Price clustering at numbers ending with ’00’

Table 2 presents the five most frequent and five least frequent two-digit ending numbers. For all the three exchanges, the most frequent ending numbers is ’00’, accounting for 7.59%, 3.13%, and 20.01% on Coincheck, BtcBox, and bitFlyer, respectively. The prices ending with ’99’ rank second and are followed by those ending with ’01’ or ’50’. Furthermore, price clustering at ’01’ and ’99’ provides evidence for strategic pricing.

Figure 1 shows the proportions of all two-digit ending numbers. First, plot (a) shows that proportions of ’00’, ’01’, and ’99’ significantly exceed those of other ending numbers on Coincheck. Second, plot (b) shows that on BtcBox, proportions of two-digit ending numbers are all around 1%, except for ’00’. Further, plot (c) reveals that price clusters at round numbers ending with ’0’ on bitFlyer, but ’00’ accounts for the most. Therefore, the proportions of the two-digit ending numbers demonstrate that the BTC/JPY prices from the three online exchanges cluster more at numbers ending with ’00’ over others. Still, the scales of price clustering vary with exchanges.

Table 2 Frequencies of two-digit ending numbers of BTC/JPY
Fig. 1
figure1

Proportions of two-digit ending numbers of BTC/JPY. This figure presents two-digit ending numbers and corresponding proportions in percentage of three online crypto exchanges during each sample period

Fig. 2
figure2

The extent of hourly price clustering of BTC/JPY. This figure presents hourly AVG and CR of three online crypto exchanges on a daily basis during each sample period

Price clustering at continuous transactions

Table 3 The scale of price clustering on hour dummies

Figure 2 illustrates the hourly AVG and CR on a daily basis with scatter points. The legend on the right side of each plot accounts for the correlation between the colors of the points and the corresponding hour intervals in the plots. To enhance readability, hours in GMT and local time JST are both given in the legend. For instance, GMT00_JST09 means hour00 in GMT and hour09 in JST, as GMT is nine hours behind JST. First, plot (a) reveals that the scatters in both plots (AVG and CR) exhibit a layered phenomenon on Coincheck from 2017, suggesting that the extent of price clustering varies considerably over time throughout a trading day since 2017, and price clustering is reduced in the early morning. Initially, as the hourly volume in BTC was relatively low and transaction counts were small (see “Appendix”), the scale of hourly price clustering on Coincheck fluctuated significantly. Then, with growing acceptance by the massive (see Hairudin et al. 2020), both hourly volume and transaction counts increased significantly since the Bitcoin bubble in 2017. Accordingly, hourly price clustering appeared to be relatively stable. Second, plot (b) shows no visible intraday pattern in the price clustering on BtcBox, but the extent of price clustering shows a more significant fluctuation. This is probably because transactions on BtcBox were not as active as those on Coincheck and bitFlyer based on hourly transaction counts. Third, plot (c) indicates a remarkable intraday pattern in the price clustering of BTC/JPY on bitFlyer during the sample period, which starts from August 1, 2017. To conclude, the intraday pattern of price clustering in BTC/JPY varies with market conditions and online crypto exchanges.

Fig. 3
figure3

Estimates from regressions of hourly AVG/CR on hour dummies. Estimates for intercepts are not reported for readability. Data from bitFlyer in regressions span continuously from August 1, 2017 to May 26, 2019, whereas data from Coincheck and BtcBox are sampled from January 1, 2015 to April 30, 2020

Figure 3 presents estimates with 95% confidence intervals from the regression results of hourly AVG/CR on 23 hour dummies except for JST09, using the data collected from Coincheck, BtcBox, and bitFlyer. Observably, estimates tend to decline from JST23 to JST04 and recover from JST05 to JST08. Alternatively, the scale of price clustering is prone to be lower during the interval from JST00 to JST07 compared with those in previous hour intervals across the three online crypto exchanges.

Table 3 details the regression results of hourly AVG/CR on hour dummies for the three online crypto exchanges. Generally speaking, the extent of price clustering, as indexed by both AVG and CR, tends to be lower from JST02 to JST07. Initially, the intercept in each regression represents the extent of price clustering at JST09, corresponding to the interval lasting from 9:00 to 9:59 JST. The intercepts in Table 3 show that the extent of price clustering is statistically significant from zero at the 1% level and obviously exceeds 1% from 9:00 to 9:59 JST. Furthermore, the coefficients of other variables are the differences in the extent of price clustering between other hour intervals and JST09. For Coincheck, the coefficients from JST02 to JST07 are negative and statistically different from zero at the 5% significance level, suggesting that the extent of price clustering is significantly lower from 2:00 to 7:59 JST in the early morning. For BtcBox, AVG is substantially higher from JST18 to JST00, but is significantly lower from JST03 to JST05. However, for the CR of BtcBox, it exhibits no similar intraday pattern. For bitFlyer, AVG and CR are considerably lower from JST00 to JST08. Furthermore, the estimates for CR of Coincheck and bitFlyer during JST02 to JST07 are notably lower than those for AVG, suggesting that the proportion of transaction amounts with the prices clustering at ’00’ is lower in the morning across Japan. Despite no opening or closing in online crypto exchanges like traditional asset markets, the prominent intraday patterns of price clustering remain available with data from Coincheck and bitFlyer.

Day-of-the-week effect on price clustering

Fig. 4
figure4

Estimates from regressions of hourly AVG/CR on the hour and weekday dummies. Estimates for intercepts are not reported for readability. Data from bitFlyer in regressions span continuously from August 1, 2017 to May 26, 2019, whereas data from Coincheck and BtcBox are sampled from January 1, 2015 to April 30, 2020

Figure 4 presents estimates with 95% confidence intervals from regression results on the hour and week dummies to examine the existence of the day-of-the-week effect on price clustering. The day-of-the-week effect on BTC price clustering was first documented by Mbanga (2019). Specifically, Mbanga (2019) found that the degree of BTC/USD price clustering at whole numbers is higher on Fridays and lower on Mondays using the daily closing price data of Bitstamps. However, empirical results in Fig. 4 show that compared to price clustering on Monday, the price clustering degrees indexed by AVG of BtcBox and CR of bitFlyer are the lowest on Sunday. In summary, except for AVG of BtcBox and CR of bitFlyer, there is no apparent day-of-the-week effect on price clustering in BTC/JPY across the three online crypto exchanges when hour dummies are incorporated.

Intraday patterns in price clustering with negotiation hypothesis

Fig. 5
figure5

Estimates from regressions of hourly AVG/CR on hour dummies with control variables. Only estimates for hourly dummies are presented, whereas estimates for intercepts and control variables (logMeanp, logCount, logVolsum, Rangep, and RV) are not reported for readability. Data from bitFlyer in regressions span continuously from August 1, 2017 to May 26, 2019, whereas data from Coincheck and BtcBox are sampled from January 1, 2015 to April 30, 2020

Figure 5 presents estimates with 95% confidence intervals from regression results of hourly AVG/CR on 23 hour dummies with control variables drawn from the negotiation hypothesis (Harris 1991; Ohta 2006; Urquhart 2017). Also, estimates for intercepts and control variables based on the negotiation hypothesis, including logMeanp, logCount, logVolsum, Rangep, and RV are not reported for readability. Observably, estimates for dummies exhibit a similar trend as those in Fig. 3, suggesting that the intraday patterns in price clustering are still available after incorporating control variables drawn from the negotiation hypothesis.

Table 4 details the regression results of models incorporating control variables. Observably, the extent of price clustering across the three online crypto exchanges remains lower from JST02 to JST07 on the whole. After adding control variables, the coefficients for CR of BtcBox from JST02 to JST07 are negative, while the coefficients for JST03, JST04, and JST05 show statistical significance from zero at the 5% level. Meanwhile, all of the coefficients from JST02 to JST07 are negative, with most showing a statistical significance from zero at the 1% level. Therefore, the phenomenon of lower price clustering from 2:00 to 7:59 JST is stable, which can not be accounted for using the negotiation hypothesis.

Table 5 indicates the regression results for hourly transaction counts (Count) exceeding 1,000 to eliminate the effect of a small number of transactions during hour intervals. According to the regression results, the coefficients from JST02 to JST07 are invariably negative, and most coefficients show a statistical difference from zero at the 5% level. For BtcBox, the low price clustering indexed by CR is apparent from JST03 to JST08 when transaction times exceed 1,000. Table 5 demonstrates that the differences in the extent of price clustering between the interval of 2:00 to 7:59 JST and other trading times remain when transactions are conducted frequently.

Table 4 The scale of price clustering on hour dummies with control variables
Table 5 The scale of price clustering when hourly Count exceeds 1,000

In addition, the signs of coefficients of the control variables based on the negotiation hypothesis in Tables 4 and 5 are not exactly as expected. This is because the data used in this study comprises time series from each exchange that cannot reveal a common trend as in previous studies (Harris 1991; Aitken et al. 1996; Ohta 2006), which used panel data.

Robustness check

Although the differences in the scales of price clustering between other hour intervals and JST09 have been demonstrated by using the regression method, pairwise comparisons of price clustering between hour intervals have not been conducted. To address this concern, this study uses the Dunn’s test (Dunn 1964) with a Bonferroni adjustment to perform nonparametric pairwise comparisons of AVG/CR by the hour, as shown in the “Additional file 1”. The null hypothesis of Dunn’s test is that the possibility of observation in one group that is greater than observation from another group equals to 0.5 (Dinno 2015). Specifically, Dunn’s z-test statistic and p-value are reported in each table. If the p-value is less than the half of the alpha, then the null hypothesis is rejected at the statistical significance level of the alpha. For example, in the comparison of AVG from Coinchek by hour, the z-test statistic of JST02 and JST09 is 8.2726, and the null hypothesis that the possibility of observing AVG during JST02 which is greater than AVG during JST09 equals to 0.5 is rejected at the 5% significance level (alpha=5%).

According to Dunn’ test on AVG/CR, the nonparametric pairwise comparisons show similar results as those from the regression method. First, results of Dunn’s test on AVG/CR of Coincheck indicate that the null hypotheses of pairwise comparisons of AVG/CR between hour intervals from 2:00 to 7:59 JST and other hour intervals are generally rejected at the 5% significance level. In other words, the scales of price clustering indexed by AVG/CR of Coincheck from 2:00 to 7:59 JST are generally statistically different from those of other hour intervals. Second, with respect to BtcBox, most of the AVG and CR from 2:00 to 7:59 JST are also statistically different from those of other hour intervals. Third, results of Dunn’s test indicate that the AVG/CR of bitFlyer is significantly different between the interval of 0:00 to 7:59 JST and other trading intervals. Overall, the nonparametric pairwise comparisons from Dunn’s test suggest that the scales of BTC/JPY price clustering indexed by AVG and CR are generally lower from 2:00 to 7:59 JST over the three online crypto exchanges, which is consistent with the empirical results from the parametric method.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Disclaimer:

This article is autogenerated using RSS feeds and has not been created or edited by OA JF.

Click here for Source link (https://www.springeropen.com/)