal and monetary policy adaptations. The results further indicate that innovations in real output largely influenced by changes in prices. Innovations in money supply induce by changes in real output. Real output innovations positively affect by crude oil prices. Money supply is positively influenced by real output. In short run, the expansionary policies are consistent and have served well in containing the inflationary expectations and by maintaining the positive external balances. However, in long run, over reliance on stabilization policies in pegged exchange rate economies like of Oman economy may provide fewer options to contain the external shocks.

This research aimed to study the impact of monetary policy on the rupiah stability. Variables used were the interest rate of Bank Indonesia Certificate (SBI), the rate of inflation (IHK), the exchange rate of rupiah against the US dollar (Kurs) and the money supply in the narrow sense (M1). Data used were of quarterly time series data of Bank Indonesia and Central Bureau of Statistic, covering 2002.1-2010.4. The analysis was undertaken by using a vector autoregression model (VAR), through the Impulse Response Function (IRF) and Forecast error variance decomposition (FEVD). The research results showed that in the sort run shocks of SBI decreased the inflation rate, and in the long run the inflation rate was constant. The exchange rate tended to be appreciated in the short run and long run although in a small magnitude. Money supply decreased with a minor fluctuation. Initially, the money supply shocks increased the interest rate of SBI, but decreased in the long run. The rate of inflation fluctuated in the sort run but it was constant in the long run. The exchange rate was depreciated both in the sort run and in the long run.

Interest in modeling the relationship between the macroeconomy and the agricultural economy has risen steadily since Schuh's 1974 article which illustrated the potential effects of macroeconomic policy shocks on the agricultural sector. A variety of authors has examined the effects of exchange rates, interest rate, money supply and general price level shocks on agricultural variables (prices, exports, etc.). A variety of techniques has also been used to examine these relationships. Both structural econometric models and time series approaches have been employed. In this study a new economietric technique, Vector Autoregressive (VAR) modeling, is used to investigate the impact of macroeconomic factors on the Canadian agricultural sector. Vector Autoregressive models (VARs) are dynamic simultaneous equation models. VAR models allow the data to provide a representation of the changes in the system without the restrictions on coefficients that are usually used in the estimation of simultaneous equation econometric models. VAR models focus on the dynamic paths of the variables in the system. They provide a concise summary of the dynamic interrelationships in an economic system. In this study, several forms of VAR models are used to examine the dynamic interaction of agricultural prices, exports and macroeconomic variables. There are a number of significant conclusions from the empirical analysis performed in this study. First, there appear to be significant macroeconomic impacts on the Canadian agricultural sector. Other studies of macroeconomic-sectoral linkages have found limited impact of macroeconomic factors. This study, however, using a relatively new methodology, has discovered a stronger integration. The strongest linkage appears to be between interest and exchange rates and agricultural output prices. There is little direct impact from domestic inflation. Such a result is not surprising given the international nature of Canadian agriculture. Input prices do not appear to be as significantly affected by macroeconomic shocks as are output prices. Such a result may be interpreted as providing support to the hypothesis that input and output prices in agriculture exhibit the fixed-price flex-price phenomenon. The methods used in this study are relatively new and they provide a flexible approach to modeling economic time series. It is apparent that the conditions assumed by the researcher significantly affect the empirical results. In this study we have modified existing techniques to provide more plausible identification restrictions on the model. The results indicate that the agricultural sector, in particular through agricultural output prices, is sensitive to exchange rate and interest rate variation. The techniques used here may be applied in future research to investigate the impact of macroeconomic variables on specific commodities and on regions of the country.

Purpose – This study attempts to analyze the dynamic relationship between the NFT index and macroeconomic factors, and make effective suggestions using research methods in the field of management finance. Design/Methodology/Approach – The study sample was from January 2020 to March 2023. The variables used in the analysis were based on monthly time series data, measured on the basis of the Metaverse–NFT Index (MVNX) index released by Wavebridge Limited in Korea to reflect the growth trend of the NFT market, money supply, US dollar–won exchange rate, gross domestic product, consumer price index, and other macroeconomic indicators. The analytical tools in this study included a unit root test based on the VAR model, the Johansen cointegration Test, Granger causality test, impulse response analysis, and variance decomposition. These methods are very effective in analyzing time series data. Findings – The results of the analysis show that macroeconomic factors, such as money supply, exchange rate, GDP, and consumer price index are important sources of information in predicting the NFT index. Research Implications – The results of this study are expected to provide practical information for NFT users, virtual asset trading platforms, investors, and policymakers related to NFT ecology. Furthermore, this study’s findings are of great significance, being the first global study to explore the relationship between NFTs and macroeconomic factors.

This study aims to conduct a comprehensive scenario analysis to predict the dynamics of price levels in Cambodia. Employing a Vector Autoregression (VAR) model, the study examines the relationships among the inflation rate, foreign exchange rate, and money supply. Rigorous unit root testing and lag order selection ensure the appropriateness and accuracy of the modeling approach. The analysis reveals cyclical patterns and mean-reverting properties among inflation, foreign exchange rates, and money supply growth, emphasizing the need for proactive monetary policy measures by the National Bank of Cambodia. The empirical results indicate that foreign exchange rate fluctuations significantly influence inflation, underscoring the importance of effective foreign exchange rate management for domestic price stability. Additionally, variations in money supply impact inflation and foreign exchange rates, highlighting the significance of prudent monetary management for economic growth and price stability. The study underscores the necessity for policymakers' vigilance in responding to the dynamic interactions among inflation, foreign exchange rates, and money supply to stabilize the economy. The study acknowledges limitations, including the focus on quarterly data and the VAR model's assumptions of linear relationships and stationary data, and proposes future research directions to further enhance the understanding of price level dynamics in Cambodia.

SUMMARY & CONCLUSIONSModeling corrosion growth for complex systems such as the oil refinery system is a major challenge since the corrosion process of oil and gas pipelines are inherently stochastic and depends on many factors including exposures to environmental conditions, operating conditions, and electrochemical reactions. Moreover, the number of sensors is usually limited, and sensor data are incomplete and scattering, which hinders the capability of capturing the corrosion growth behaviors. Therefore, this paper proposes Multi-sensor Corrosion Growth Model with Latent Variables to predict the corrosion growth process in oil refinery piping. The proposed model is a combination of the hierarchical clustering algorithm and the vector autoregression (VAR) model. The clustering algorithm aims to find the hidden (i.e., latent) data clusters of the measured time series data, from which the time series from the same cluster will be included in the VAR model to predict the corrosion depth from multiple sensors. The model can capture the relationship between sensor time series data and identify latent variables. A real case study of an oil refinery system, in which in-line inspection (ILI) data were collected, was utilized to validate model. Regarding corrosion growth prediction, the paper compared the prediction accuracy of VAR model with other three forms of power law model, which is widely accepted to expect the time-dependent depth of corrosion such as power function (PF), PF with initiation time of corrosion (PFIT), and PF with initiation time of corrosion and covariates (PFCOV). The results showed that VAR model has the lowest prediction error based on the mean absolute percentage error (MAPE) evaluation for test data. Finally, the proposed model is believed to be useful for dealing with a complex system that has a variety of corrosion growth behaviors, such as the oil refinery system, as well as it can be applied in other real-time applications.

Recent events have highlighted the potential importance of nonlinear efiects of flscal variables (notably debt and deflcits) on interest rates: While in times when government solvency is not a concern the standard crowding-out efiects are of moderate magnitude, in times when default risk becomes an issue the interest rate efiects can become very large. This paper provides new evidence on the magnitude of these efiects. For the case when default risk is not a concern, it uses an arbitrage-free term structure model to estimate the dynamic efiects of flscal policy shocks on interest rates along the entire maturity spectrum. For the case when default risk becomes a concern (thereby violating a central assumption of the term structure model), I present evidence based on EMU government bond spread regressions on time-varying efiects of national flscal policies on spreads as well as the time-varying sensitivity of yield spreads to international risk aversion as a function of the state of flscal policy. JEL classiflcation: E6, H6.

In foreign trade, exchange rates are one of the big factors that make a big difference. And although each country has its own currency, they all have different monetary values. To show how much one country's currency is worth compared to another country's currency, we need a measure called the exchange rate. The aim of this research is to find out how the exchange rate is related to things such as the amount of money in circulation, non-oil and gas exports, the balance of payments, and Indonesia's benchmark interest rate. A multiple regression analysis model was used to conduct the research. This research shows that the IDR/USD Exchange Rate is closely related to Indonesia's Balance of Payments, Money Supply (M2), Non-Oil and Gas Exports, and Reference Interest Rates. This relationship is real and good.

Bayesian non-parametric methods based on Dirichlet process mixtures have seen tremendous success in various domains and are appealing in being able to borrow information by clustering samples that share identical parameters. However, such methods can face hurdles in heterogeneous settings where objects are expected to cluster only along a subset of axes or where clusters of samples share only a subset of identical parameters. We overcome such limitations by developing a novel class of product of Dirichlet process location-scale mixtures that enables independent clustering at multiple scales, which results in varying levels of information sharing across samples. First, we develop the approach for independent multivariate data. Subsequently we generalize it to multivariate time-series data under the framework of multi-subject Vector Autoregressive (VAR) models that is our primary focus, which go beyond parametric single-subject VAR models. We establish posterior consistency and develop efficient posterior computation for implementation. Extensive numerical studies involving VAR models show distinct advantages over competing methods in terms of estimation, clustering, and feature selection accuracy. Our resting state fMRI analysis from the Human Connectome Project reveals biologically interpretable connectivity differences between distinct intelligence groups, while another air pollution application illustrates the superior forecasting accuracy compared to alternate methods.

The objective of the study was to examine the trend of inflation and its key determinants in Tanzania. We used secondary time series data observed annually from January 1970 to 2020 which are inflation rate, GDP, Exchange rate and money supply. The vector autoregressive (VAR) model was employed for modeling. Augmented Dickey-Fuller test (ADF) found that inflation rate, Gross Domestic Product (GDP), exchange rate and Money supply (M3) were initially non-stationary but they became stationary after first differencing so as to proceed with the analysis. Preliminary tests before obtaining vector auto regressive model were carried out before determining the relationship between the variables. Diagnostic test such as serial correlation, heteroscedasticity, stability and normality were also important to evaluate the model assumptions and investigate whether or not there are observations with a large, undue influence on the analysis. We used Granger causality test (GCT) to determine causal- effect relationship between the variables. The results show that, there is a long run relationship between the variables, also the results showed that exchange rate and money supply (M3) both have a positive impact on inflation rate while gross domestic product (GDP) revealed a negative impact on inflation rate. Finally, the forecast of inflation rate for 15 years ahead was performed. The study recommends that the government should pursue both contractionary monetary policy and fiscal policy in order to control inflation in the country.

Monetary policy is crucial for sustaining Indonesia's macroeconomic stability, especially through the benchmark interest rate (BI Rate), which serves as the primary tool of Bank Indonesia. This research revisits the transmission of monetary policy within a contemporary framework marked by post-pandemic recovery, global monetary tightening, and domestic policy shifts under the new administration in 2024. Utilizing monthly time series data from January 2010 to March 2025, this study applies the Vector Autoregression (VAR) and Vector Error Correction Model (VECM) methodologies to examine the dynamic relationships among inflation, the exchange rate (USD/IDR), and the BI Rate. The results affirm the presence of long-term relationships among the three variables, aligning with earlier research, while also revealing significant short-term dynamics that indicate an increased sensitivity of the exchange rate and inflation to interest rate changes during times of global uncertainty. By extending the analysis period to 2025 and considering the context of post-pandemic recovery and policy transitions, this study offers updated empirical insights into the changing effectiveness of Indonesia's monetary policy transmission mechanism. The findings provide important implications for policymakers in developing interest rate strategies aimed at achieving a balance between inflation control, exchange rate stability, and economic recovery.

Shocks effects of macroeconomic variables on natural gas consumption in Nigeria: Structural VAR with sign restrictions

Structurally regularized learning methods have been attracting attention in the field of statistics, machine learning, and signal processing as useful analysis tools for learning in high-dimensional settings. Using these methods, specific structure can be represented in parameters. In multivariate time series data, it is important to capture time-delay structure where necessary lag length to explain each variable is different. In this paper, we deal with a problem to discover the optimal number of order for each variable in VAR models. When we apply conventional structurally regularized learning methods such as Group Lasso, some problems, which include loss of necessary coefficients, occur. To overcome these problems, we propose a method based on the Latent Group LASSO regularization. To apply it to VAR models, we introduce overlapped coefficient groups in time direction and use a heavy-tailed distribution, such as Student's t-distribution, as a prior to enhance its sparsity. We evaluated the effectiveness of the proposed method using artificial data and actual data set (Beijing PM2.5 data set). As the result, we obtained the sparse models that capture ununiform time-delay structure represented by fewer variables with the same degree of forecast accuracy comparing with ordinary VAR models.