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Volatility analysis of a coin

Source: R/fct_volatility.R
volatility_analysis.Rd

Is the coin's recent volatility normal? The analysis looks at the daily log returns, log(close(t) / close(t-1)), in two ways.

The last month (month_days days): its volatility, the standard deviation of the daily returns times sqrt(365), against the year before it and against every past period of the same length; an F test and the Fligner-Killeen test, which is robust to a few extreme days, of whether its variance is larger than the year before; its largest daily move, in standard deviations of the year before; and its return against every past period of the same length.

The last days (recent_days days): their return against every past period of as many days; the same, in standard deviations of the year before; a GARCH(1,1) model with Student-t errors (see garch_fit()), fitted to the garch_years years before them, which judges each day against the volatility the model expected for it given the days before; and each day's volume against the month_days days before it (see volume_ratio()), judged by how often the coin's volume was as far from usual.

The next days (forecast_days days): the same model, with its variance brought up to the last day, forecasts the volatility and the range of the price (see garch_forecast()), and gives the value at risk and the expected shortfall of the next day (see garch_risk()). A Kupiec test (see kupiec_test()) checks how often the model's value at risk was exceeded over the last year. The value at risk and expected shortfall of the last year's daily returns are given without the model too.

Usage

volatility_analysis(
  history,
  month_days = 30,
  recent_days = 2,
  garch_years = 4,
  forecast_days = 7,
  level = 0.95
)

Arguments

history

Price history of one coin from get_history(), sorted by date. The comparisons use the whole history, so pass all of it.

month_days

Days in the month.

recent_days

Days in the recent move.

garch_years

Years of history to fit the GARCH model to.

forecast_days

Days to forecast.

level

Probability of the forecast ranges, and of the value at risk: 0.95 is the 95% range and the worst 5% of days.

Value

NULL when the history is shorter than a year and a month, or the price did not move at all in the year before the month or the last days, otherwise a list with

  • coin, first_date and last_date;

  • month: a list of the month's measures, see the code;

  • recent: a list of the measures of the last days, with a days data frame of each day's return, GARCH measures, volume, volume_ratio and volume_one_in_days (NA without volume);

  • garch: the fitted model, or NULL when it could not be fitted or there are fewer than 500 days before the last days;

  • forecast: NULL without a model, otherwise a list with days, a data frame with a row per day ahead: its date, sigma (the daily standard deviation the model expects, in percent) and the closes low, low_50, median, high_50 and high of the ranges (see garch_forecast()); sigma and sigma_long_run, the daily standard deviation expected for the next day and in the long run; half_life, the days for the volatility to get half-way back to the long run; var and es, the value at risk and expected shortfall of the next day; and backtest, the days, exceedances and p_value of the Kupiec test;

  • history_risk: var and es of the daily returns of the last days (365) days, in percent;

  • series: a data frame with a row per day and the columns date, close, volume, return_pct, volume_ratio (see volume_ratio()), volatility_month (annualized, in percent), garch_sigma (the daily standard deviation the model expected, in percent), garch_z (the day's move in those standard deviations) and garch_var (the model's value at risk for the day, in percent);

  • settings: month_days, recent_days, garch_years, forecast_days and level.

Examples

btc <- get_history("Bitcoin (BTC)", as.Date("2013-04-29"))
analysis <- volatility_analysis(btc)
analysis$month$level
#> [1] "normal"
analysis$recent$days
#>         date return_pct   garch_z one_in_days      volume volume_ratio volume_one_in_days
#> 1 2026-11-04   3.956612  1.707661    32.41037 40881988659     1.642935           8.925573
#> 2 2026-11-05  -5.550836 -2.299618    69.06806 48407763452     1.945375          15.234528
analysis$forecast$days
#>         date    sigma      low   low_50   median  high_50     high
#> 1 2026-11-06 3.028457 71812.70 74940.07 75976.19 77026.63 80381.05
#> 2 2026-11-07 3.041512 70249.07 74447.70 76000.15 77617.44 82308.00
#> 3 2026-11-08 3.053994 68992.06 74056.90 76027.99 78066.46 83944.18
#> 4 2026-11-09 3.065930 68030.44 73771.04 76103.36 78490.85 85229.47
#> 5 2026-11-10 3.077346 67114.49 73501.29 76140.12 78840.72 86388.32
#> 6 2026-11-11 3.088267 66228.78 73250.13 76174.89 79172.76 87387.87
#> 7 2026-11-12 3.098717 65546.97 73067.49 76215.12 79476.53 88413.71
volatility_text(analysis)
#> $month
#> $month$headline
#> [1] "Volatility of the last 30 days: normal"
#> 
#> $month$points
#> [1] "37.5% a year, against 45.1% in the year before and a median of 55.8% for all 30-day periods since 2013: the 19th percentile."           
#> [2] "No significant difference from the year before (variance ratio 0.69, p = 0.88 and 0.57)."                                               
#> [3] "The largest day, 5 Nov (−5.55%), was 2.4 standard deviations of the year before: common, as days that large come about 11 times a year."
#> [4] "The return of the 30 days, −11.2%, is in the 21st percentile of all 30-day periods: an ordinary month."                                 
#> 
#> 
#> $recent
#> $recent$headline
#> [1] "Last 2 days: −1.8% together, a normal fall"
#> 
#> $recent$points
#> [1] "Day by day: 4 Nov +3.96%, 5 Nov −5.55%."                                                                                                                                                                       
#> [2] "Since 2013, 2-day moves this large came about 94 times a year (the 26th percentile)."                                                                                                                          
#> [3] "Against the volatility of the year before, the move is −0.6 standard deviations, which came about 70 times a year."                                                                                            
#> [4] "A GARCH model fitted to the 4 years before saw +1.7 and −2.3 standard deviations (−0.6 together), given the volatility it expected: about 1 in 5 days. The days went opposite ways, so they partly cancel out."
#> [5] "The most extreme single day, 5 Nov (−5.55%), was −2.3 standard deviations: an unusual fall, about 1 in 69 days (about 5.3 times a year)."                                                                      
#> [6] "Volume: 4 Nov $40.9bn and 5 Nov $48.4bn, 1.6 and 1.9 times the median of the 30 days before; 5 Nov is normal for the coin, as volume that far above its month came about 24 times a year."                     
#> 
#> 
#> $forecast
#> $forecast$headline
#> [1] "Expected move on 6 Nov (95% range): −5.4% to +5.8%"
#> 
#> $forecast$points
#> [1] "Over the next 7 days, to 12 Nov (95% range): −13.7% to +16.4%, a close between $65,547 and $88,414."                                             
#> [2] "The model expects the volatility on 6 Nov to be 9% below its long-run level of the last 4 years: it should rise towards it, half-way in 17 days."
#> [3] "Value at risk: on 1 day in 20, the loss on 6 Nov would exceed 4.1%, and average 6.5% on those days (the 95% VaR and expected shortfall)."        
#> [4] "In the last year, the worst 5% of days lost at least 3.4%, and 5.1% on average."                                                                 
#> [5] "Check: losses beyond the model's daily VaR came on 17 of the last 365 days (4.7%), in line with the 5% expected (Kupiec test p = 0.76)."         
#> 
#>