Package 'weatherMRJD'

Title: Weather Analysis and Markov Regime Switching Jump Diffusion Models
Description: Provides statistical tools for analyzing weather patterns, temperature anomalies, and climate risk. Implements Markov regime-switching jump diffusion (MRJD) models to capture abrupt shifts, extreme weather events, and structural breaks in environmental time series data. Estimates model parameters using maximum likelihood estimation and offers utility functions for simulating regime-dependent stochastic processes. The regime-switching methodology is based on Hamilton (1989) "Analysis of Time Series Subject to Changes in Regime" <doi:10.2307/1912559>.
Authors: Okechukwu J. Obulezi [aut, cre] (ORCID: <https://orcid.org/0000-0002-7753-1868>)
Maintainer: Okechukwu J. Obulezi <[email protected]>
License: MIT + file LICENSE
Version: 0.1.1
Built: 2026-10-09 11:28:45 UTC
Source: https://github.com/cran/weatherMRJD

Help Index

Calibrate Dynamic SDE and Jump Parameters

Description

Estimates mean-reversion speed, unconditional volatility, and jump characteristics.

Usage

calibrate_mrjd(residuals, n_years, threshold_sigma = 2.5)

Arguments

residuals

Numeric vector of detrended temperature residuals X(t).
n_years

Numeric scalar representing total observation period in years.
threshold_sigma

Threshold multiplier for jump identification (default: 2.5).

Value

A named list of calibrated stochastic differential parameters.

Examples

set.seed(123)
res <- stats::rnorm(730, sd = 2)
calib <- calibrate_mrjd(res, n_years = 2)
print(calib$kappa)

Fit Fourier Seasonal Baseline Trend

Description

Fits a truncated Fourier series to daily atmospheric temperature observations.

Usage

fit_seasonal_trend(temp, day_of_year)

Arguments

temp

Numeric vector of observed daily average temperatures.
day_of_year

Numeric vector of day-of-year indices (1 to 365/366).

Value

A list containing the fitted OLS model, fitted values, and isolated residuals.

Examples

doy <- rep(1:365, times = 2)
temp <- 15 + 10 * sin(2 * pi * doy / 365) + stats::rnorm(730, sd = 2)
fit <- fit_seasonal_trend(temp, doy)
print(fit$rmse)

Price HDD and CDD Weather Derivatives

Description

Evaluates fair values and Monte Carlo standard errors for HDD and CDD Call Options.

Usage

price_weather_option(
  temp_paths,
  strike,
  type = c("HDD", "CDD"),
  r = 0.04,
  base_temp = 18
)

Arguments

temp_paths

Matrix of simulated temperature paths from simulate_weather_paths.
strike

Strike index level K.
type

Option contract type: "HDD" or "CDD".
r

Risk-free discount rate (default 0.04).
base_temp

Threshold index baseline (default 18.0 deg C).

Value

A list containing estimated price, standard error, and index distribution metrics.

Examples

paths <- simulate_weather_paths(n_paths = 100, days = 90)
hdd_opt <- price_weather_option(paths, strike = 500, type = "HDD")
print(hdd_opt$price)

Simulate Temperature Paths via Non-Homogeneous Jump-Diffusion

Description

Generates discretized Monte Carlo sample trajectories of daily average temperatures.

Usage

simulate_weather_paths(
  n_paths = 5000,
  days = 365,
  kappa = 0.08,
  sigma_0 = 2.5,
  lambda_0 = 0.05,
  lambda_1 = 0.03,
  mu_jump = -3,
  sigma_jump = 1.5,
  baseline_temp = 14.5,
  amplitude_temp = 11.2
)

Arguments

n_paths

Integer count of simulation paths.
days

Horizon length in days (default 365).
kappa

Mean-reversion speed.
sigma_0

Baseline volatility.
lambda_0

Baseline jump intensity.
lambda_1

Amplitude of dynamic seasonal jump intensity.
mu_jump

Mean jump magnitude.
sigma_jump

Volatility of jump magnitude.
baseline_temp

Baseline temperature parameter A.
amplitude_temp

Seasonal temperature amplitude.

Value

An (n_paths x days) matrix of simulated daily temperatures.

Examples

paths <- simulate_weather_paths(n_paths = 50, days = 30)
dim(paths)