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Wavelet coherence of time series provides valuable information about dynamic correlation and its impact on time scales. Here, the authors analyze the wavelet coherence of major real estate markets data, and take the USA, Hong Kong of China, Canada, Japan, and Developed Europe real estate market prices as time series. The wavelet coherence results show relationships among these markets, the correlations between the two and three markets (by multiple wavelet coherence) and how these relationships vary in the time-frequency space. These relationships allow the authors to build VARMA models of real estate data which produce forecasts with small errors.

Wavelet coherence of time series provide valuable information about dynamic correlation and its impact on time scales. Here we analyze the wavelet coherence of FTSE100 and S&P 500 with selected Asian markets of S&P/ASX 200 (Australia), S&P/ASX200 A-REIT (Australia), BIST (Turkey), HIS (Hong Kong), IDX (Indonesia), KLSE (Malaysia), KOSPI (Korea), N225 (Japan), RTS (Russia), Shenzhen (China), 0050.TW (Taiwan). Wavelet coherence results revealed interconnected relationships between stock markets and how these relationships vary in the time–frequency space. We conclude that developed economy stock markets have strong influences over Asian stock markets, although market dependencies vary by country and change over time. We also suggested that because co-movements shift over time, short term and middle term diversification could be more beneficial taking into account the degree of interrelations. From investors point of view, these relationships provides beneficial information, especially for portfolio diversification and risk elimination.

Abstract. Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations.In this work, we have studied the chaoticity properties of FIGARCH (p,d,q) processes by computing mutual information, correlation dimensions, FNNs (False Nearest Neighbour), the largest Lyapunov exponents (LLE) for both the stochastic difference equation and for the financial time series by applying Wolf's algorithm, Kant'z algorithm and Jacobian algorithm. Although Wolf's algorithm produced positive LLE's, Kantz's algorithm and Jacobian algorithm which are subsequently developed methods due to insufficiency of Wolf's algorithm generated negative LLE's constantly.So, as well as experimenting Wolf's methods' inefficiency formerly pointed out by Rosenstein (1993) and more recently Dechert and Gencay (2000), based on Kantz's and Jacobian algorithm's negative LLE outcomes, we concluded that it can be suggested that FIGARCH (p,d,q) is not deterministic chaotic process.