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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.

In this chapter we perform a Monte Carlo simulation study of the errors-in-variables model examined in Ramsey, Gallegati, Gallegati, and Semmler (2010) by using a wavelet multiresolution approximation approach. Differently from previous studies applying wavelets to errors-in-variables problem, we use a sequence of multiresolution approximations of the variable measured with error ranging from finer to coarser scales. Our results indicate that multiscale approximations to the variable observed with error based on the coarser scales provide an unbiased asymptotically efficient estimator that also possess good finite sample properties.

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.

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.

Apart from the well-known, high persistence of daily financial volatility data, there is also a short correlation structure that reverts to the mean in less than a month. We find this short correlation time scale in six different daily financial time series and use it to improve the short-term forecasts from generalized auto-regressive conditional heteroskedasticity (GARCH) models. We study different generalizations of GARCH that allow for several time scales. On our holding sample, none of the considered models can fully exploit the information contained in the short scale. Wavelet analysis shows a correlation between fluctuations on long and on short scales. Models accounting for this correlation as well as long-memory models for absolute returns appear to be promising.

Purpose – The purpose of this paper to immobilization provides biosorbent particle with density and mechanichal strength, immobilization can save the cost of separating from biomass, can be regeneration and to increase adsorption capacity for metal ions.

Design/Methodology/Approach – The parameters affecting the adsorption, such as initial metal ion concentration, pH, contact time, and temperature, were studied. The analysis of biosorbent functional group was carried out by Fourier Transform Infrared Spectroscopy, SEM-EDX, for elemental analysis.

Findings – Optimum pH condition for biosorption Cd(II) was pH 5, contact time was 45 min, and initial concentration was 250 mg/L. Biosorbent analysis was characterized using SEM-EDX and FTIR analysis. Kinetics adsorption was studied and analyzed in terms of the pseudo-first-order, pseudo-second-order, and intraparticle diffusion kinetics models. The result showed that the biosorption for Cd(II) ion followed the pseudo-second-order kinetic model. Biosorption data of Cd(II) ion at 300°K, 308°K, and 318°K was analyzed with Temkin, Langmuir, and Freundlich isotherms. Biosorption of Cd(II) by durian seed immobilization in alginate according to the Langmuir isotherm equation provided a coefficient correlation of r² = 0.939 and maximum capacity biosorption of 25.05 mg/g.

Purpose – In this research, we have prepared activated carbon (AC) from the waste of banana peels (Musa acuminate L.) using potassium hydroxide (KOH) for carbon monoxide (CO) adsorption from motorcycle gas emission.

Design/Methodology/Approach – The activation was conducted using a chemical activator (KOH) at various concentrations of 1, 2, and 3 N for 1, 2, and 3 h, respectively. Characteristics of banana peels AC (BPAC) produced were analyzed using the Fourier-transform infra-red spectroscopy and scanning electron microscopy.

Findings – Results showed that KOH concentration and activation time strongly affected the CO adsorption and opening of the AC surface pore. There was an increase in the CO sorption when the KOH concentration was increased up to 3 N concentration. The highest CO adsorption from the emission occurred at 70.95% under KOH concentration of 3 N during the 3-h preparation.

Research Limitations/Implications – BPAC has been used as an adsorbent for only CO from motorcycle gas emission but not as an adsorbent for HC, NO, NO_x, or H₂S.

Practical Implications – BPAC can be used as the potential adsorbent for the removal of CO from motorcycle gas emission, and it is an environmental friendly, low cost, and easy to make adsorbent.

Originality/Value – In this study, the AC is made from biomass and is used in wastewater treatment, but limited studies are found on the removal of CO from motorcycle gas emission.

Purpose – In this study, the possibility of the application of rice husks for adsorbing Mn(II) ion in the water phase has been studied.

Design/Methodology/Approach – Experimental studies have been initiated by preparing activated carbon from rice husks. The activation of rice husks was done using both physical and chemical treatment methods through heating at 110 °C and washing with citric acid activator at 0.2 M, 0.4 M, and 0.6 M. The adsorption tests were conducted as two part tests: preliminary and primary. The preliminary test was conducted to choose the best condition of four independent variables, i.e., contact time (0–120 minutes), activator concentrations (0.2, 0.4, and 0.6 M), initial Mn(II) concentrations (10, 20, 50, 100, 200, and 400 mg/L), and adsorption temperatures (30, 47, and 67 °C).

Findings – By identifying the substituted groups using Fourier Transform Infrared Spectroscopy after activation with citric acid, it was found that the highest transmittance percentage was present in activated carbon with 0.2 M of citric acid. The best adsorption capacity and efficiency was 13.87 mg/g and 79.60%, respectively, which were obtained at 200 mg/L initial concentration with a 0.2 M citric acid concentration for 120 min contact time at 47 °C. These results lead to a conclusion that rice husks after activation with citric acid can be applied as an adsorbent for Mn(II) adsorption in the water phase.

Research Limitations/Implications – The activated carbon produced was only applicable for the adsorption of Mn(II) ions from the water phase, but not applicable for the adsorption of other heavy metals ions.

Practical Implications – Rice husks were potentially prepared as an adsorbent for Mn(II) ion adsorption in the water phase that was low cost, environmental friendly, and easy to prepare.

Originality/Value – Activated carbon prepared from biomass was mostly carried out using acids at high concentrations while the study was conducted using weak acids (citric acid) at low concentrations.