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Window effect with Markov-switching GARCH model in cryptocurrency market

https://doi.org/10.1016/j.chaos.2021.110902Get rights and content

Highlights

  • This study investigates the window effect in cryptocurrency market.

  • Window size does not change size effect and leverage effect for in-sample estimation. However, it changes out-of-sample risk forecast.

  • For Bitcoin, one window size consistently outperforms other window sizes in out-of-sample forecast, which provides a possibility to get better out-of-sample forecast by choosing better windows from the historical data.

Abstract

The non-stationarity of cryptocurrency is mainly attributed to structural breaks. Many studies use the rolling windows to deal with structural breaks. However the selection of windows is an open question without a systematic answer. This study investigates the window effect on in-sample coefficient estimation and out-of-sample forecasting. The results provide evidence on the stability of coefficient estimation under various window selections. However, in forecast, some specific window size shows much better accuracy of left-tail predictions in stable patterns. It provides a possibility to get better out-of-sample forecast by choosing a window from the historical data.

Introduction

Cryptocurrencies, such as Bitcoin, Ethereum, XRP, Bitcoin Cash, have been witnessed incomparable volatility [1], [2]. One issue is the instability of estimation. Bariviera [3] finds that Bitcoin returns exhibit structural break around 2014. Before 2014, the estimated Hurst exponents are much greater than 0.5, whereas after 2014 the Hurst exponent generally fluctuates around 0.5, which is compatible with the efficient market hypothesis. Bouriet et al. [4] find the static models and rolling windows lead to contradictory result. In the static model, there is no significant evidence of herding in cryptocurrencies. Conversely, results from a rolling window analysis suggest significant herding behavior, based on windows of 250 observations.

Pesaran and Timmermann [5] propose a cross-validation method to deal with the selection of the window size under one break assumption. The idea behind the cross-validation method is that estimation including the break point sometimes improves the bias-variance trade-off. In practice, the selection of estimation window size is still an open question. Examples of various selection of windows include: Fang et al. [6] discuss the long memory phenomenon in Bitcoin markets and the CSI 300 with sliding window size of 200 observations. Tiwari et al. [7] compute estimates of long-memory parameters with overlapping windows of each 300 observations of daily returns. Zargar and Kumar [8] use non-overlapping quarterly rolling windows about 100 days. Ardia et al. [9] analyze the volatility using rolling windows of 1000 daily log-returns. Mensi et al. [10] discuss long memory in both price and conditional volatility with observations from 2011 to 2018 for Bitcoin and from 2015 to 2018 for Ethereum.

In this paper, the main interests focus on two questions. The first question is: whether the choices of window size change in-sample estimation results? Despite the fact that the selection of window size changes in practice and a few studies about window size build their estimation methods to allow for structural breaks [5], this question has not fully been answered empirically. The second question is: whether the choices of window size change out-of-sample forecast performance? Inoue et. al [11] focus on the forecast performance based on autoregressive (AR) models and autoregressive distributed lag (ADL) models by minimizing the mean squared forecast error similar to Pesaran and Timmermann [5]. Explored further from Inoue's study, this study chooses more flexible models to accommodate high volatility of cryptocurrencies.

Section snippets

Methodology

Evidences show structural break and regime switching in cryptocurrencies. In this paper, to briefly distinguish regime switching and structural break, structural break refers to the structural changes with one cutting point along the timeline. For example, all observations before the cutting point show high volatility, but all observations after the cutting point show low volatility. However, regime switching does not show clear segments along the timeline. For example, the high-volatility

Data

I use daily closing-prices of Bitcoin (BTC), Ethereum (ETH) and Ripple (XRP) in USD downloaded from Investing.com, since they are the top three cryptocurrencies by market capitalization. The time period varied, for BTC ranging from 7/18/2010 to 5/26/2020. For Ethereum, it ranges from 3/10/2016, to 5/27/2020. For XRP, it ranges from 1/22/2015, to 5/26/2020.

Table 1 reports the descriptive statistics of the three cryptocurrency returns, whose means are all positive. BTC exhibits the largest

Conclusion

This study contributes to understanding selection of window size in out-of-sample forecast of cryptocurrencies. Out-of-sample forecast is important in economics and finance. The popular structural changes and regime switching challenge the accuracy of forecast. Without a systematic guidance, practitioner used to choose different window lengths in an ad hoc manner.

The results have relevant implications for practitioners. Firstly, this study supports previous practitioner behavior on the

CRediT authorship contribution statement

Chuanzhen Wu: Conceptualization, Methodology, Software, Writing - original draft, Writing - review & editing, Visualization.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (19)

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