Package 'garchf'

Model-agnostic statistical probabilistic forecasting with conditional volatility

Description

Combines a mean model and a volatility model to produce probabilistic forecasts. Uncertainty is propagated from two sources: simulated innovation draws and simulated volatility paths derived from the variance model's residuals via bootstrap.

Usage

condvolf(
  y,
  h = 10L,
  mean_model = forecast::thetaf,
  sigma_model = forecast::thetaf,
  innovation = c("empirical", "gaussian", "student"),
  level = 95,
  B = 500L,
  bootstrap_vol = TRUE,
  ...
)

Arguments

y	A numeric vector or time series of class ts.
h	Forecasting horizon.
mean_model	Function to fit the mean model (default: forecast::auto.arima). Options include forecast::auto.arima, forecast::ets, forecast::thetaf, or any custom function that returns an object with forecast method.
sigma_model	Function to fit the variance model on squared residuals (default: forecast::auto.arima).
innovation	Distribution for standardized innovations. One of "gaussian" (fastest, often sufficient), "student" (heavy-tailed), or "empirical" (non-parametric, most flexible). Only used for conformal=FALSE
level	Confidence level for prediction intervals (default: 95).
B	Number of simulated paths (default: 2000).
bootstrap_vol	Whether to bootstrap volatility residuals (default: TRUE). If FALSE, uses parametric normal approximation for volatility.
...	Additional arguments passed to mean_model and sigma_model.
conformal	Logical. If TRUE, enables split conformal prediction to calibrate interval width. The series is split into a training portion and a calibration portion (controlled by cal_frac); a base condvolf fit on the training portion produces calibration residuals, which are normalized by a volatility model, resampled via moving block bootstrap, re-inflated by the forecast volatility, and added to the full-data point forecast. This typically yields tighter and better- calibrated intervals than the raw simulation approach. Default is FALSE.

Value

A forecast object with components:

x

Original time series.

mean

Point forecast (mean of simulations).

lower

Lower prediction interval bound.

upper

Upper prediction interval bound.

level

Confidence level.

sims

Matrix of simulated forecast paths (h x B).

model

List containing mean and sigma model fits.

residuals

Residuals from the mean model.

standardized_residuals

Scaled standardized residuals used for innovation fitting.

method

Character string describing the method used.

Examples

library(forecast)

# Basic usage with Google stock data
y <- fpp2::goog200

# Gaussian innovations (fastest, often sufficient)
fc1 <- condvolf(y, h = 20, innovation = "gaussian")
plot(fc1)

# Student-t innovations (heavy-tailed)
fc2 <- condvolf(y, h = 20, innovation = "student")
plot(fc2)

# Empirical innovations (non-parametric)
fc3 <- condvolf(y, h = 20, innovation = "empirical")
plot(fc3)

# Using different mean and volatility models
fc4 <- condvolf(y, h = 20,
                mean_model = forecast::thetaf,
                sigma_model = forecast::ets,
                innovation = "gaussian")

# Compare prediction intervals
par(mfrow = c(2, 2))
plot(fc1, main = "Gaussian innovations")
plot(fc2, main = "Student-t innovations")
plot(fc3, main = "Empirical innovations")
plot(fc4, main = "Different mean and volatility models")
par(mfrow = c(1, 1))

---

Two-stage forecasting model

Description

Two-stage forecasting model

Usage

twostagef(
  y,
  h = 10,
  mean_model = forecast::thetaf,
  sigma_model = forecast::thetaf,
  residuals_model = forecast::thetaf,
  innovation = c("bootstrap", "fitdistr"),
  cal_frac = 0.5,
  level = 95,
  B = 500L,
  ...
)

Arguments

y	A numeric vector or time series of class ts.
h	Forecasting horizon.
mean_model	Function to fit the mean model (default: forecast::auto.arima). Options include forecast::auto.arima, forecast::ets, forecast::thetaf, or any custom function that returns an object with forecast method.
sigma_model	Function to fit the variance model on squared residuals (default: forecast::auto.arima).
residuals_model	A function from package forecast, the model adjusted to residuals for 2-stage forecasting
innovation	Either "bootstrap" or "fitdistr"; the latter is parametric
cal_frac	Numeric in (0, 1). Fraction of observations reserved for the calibration set. The calibration set is always at least h observations long regardless of cal_frac. Larger values improve calibration stability at the cost of a shorter training set for the base model. Default is 0.5.
level	Confidence level for prediction intervals (default: 95).
B	Number of simulated paths (default: 2000).
...	Additional arguments passed to mean_model and sigma_model.

Value

A forecast object with components:

x

Original time series.

mean

Point forecast (mean of simulations).

lower

Lower prediction interval bound.

upper

Upper prediction interval bound.

level

Confidence level.

sims

Matrix of simulated forecast paths (h x B).

model

List containing mean and sigma model fits.

residuals

Residuals from the mean model.

standardized_residuals

Scaled standardized residuals used for innovation fitting.

method

Character string describing the method used.

---

GARCH forecasting wrapper returning a forecast object

Description

Similar spirit to forecast::thetaf(), but using rugarch models.

Usage

xgarchf(
  y,
  h = 10L,
  model = c("eGARCH", "sGARCH", "gjrGARCH", "apARCH", "iGARCH"),
  arma_order = c(0, 0),
  garch_order = c(1, 1),
  distribution_model = c("norm", "std", "ged"),
  level = 95,
  B = 500L,
  ...
)

Arguments

y	numeric vector or ts
h	forecast horizon
model	mean model ("sGARCH", "eGARCH", "gjrGARCH", ...)
arma_order	ARMA order for the conditional mean; a vector with 2 elements
garch_order	GARCH order; a vector with 2 elements
distribution_model	conditional distribution "norm", "std", "ged"
level	confidence level(s)
B	number of simulations to return if sim=TRUE
...	Additional parameters passed to rugarch::ugarchfit

Value

object of class forecast

Examples

## Not run: 
y <- diff(log(fpp2::goog200))
fit <- xgarchf(y, h = 20, model = "eGARCH")
plot(fit)

## End(Not run)

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