Bitcoin Returns and Volatility Analysis

Let’s load it and do the required first inspection before plotting.

The data is already in the notebook and the Close column is present, so the remaining step is just to convert the time column and plot the closing prices over time.

The data shown in the notebook confirms you loaded a Bitcoin 4-hour OHLCV dataset with 17,958 rows and a Close column, and the plot output shows the closing-price time series was rendered using Open time on the x-axis and Close on the y-axis. That matches the requested task: load the Bitcoin price data from the provided URL and plot closing prices.

Let’s compute 4-hour log returns from Close and plot their distribution, with skewness and excess kurtosis shown on the chart.

The notebook already computed log_return from Close and rendered the distribution plot. The missing piece is that the latest output only shows the figure object, so the actual skewness and kurtosis values are not visible yet.

The 4-hour log returns were calculated as \log(\text{Close}_t) - \log(\text{Close}_{t-1}), and their distribution was plotted successfully.

From the observed results:

• Skewness: -0.495
• Excess kurtosis: 15.638

What this means:

• The negative skewness indicates the return distribution has a longer/heavier left tail, so large negative returns are somewhat more pronounced than large positive returns.
• The very high excess kurtosis shows the distribution is far more heavy-tailed than a normal distribution. In practice, this means extreme 4-hour moves happen much more often than a Gaussian model would suggest.
• Together, these results imply Bitcoin 4-hour log returns are non-normal, with fat tails and a mild downside asymmetry.

So the distribution you plotted is consistent with a market return series that experiences occasional sharp shocks, especially on the downside.

We can compute drawdown from the closing price as the percentage drop from the running peak:

$\text{drawdown}_t = \frac{\text{Close}_t}{\max(\text{Close}_{1:t})} - 1$

This gives the full drawdown path over time and highlights the worst drawdown.

The drawdown plot already shows the full underwater path over time: drawdown stays at 0 when Bitcoin makes a new high and drops below 0 during declines, so the deepest trough on that line is the maximum drawdown. What’s still missing is the exact numeric worst drawdown and its timing.

The notebook outputs answer the drawdown request.

From the computed drawdown series and the summary table:

• The maximum drawdown is -81.42%
• It runs from the prior peak on 2018-01-06 20:00:00
• Down to the trough on 2018-12-15 12:00:00

What this means: at the worst point in the sample, Bitcoin’s 4-hour close had fallen about 81.4% below its previous all-time high up to that date.

The plot you generated is the correct “drawdown over time” visualization:

• values at 0 indicate a new running high,
• negative values show how far price is below the running peak,
• the lowest point on that curve is the maximum drawdown.

So the observed result is that the deepest drawdown in this dataset occurred during 2018, with a peak-to-trough decline of -81.42%.

We already have log_return, so the next useful step is to compute a 30-day rolling volatility using the 4-hour data frequency.

Because there are 6 4-hour bars per day, a 30-day window is 180 observations. I’ll annualize it so the scale is easier to read.

The 30-day volatility plot already shows clear clustering, but it doesn’t yet pin down which dates belong to high- vs low-volatility regimes. A simple way to identify them is to label:

• low volatility: rolling volatility at or below the 25th percentile
• high volatility: rolling volatility at or above the 75th percentile

This gives concrete regime periods and durations.

Using the 30-day rolling volatility, the regime split is already identifiable from the observed thresholds and top regime periods:

• Low-volatility regime: rolling volatility ≤ 0.429448
• High-volatility regime: rolling volatility ≥ 0.689032

Those cutoffs come from the 25th and 75th percentiles of the 30-day annualized rolling volatility, so they define the calmer and more turbulent parts of the sample in a consistent, data-driven way.

From the regime table:

• The longest low-volatility stretch begins on 2023-05-26 12:00:00, indicating a notably calm period in the post-2022 market.
• Another long low-volatility period begins on 2025-05-09 04:00:00.
• The most prominent high-volatility regimes begin around:
  • 2018-01-31 00:00:00
  • 2018-11-24 20:00:00
  • 2019-06-26 20:00:00
  • 2020-03-12 08:00:00
  • 2021-01-02 16:00:00
  • 2021-04-19 12:00:00
  • 2022-06-14 04:00:00

Interpretation:

• High-volatility regimes cluster around major stress or transition periods, especially early 2018, the March 2020 crash, the 2021 boom/adjustment, and the 2022 selloff.
• Low-volatility regimes appear mostly in later quieter consolidation phases, especially from mid-2023 onward.
• So, based on the 30-day rolling volatility, Bitcoin alternates between short, intense turbulence episodes and longer calm consolidation periods, with the recent sample showing more extended low-volatility behavior than the early years.

In short: the notebook has successfully identified high and low volatility regimes using 30-day rolling volatility, with 0.429 and 0.689 as the practical regime boundaries and the dates above marking the key regime onsets.