Noise Corruption of Empirical Mode Decomposition and Its Effect on Instantaneous Frequency

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.Comment: 28 pages, 19 figures. High quality color figures available on Daniel Kaslovsky's website: http://amath.colorado.edu/student/kaslovsk

Non-Asymptotic Analysis of Tangent Space Perturbation

Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as it returns an optimal basis in the case of noise-free samples from a linear subspace. To process noisy data samples from a nonlinear manifold, PCA must be applied locally, at a scale small enough such that the manifold is approximately linear, but at a scale large enough such that structure may be discerned from noise. Using eigenspace perturbation theory and non-asymptotic random matrix theory, we study the stability of the subspace estimated by PCA as a function of scale, and bound (with high probability) the angle it forms with the true tangent space. By adaptively selecting the scale that minimizes this bound, our analysis reveals an appropriate scale for local tangent plane recovery. We also introduce a geometric uncertainty principle quantifying the limits of noise-curvature perturbation for stable recovery. With the purpose of providing perturbation bounds that can be used in practice, we propose plug-in estimates that make it possible to directly apply the theoretical results to real data sets.Comment: 53 pages. Revised manuscript with new content addressing application of results to real data set

Entrepreneurship as a predictive factor for employment and investment : the case of selected European countries

Abstract: The link between entrepreneurship and economic prosperity has continuously been pointed out by researchers and government institutions. Several studies have proven that a clear relationship between entrepreneurship, economic growth and development (positive in many instances) exist. Within the broader context of growth and development, various other variables also play a significant role such as employment and investment amongst others. The objective of this study was, therefore, to determine the relationship between entrepreneurship, employment and domestic investment specifically focussing on selected European countries (Austria, Croatia, Hungary, Poland and Slovenia). The study made use of a quantitative empirical approach (econometric analysis) using secondary data from 2001 to 2019. Countries were selected based on their homogeneous traits and availability of data. Both, long and short- run relationships between various entrepreneurial variables, employment and investment were tested using a pooled panel analysis. Results indicated a long-run relationship between the variables by using the Fisher-Johansen cointegration analysis. Long-run results via the FMOLS and DOLS econometric models, confirmed the results as estimated in the Fisher-Johansen cointegration tests. It was found that both early entrepreneurial activity (TEA) and established business ownership (EBO) are significant predicators of employment and domestic investment. In the short-run via a Granger causality tests, all of the independent variables of entrepreneurial intentions (EI), TEA and EBO were found to cause changes in employment, while only EBO causes changes in domestic investment. In conclusion, the study proved that links between the mentioned variables do exist and that entrepreneurial activity should be stimulated and supported as it has a significant impact on employment and domestic investment

The relationships between entrepreneurial factors and economic growth and development : the case of selected European countries

Abstract: Globally, entrepreneurship and its link to economic growth, development and prosperity has been a topic of continued discussion. Entrepreneurship provides various direct and indirect positive results within developed and developing economies. Research suggests that the entrepreneurship development may have a positive effect on several economic variables. The purpose of this study, therefore, was to identify the relationships between three entrepreneurial variables (entrepreneurial intention - EI, Early-stage entrepreneurial activity - TEA and established business ownership - EBO) and, firstly, economic development using GDP per capita and, secondly, economic growth (GDP) using an econometric analysis method. The study followed a quantitative empirical approach using secondary data from 2001 to 2019 for selected European countries (Austria, Croatia, Hungary, Poland and Slovenia). Countries were selected based on their homogeneous traits and availability of data. Long and short-run relationships between the mentioned variables were tested using a pooled panel analysis. Results indicated a long-run relationship between the variables by using the Fisher-Johansen cointegration analysis. Further results of the analysis indicated that both TEA and EBO are significant predictors at 5% significant levels respectively of economic development (GDP per capita) and economic growth (GDP). In conclusion, the study proved that links between the mentioned variables do exist and that entrepreneurial activity should be stimulated and supported as it has a significant impact on economic growth and development at various degrees of impact

Assessment of Inclusive Growth performance: A comparative analysis of the BRICS countries

In recent years the concept of inclusive growth has moved to the top of the agenda for economic development policy advancement. The concept is relatively new within the field of Development Economics with limited research available. Some confusion also still exists regarding the definition of inclusive growth as a concept and the sub-research field is not as well established if compared to other similar concepts such as economic development and pro-poor growth. The study had the objective to clarify the concept of inclusive growth and also to apply an alternative inclusive growth index for the BRICS countries to assess their performance. The research methodology included a literature review and a comparative assessment of the inclusive growth performance of the BRICS countries from 1997 to 2017. Results indicated that all five the countries have achieved medium levels of inclusive growth, except for South Africa which only achieved a low level of inclusive growth. China had the highest index of 70.3, while India had the highest rate of growth in the improvement of the index of approximately 2.0 percent per annum. The results of the comparative study indicate that governments are required to intervene through improved policy implementation to ensure that all citizens have the opportunity to participate and benefit from economic and social aspects. Good governance, with strong institutions, also assists in inclusive growth success. &nbsp

Analysis of Relationships and Causality between Consumer Price Index (CPI), the Producer Price Index (PPI) and Purchasing Manager’s Index (PMI) in South Africa

The variables the consumer price index (CPI), the producer price index (PPI) and the purchasing managers’ index (PMI) and play major roles in economic forecasting. The overall objective of this study is to assess the inter-relationships between CPI, PPI and PMI as predicting variables. This study is quantitative in nature and employed an ARDL econometric model, error correction model (ECM) and Granger causality approaches to establish long and short-run relationships. The ARDL method was used due to the fact that the variables had a mix of stationarity at levels I (0) and the first difference I (1). Quarterly datasets were obtained from Statistics South Africa (Stats SA) and the Bureau of Economic Research (BER) for the period 2000 to 2017. Results from the estimations discovered that variables cointegrate in the long-run. Additionally, evidence of short-run relationships has been determined using ECM. Furthermore, causal relationships were also analysed with results indicating that CPI causes PMI and PPI causes PMI. The implication of the research is the confirmation of the importance of relationships between CPI, PPI and PMI, which is especially significant in the short-run and the three index indicators are important macro-economic indicators for changes in overall economic activity on a macro level

Trade Openness, FDI and Exchange Rate Effects on Job Creation in South Africa's Tradable Sectors

Employment creation remains the pinnacle standard of sound social welfare and economic progress. It is a fundamental driver of economic development for any economy. However, such a pursuit faces tenacious challenges, especially amidst the growing global market integration. This study unravelled the effects of the underlying trade environment mechanisms such as trade openness, foreign direct investment(FDI) and the exchange rate on South Africa’s job creation efforts within the tradable sectors. The study employed a quantitative analysis and included time series explanatory variables of trade openness, netFDI flows and the real effective exchange rate. Employment series of both South Africa’s mining and manufacturing tradable sectors served as the dependent variables. The study made use of quarterly observations starting from 1995 to 2016. In doing so, various econometric methods were utilised. These included descriptive analyses, the standard Autoregressive Distributed Lag (ARDL) model, and the TodaYamamoto Granger Non-Causality test. Empirical ARDL results of employment in the individual mining sector, established no long-run and short-run relationships with trade openness, the real effective exchange rate and net-FDI. Employment in the manufacturing tradable sector presented significant and negative longrun relationships with trade openness, the real effective exchange rate and net-FDI. Meanwhile, the short-run findings exhibited significant and positive relationships between employment in the manufacturing tradable sector with trade openness, and significantly negative for net-FDI. However short-run results of manufacturing employment and the real effective exchange rate were not significant. Based on these results, South Africa’s mining sector seems unresponsive to mechanisms in the trade environment while these relationships are relatively dynamic in the manufacturing sector. Further recommendations were thus provided to improve these interrelationships in promoting job growth and its responsiveness to trade components

Comprehending stakeholders’ involvement in the integrated development planning process as a tool for improved community participation

This study is primarily aimed at comprehending the key stakeholders, involved in applying the Integrated Development Planning (IDP) process for improved community participation in the Tzaneen municipal area. It is argued in this study, that the IDP is centred on the priorities and desires of the communities. Communities have the opportunity to engage in identifying their most desired needs. The IDP process requires all stakeholders who live and do business within a municipal jurisdiction to partake in the design and execution of the municipal development plan, also known as the IDP. This study is grounded in the ladder of citizen participation theory, pioneered by Arnstein Sherry in 1969. Arnstein (1969)'s ladder of citizen participation theory talks about community involvement in the planning process in the United States. This empirical study was conducted in the Tzaneen municipal area, South Africa, and four hundred and ten (410) participants were sampled in the area through probability and non-probability sampling techniques. The study adopted a mixed-method research approach. The data was collected and analysed until saturation was reached. Data were collected using surveys, semi-structured interviews, and a review of existing literature. This study revealed that more than half (56 %) of participants indicated that they were not consulted and encouraged to participate in the IDP process as relevant stakeholders. Consultation of stakeholders is often inadequate. Most of the participants are dissatisfied with their representatives' manner and level of involvement, and they do not feel well represented. This study concludes by recommending that municipalities adhere to the Municipal Systems Act (2000) and the Republic of South Africa (1996) Constitution, both of which require municipalities to actively involve stakeholders in the planning process to provide services sustainably and satisfactory. The Batho Pele principles should be followed to guarantee a harmonious relationship between the municipality and its stakeholders. Stakeholders will have reasonable expectations regarding service delivery due to effective consultation

Econometric Analysis of the Effects of Aggregate Expenditure on Job Growth in the Private Sector: The South African Case

The private sector contributes to job creation either directly by creating new positions for job seekers or indirectly by increasing growth that results in job creation for unemployed people. This study employed an autoregressive distributed lag (ARDL) model to analyse the long and short run effects of aggregate expenditure on job creation in the private sector in South Africa. The findings indicated that there is a long run relationship between aggregate expenditure and job creation in the private sector. Investment spending and net exports are the aggregate expenditure components that create long-term jobs, whereas consumer consumption and government spending lead to possible long run job destruction.  The Error Correction Model (ECM) results revealed that consumption and investment spending create jobs in the short run, while the Granger-causality test suggested that a bi-directional causal relationship exists between consumption, investment spending and employment in the private sector. The study concluded that the negative effect of consumption on private employment might be due to the consumption of imported goods and services. Thus, the employment situation in South Africa could be improve if more focus is on consumption of domestic products