Metric dimensions of bicyclic graphs

The distance d(va, vb) between two vertices of a simple connected graph G is the length of the shortest path between va and vb. Vertices va, vb of G are considered to be resolved by a vertex v if d(va, v) 6= d(vb, v). An ordered set W = fv1, v2, v3, . . . , vsg V(G) is said to be a resolving set for G, if for any va, vb 2 V(G), 9 vi 2 W 3 d(va, vi) 6= d(vb, vi). The representation of vertex v with respect to W is denoted by r(vjW) and is an s-vector(s-tuple) (d(v, v1), d(v, v2), d(v, v3), . . . , d(v, vs)). Using representation r(vjW), we can say that W is a resolving set if, for any two vertices va, vb 2 V(G), we have r(vajW) 6= r(vbjW). A minimal resolving set is termed a metric basis for G. The cardinality of the metric basis set is called the metric dimension of G, represented by dim(G). In this article, we study the metric dimension of two types of bicyclic graphs. The obtained results prove that they have constant metric dimension

Effect of monetary policy on the Nigerian stock market: A smooth transition autoregressive approach

This paper examines the nonlinear effect of monetary policy decisions on the performance of the Nigerian Stock Exchange market, by employing the Smooth Transition Autoregressive (STAR) model on monthly data from 2013 M4 to 2019 M12 for All Share Index and monetary policy instrument. This study considers the two regimes characterizing the stock market, which are the lower regime (the bear market) and the upper regime (the bull market). The results show evidence of nonlinear effect of monetary policy on the stock exchange market. Monetary policy rate, money supply, lagged monetary policy rate and lagged treasury bill rate are found to have significant positive effects on the stock exchange market in the lower regime while current treasury bill rate shows a negative effect. In the upper regime, money supply and lagged treasury bill rate have significant negative effect on the stock market. The current treasury bill rate is found to have a positive effect on the stock exchange market. It is recommended that the Central Bank of Nigeria should maintain a stable money supply growth that is consistent with increased activities in the Nigerian stock market

Most stringent test of null of cointegration: A Monte Carlo comparison

To test for the existence of long run relationship, a variety of null of cointegration tests have been developed in literature. This study is aimed at comparing these tests on basis of size and power using stringency criterion: a robust technique for comparison of tests as it provides with a single number representing the maximum difference between a test’s power and maximum possible power in the entire parameter space. It is found that in general, asymptotic critical values tends to produce size distortion and size of test is controlled when simulated critical values are used. The simple LM test based on KPSS statistic is the most stringent test at all sample sizes for all three specifications of deterministic component, as it has the maximum difference approaching to zero and lesser than 20% for the entire parameter space

Subsample stability, change detection and dynamics of oil and metal markets: A recursive approach

The analysis of historical price data for patterns and using such patterns for predictions and policy recommendations has become ubiquitous in the existing economics literature. These predictions and recommendations are premised on the stability of the statistical properties and inter-variable dynamics for which a single regime or few number of regimes can capture. This, however, is a strong assumption with serious repercussions if violated. In this study, the appropriateness of the stability assumption is questioned using various recursive regressions to test stability, consistency of stationarity and stability in inter-variable dynamics between crude oil, gold, silver, and platinum prices. Using monthly data sourced from the World Bank Commodity Price Data (Pink Sheet) from January 1, 9960 to March 2022, our empirical analysis found level prices of oil, gold, and platinum to be consistently non-stationary with rare exceptions. The level price of silver however is found to be inconsistent with multiple regime switches while the logged series of all variables yielded non-stationarity. The default is stationarity for all the variables when price series are logged differenced and/or differenced for oil, silver, and platinum. Differenced gold prices resulted in inconsistent stationarity with multiple regime changes. Even if rare, the stationarity of all the variables is dependent on time and sample size due to the inconsistence in the stationarity verdict. On the bi-variate relationship in the long run, only level silver prices are found to be cointegrated with oil while logged silver prices are inconsistently cointegrated with logged oil prices. Also, in the short-run, only log of oil prices is found to Granger cause log of silver prices. It is thus recommended that researchers and policy makers be tempered in extrapolating statistical findings in general and the price and interprice dynamics of oil, gold, silver and platinum into the future

The language of sustainability: Exploring the implications of metaphors on environmental action and finance

The relationship between humans and the environment is complex. To capture this complex relationship, metaphors/concepts have always been used. The most prominent of these metaphors/conceptions is the limits concept. This views the natural environment in terms of its carrying capacity and contend that human actions must be controlled so as not to overwhelm the environment. For overburdening the environment will result in a collapse of the natural system. The environmental optimists on the other hand discount the carrying capacity contending that human ingenuity and the market mechanism will overcome any temporary environmental problems that may arise. A tempered version of both is the political-ecological class of metaphors/conceptions which emphasize the political, cultural, and economic factors responsible for environmental decay and/or restoration. In this study, the implications of these metaphors/conceptions on environmental action and environmental finance are examined. It is concluded that, the limits conception views environmental action as a top-bottom endeavor and places governmental and multilateral organizations at the center of environmental and climate finance. The neoclassical and technological optimist concepts contend that, the current capitalist structure is well suited to tackle environmental externalities and government policy should encourage eco-innovation preferable through public-private partnerships. The tapestry and the political-ecological class of metaphors envisages a role for central authorities as well as private local individuals with crowdfunding and corporate social/environmental responsibilities along with governmental and multilateral aid and public-private partnerships being some of the main sources of funds for environmental protection and restoration

A comparative assessment of frequentist forecasting models: Evidence from the S&P 500 pharmaceuticals index

This paper compares three forecasting methods, the autoregressive integrated moving average (ARIMA), generalized autoregressive conditional heteroscedasticity (GARCH), and neural network autoregression (NNAR) methods, using the S&P 500 Pharmaceuticals Index. The objective is to identify the most accurate model based on the mean average forecasting error (MAFE). The results consistently show the NNAR model to outperform ARIMA and GARCH and to exhibit a significantly lower MAFE. The existing literature presents conflicting findings on forecasting model accuracy for stock indexes. While studies have explored various models, no universally applicable model exists. Therefore, a comparative analysis is crucial. The methodology includes data collection and cleaning, exploratory analysis, and model building. The daily closing prices of pharmaceutical stocks from the S&P 500 serve as the dataset. The exploratory analysis reveals an upward trend and increasing heteroscedasticity in the pharmaceuticals index, with the unit root tests confirming non-stationarity. To address this, the dataset has been transformed into stationary returns using logarithmic and differencing techniques. Model building involves splitting the dataset into training and test sets. The training set determines the best-fit models for each method. The models are then compared using MAFE on the test set, with the model possessing the lowest MAFE being considered the best. The findings provide insights into model accuracy for pharmaceutical industry indexes, aiding investor predictions, with the comparative analysis emphasizing tailored forecasting models for specific indexes and datasets

A Monte Carlo Comparative Simulation Study for Identification of the Best Performing Panel Cointegration Tests

In this paper the performance of nine panel cointegration tests, having the null hypothesis of no cointegration, with respect to weighted average rank scores under the whole space of alternative using Monte Carlo simulations have been carried out. Our results indicate that PdPtp, PAWS and PdP_V tests are the only three best performing tests among all panel cointegration tests whether time and cross sectional dimensions are small, medium or large. However, PDFTstar, PDFTrhostar and PdGtp panel cointegration tests have also identified as best performer at large cross sectional dimensions

Is the effect of a health crisis symmetric for physical and digital financial assets? An assessment of gold and bitcoin during the pandemic

The emergence of the covid-19 health crisis, in this advanced technological era where connections between markets, nations, and economies have grown stronger than ever before, the shock of the COVID-19 pandemic quickly had an impact on both physical and digital financial assets. The Chinese financial market experienced the first consequences of the covid-19 pandemic, then spilled over to other financial markets, including those for cryptocurrencies and the precious metals. This study examines the impact of the covid-19 pandemic on the volatilities of the dynamics of bitcoin and gold. Both assets share some characteristics, such as online trading platforms, however, gold is a tangible financial asset unlike bitcoin, which is digitally generated without any physical form. This study argues that the similarities and differences between bitcoin and gold play major roles in how the covid19 crisis affected their respective dynamics. Using daily data ranging from 9/22/2014 to 1/ 31/2023 and employing ARMA as the mean equation for GARCH model, the impact of the health crisis (covid-19) is examined on the volatilities of the prices and volumes of bitcoin and gold. Empirical evidence points out that, the pandemic has a symmetric impact on the volatilities of bitcoin and gold price returns, causing them to be more volatile. The impact of the covid-19 observed on the volume returns of the assets, however, is asymmetrical. The empirical results give evidence to the role that the vital differences existing between these assets played during the covid-19 pandemic

Constant time calculation of the metric dimension of the join of path graphs

The distance between two vertices of a simple connected graph G, denoted as (Formula presented.), is the length of the shortest path from u to v and is always symmetrical. An ordered subset (Formula presented.) of (Formula presented.) is a resolving set for G, if for ∀ (Formula presented.), there exists (Formula presented.) ∋ (Formula presented.). A resolving set with minimal cardinality is called the metric basis. The metric dimension of G is the cardinality of metric basis of G and is denoted as (Formula presented.). For the graph (Formula presented.) and (Formula presented.), their join is denoted by (Formula presented.). The vertex set of (Formula presented.) is (Formula presented.) and the edge set is (Formula presented.). In this article, we show that the metric dimension of the join of two path graphs is unbounded because of its dependence on the size of the paths. We also provide a general formula to determine this metric dimension. We also develop algorithms to obtain metric dimensions and a metric basis for the join of path graphs, with respect to its symmetries

Roling-window bounds testing approach to analyze the relationship between oil prices and metal prices

[ArticleInPress]This paper is to find how the existence of a long-run relationship between oil prices and metals prices evolved for the time from January 1979 to December 2017. The rolling-window autoregressive lag mod- eling (RARDL) testing approach of cointegration has been introduced and applied to assess the long-run relationship considering four rolling windows of 5, 10, 15, and 20 years. The empirical evidence concludes that for a small rolling window of 5 years, there is no evidence of the long-run relationship between oil prices and metals prices, i.e. gold, platinum, and silver. However, there is a long-run relationship between oil prices and steel prices from December 2003 to December 2014. At larger rolling windows of 10, 15 and 20 years, oil prices and gold prices are not cointegrated; however, steel, silver, and platinum have a long-run relationship with oil prices in different periods