We study the time varying co-movement patterns of the crypto-currency prices with the help of wavelet-based methods; employing daily bilateral exchange rate of four major crypto-currencies namely Bitcoin, Ethereum, Lite and Dashcoin. First, we identify Bitcoin as potential market leader using Wavelet multiple correlation and Cross correlation. Further, Wavelet Local Multiple Correlation for the given crypto-currency prices are estimated across different time-scales. From the results, it is found that that the correlation follows an aperiodic cyclical nature, and the crypto-currency prices are driven by Bitcoin price movements. Based on the results obtained, we suggest that constructing a portfolio based on crypto-currencies may be risky at this point of time as the other crypto-currency prices are mainly driven by Bitcoin prices, and any shocks in the latter is immediately transformed to the former.

Purpose: The purpose of this paper is to assess to what extent intraday data can explain and predict long-term memory.Design/methodology/approach: This article analysed the presence of long-memory volatility in five Asian equity indices, namely, SENSEX, CNIA, NIKKEI225, KO11 and FTSTI, using five-min intraday return series from 05 January 2015 to 06 August 2015 using two approaches, i.e. conditional volatility and realized volatility, for forecasting long-term memory. It employs conditional-generalized autoregressive conditional heteroscedasticity (GARCH), i.e. autoregressive fractionally integrated moving average (ARFIMA)-FIGARCH model and ARFIMA-asymmetric power autoregressive conditional heteroscedasticity (APARCH) models, and unconditional volatility realized volatility using autoregressive integrated moving average (ARIMA) and ARFIMA in-sample forecasting models to estimate the persistence of the long-term memory.Findings: Given the GARCH framework, the ARFIMA-APARCH long-memory model gave the better forecast results signifying the importance of accounting for asymmetric information when modelling volatility in a financial market. Using the unconditional realized volatility results from the Singapore and Indian markets, the ARIMA model outperforms the ARFIMA model in terms of forecast performance and provides reasonable forecasts.Practical implications: The issue of long memory has important implications for the theory and practice of finance. It is well-known that accurate volatility forecasts are important in a variety of settings including option and other derivatives pricing, portfolio and risk management.Social implications: It could be said that using long-memory augmented models would give better results to investors so that they could analyse the market trends in returns and volatility in a more accurate manner and reach at an informed decision. This is useful to minimize the risks.Originality/value: This research enhances the literature by estimating the influence of intraday variables on daily volatility. This is one of very few studies that uses conditional GARCH framework models and unconditional realized volatility estimates for forecasting long-term memory. The authors find that the methods complement each other.