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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 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).

While it has been claimed in many empirical studies that the political futures market can forecast better than the polls, it is unclear upon which our forecast should be based. Standard practice seems to suggest the use of the closing price of the market, as a reflection of the continuous process of information revealing and aggregation, but we are unsure that this practice applies to thin markets. In this chapter, we propose a number of reconstructions of the price series and use the closing price based on these reconstructed series as the forecast. We then test these ideas by comparing their forecasting performance with the closing price of the original series. It is found that forecasting accuracy can be gained if we use the closing price based on the smoothing series rather than the original series. However, there is no clear advantage by either using more sophisticated smoothing techniques, such as wavelets, or using external information, such as trading volume and duration time. The results show that the median, the simplest smoothing technique, performs rather well when compared with all complications.

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.

Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.