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The author develops and extends the asymptotic F- and t-test theory in linear regression models where the regressors could be deterministic trends, unit-root processes, near-unit-root processes, among others. The author considers both the exogenous case where the regressors and the regression error are independent and the endogenous case where they are correlated. In the former case, the author designs a new set of basis functions that are invariant to the parameter estimation uncertainty and uses them to construct a new series long-run variance estimator. The author shows that the F-test version of the Wald statistic and the t-statistic are asymptotically F and t distributed, respectively. In the latter case, the author shows that the asymptotic F and t theory is still possible, but one has to develop it in a pseudo-frequency domain. The F and t approximations are more accurate than the more commonly used chi-squared and normal approximations. The resulting F and t tests are also easy to implement – they can be implemented in exactly the same way as the F and t tests in a classical normal linear regression.

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

Purpose – The purpose of this paper is to examine the relationship between banking sector efficiency and economic growth in Africa.

Methodology/approach – The paper used the stochastic frontier approach stating the banking sector cost function as a Fourier flexible to estimate bank efficiency. We then used the Arellano–Bond GMM estimator to investigate the relationship between banking sector efficiency and economic growth. Annual data for banking sector financial statements were used in estimating efficiency scores.

Findings – The study found banking sector efficiency in the sample to be 69%. We also found a positive relationship between banking sector efficiency and economic growth, confirming the critical role banks play in the economy.

Practical implications – Banking sector efficiency score of 69% implies banks in Africa could save up to 31% of their total cost if they were to operate efficiently. Policy direction should therefore focus on policies and incentives that will improve the efficiency of the banking sector and hence economic growth. The study brings to the fore the importance of the qualitative aspect of the banking sector in allocating financial resources in the real economy. Focus in the real economy should not be only on the size of the banking system but also on the quality with which resources are allocated.

Originality/value of paper – This study is among the first dedicated solely to African countries. It does set the pace for future research in the area and also confirms in Africa the Schumpeterian hypothesis that the banking sector is key in allocating resources in the real economy.

This chapter examines factors that cause violations of regularity conditions and biases in estimates of substitution. In the context of the Fourier demand system, failing to impose curvature restrictions but correcting for serial correlation results in few violations of the curvature conditions. In contrast, imposing curvature restrictions without correcting for serial correlation biases substitution estimates and can cause violations of monotonicity. For serially correlated data, results suggest that correcting for serial correlation may be more important than imposing curvature. Furthermore, the artificially break-adjusted data that are inconsistent with consumer optimization can severely bias estimates. Results from the Bank of England's (BOE) preferred non-break-adjusted data establish that money and goods are substitutes in demand.

The size and number of employment subcenters have increased in large metropolitan areas as the spatial distribution of jobs has become increasingly decentralized. Although employment decentralization is not a new phenomenon, only recently have concentrations of employment outside the central city begun to rival the traditional central business district (CBD) in size and scope. Because of this change, neither theoretical nor empirical models in urban economics now rely solely on the traditional monocentric city model of Muth (1969) and Mills (1972). Instead, recent research incorporates some version of a polycentric model, a trend that Anas et al. (1998) document in their excellent review article.

The purpose of this chapter is to analyze the possible portfolio diversification opportunities between Asian Islamic market and other regions’ Islamic markets; namely USA, Europe, and BRIC. This study makes the initial attempt to fill in the gaps of previous studies by focusing on the proxies of global Islamic markets to identify the correlations among those selected markets by employing the recent econometric methodologies such as multivariate generalized autoregressive conditional heteroscedastic–dynamic conditional correlations (MGARCH–DCC), maximum overlap discrete wavelet transform (MODWT), and the continuous wavelet transform (CWT). By utilizing the MGARCH-DCC, this chapter tries to identify the strength of the time-varying correlation among the markets. However, to see the time-scale-dependent nature of these mentioned correlations, the authors utilized CWT. For robustness, the authors have applied MODWT methodology as well. The findings tend to indicate that the Asian investors have better portfolio diversification opportunities with the US markets, followed by the European markets. BRIC markets do not offer any portfolio diversification benefits, which may be explained partly by the fact that the Asian markets cover partially the same countries of BRIC markets, namely India and China. Considering the time horizon dimension, the results narrow down the portfolio diversification opportunities only to the short-term investment horizons. The very short-run investors (up to eight days only) can benefit through portfolio diversification, especially in the US and European markets. The above-mentioned results have policy implications for the Asian Islamic investors (e.g., Portfolio Management and Strategic Investment Management).

This study compares the performance of two types of clustering methods, time-based and non-time-based clustering, in the identification of river discharge patterns at the Johor River basin during the northeast monsoon season. Time-based clustering is represented by employing dynamic time warping (DTW) dissimilarity measure, whereas non-time-based clustering is represented by employing Euclidean dissimilarity measure in analysing the Johor River discharge data. In addition, we combine each of these clustering methods with a frequency domain representation of the discharge data using Discrete Fourier Transform (DFT) to see if such transformation affects the clustering results. The clustering quality from the hierarchical data structures of the identified river discharge patterns for each of the methods is measured by the Cophenetic Correlation Coefficient (CPCC). The results from the time-based clustering using DTW based on DFT transformation show a higher CPCC value as compared to that of non-time-based clustering methods.