Forecasting and trading cryptocurrencies with machine learning under changing market conditions

Sebastião, Helder; Godinho, Pedro

doi:10.1186/s40854-020-00217-x

Financial Innovation

Table 5 Sets of variables used in the models

From: Forecasting and trading cryptocurrencies with machine learning under changing market conditions

Variables	Returns	Volatility	Other trading variables	Network	Daily dummies	# variables
Bitcoin
Linear	BTC[− 1, − 2]	RR[− 1]	No	No	Yes	14
	ETH[− 1]	\(\sigma\)[− 1, − 2]
	LTC[− 1]	\(\sigma\)[− 1, − 2]
Linear-binary	BTC[− 1, …, − 7]	RR[− 1]	Yes	Yes	Yes	48
	ETH[− 1, …, − 7]	\(\sigma\)[− 1, …, − 7]
	LTC[− 1, …, − 7]	\(\sigma\)[− 1, …, − 7]
RF	BTC[− 1, − 2]	RR[− 1]	No	No	Yes	16
	ETH[− 1, − 2]	\(\sigma\)[− 1, − 2]
	LTC[− 1, − 2]	\(\sigma\)[− 1, − 2]
RF-binary	BTC[− 1, − 2]	RR[− 1]	No	No	Yes	14
	ETH[− 1]	\(\sigma\)[− 1, − 2]
	LTC[− 1]	\(\sigma\)[− 1, − 2]
SVM	BTC[− 1, − 2]	RR[− 1]	No	No	Yes	16
	ETH[− 1, − 2]	\(\sigma\)[− 1, − 2]
	LTC[− 1, − 2]	\(\sigma\)[− 1, − 2]
SVM-binary	BTC[− 1, − 2]	RR[− 1]	Yes	Yes	Yes	26
	ETH[− 1]	\(\sigma\)[− 1, − 2]
	LTC[− 1]	\(\sigma\)[− 1, − 2]
Ethereum
Linear	ETH[− 1, − 2]	RR[− 1]	No	No	Yes	14
	BTC[− 1]	\(\sigma\)[− 1, − 2]
	LTC[− 1]	\(\sigma\)[− 1, − 2]
Linear-binary	ETH[− 1, − 2, − 3]	RR[− 1]	Yes	Yes	Yes	32
	BTC[− 1, − 2, − 3]	\(\sigma\)[− 1, − 2, − 3]
	LTC[− 1, − 2, − 3]	\(\sigma\)[− 1, − 2, − 3]
RF	ETH[− 1, − 2]	RR[− 1]	No	No	Yes	16
	BTC[− 1, − 2]	\(\sigma\)[− 1, − 2]
	LTC[− 1, − 2]	\(\sigma\)[− 1, − 2]
RF-binary	ETH[− 1, − 2]	RR[− 1]	No	No	Yes	16
	BTC[− 1, − 2]	\(\sigma\)[− 1, − 2]
	LTC[− 1, − 2]	\(\sigma\)[− 1, − 2]
SVM	ETH[− 1, …, − 4]	RR[− 1]	No	No	Yes	24
	BTC[− 1, …,-4]	\(\sigma\)[− 1, …, − 4]
	LTC[− 1, …,-4]	\(\sigma\)[− 1, …, − 4]
SVM-binary	ETH[− 1, …, − 5]	RR[− 1]	No	No	Yes	28
	BTC[− 1, …, − 5]	\(\sigma\)[− 1, …, − 5]
	LTC[− 1, …, − 5]	\(\sigma\)[− 1, …, − 5]
Litecoin
Linear	LTC[− 1, …, − 6]	RR[− 1]	No	No	Yes	32
	BTC[− 1, …, − 6]	\(\sigma\)[− 1, …, − 6]
	ETH[− 1, …, − 6]	\(\sigma\)[− 1, …, − 6]
Linear-binary	LTC[− 1, …, − 6]	RR[− 1]	Yes	Yes	Yes	44
	BTC[− 1, …, − 6]	\(\sigma\)[− 1, …, − 6]
	ETH[− 1, …, − 6]	\(\sigma\)[− 1, …, − 6]
RF	LTC [− 1, − 2]	RR[− 1]	No	No	Yes	16
	BTC[− 1, − 2]	\(\sigma\)[− 1, − 2]
	ETH[− 1, − 2]	\(\sigma\)[− 1, − 2]
RF-binary	LTC [− 1]	RR[− 1]	No	No	Yes	12
	BTC[− 1]	\(\sigma\)[− 1]
	RTH [− 1]	\(\sigma\)[− 1]
SVM	LTC [− 1, …, − 5]	RR[− 1]	Yes	Yes	Yes	40
	BTC[− 1, …, − 5]	\(\sigma\)[− 1, …, − 5]
	ETH[− 1, …, − 5]	\(\sigma\)[− 1, …, − 5]
SVM-binary	LTC [− 1, − 2,-3]	RR[− 1]	No	No	Yes	20
	BTC[− 1, − 2,-3]	\(\sigma\)[− 1, − 2, − 3]
	ETH[− 1, − 2,-3]	\(\sigma\)[− 1, − 2, − 3]

This table shows the best input sets obtained in the validation sample, i.e. those variables that maximize the 1-step out-of-sample average return, based on a rolling window with a length of 648 days. These sets of variables are then used in the test sample. The second column refers to the lagged returns of the three cryptocurrencies, which could go up to lag 7. The third column refers to two volatility estimators of the dependent cryptocurrency, namely the relative price range, \(RR_{t}\), and the range estimator of Parkinson (1980), \(\sigma_{t}\). For the first estimator only the first lag is used, while for \(\sigma_{t}\) it was considered a maximum lag structure up to lag 7. The number of lags used in these variables are in squared brackets. The fourth column refers to other trading variables, namely the daily trading volume and market capitalization. The fifth column refers to network variables. All the models that include these variables, consider a subset of the initial network variables, however all these subsets do not include the median transaction value and the number of transactions on the public blockchain. The sixth column refers to dummies corresponding to the day-of-the-week.

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