Package {MAARTS}

Type:	Package
Title:	Merger and Acquisition Autoregressive Time-Series Models
Version:	1.0.0
Description:	Implements comprehensive Merger and Acquisition ('M&A') Autoregressive ('AR') time-series models with full statistical analysis capabilities. The package provides parameter estimation, forecasting with confidence intervals (80%, 90%, 95%, 99%), descriptive statistics, stationarity tests (Augmented Dickey-Fuller ('ADF'), Phillips-Perron, Kwiatkowski-Phillips-Schmidt-Shin ('KPSS'), Dickey-Fuller Generalized Least Squares ('DF-GLS')), autocorrelation analysis (Autocorrelation Function ('ACF'), Partial Autocorrelation Function ('PACF')), model diagnostics (Ljung-Box, Box-Pierce), accuracy measures (Mean Squared Error ('MSE'), Mean Absolute Error ('MAE'), Mean Absolute Scaled Error ('MASE'), Root Mean Squared Error ('RMSE'), Symmetric Mean Absolute Percentage Error ('SMAPE'), F-statistic), residual diagnostics (normality tests, heteroscedasticity tests), model stability analysis, impulse response, information criteria (Akaike Information Criterion ('AIC'), Bayesian Information Criterion ('BIC'), Hannan-Quinn Information Criterion ('HQIC')), structural break analysis, spectral analysis, and Monte Carlo simulation. Models are based on: Kumar, Mudassir, and Agiwal (2024) https://ph02.tci-thaijo.org/index.php/thaistat/article/view/253436, Kumar, Mudassir, and Srivastava (2025) <doi:10.1007/s44199-025-00104-3>, Kumar and Mudassir (2025) <doi:10.19139/soic-2310-5070-2029>.
License:	GPL-3
Depends:	R (≥ 4.0.0)
Imports:	forecast, tseries, urca, stats, graphics, grDevices, utils, lmtest, sandwich, nortest, moments, strucchange, ggplot2, gridExtra, MASS, numDeriv
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
Config/testthat/edition:	3
Encoding:	UTF-8
Language:	en-US
LazyData:	true
RoxygenNote:	7.3.3
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2026-07-17 15:09:00 UTC; 30017827
Author:	Shikhar Tyagi [aut, cre], Mohd Mudassir [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-07-26 11:00:02 UTC

MAARTS: Merger and Acquisition Autoregressive Time-Series Models

Description

The MAARTS package provides a complete framework for M&A time-series analysis including:

• Model estimation: Merged Autoregressive Spline (M-ARS), Multiple-Merger Autoregressive (MM-AR), Multiple-Merger Autoregressive with Explanatory Series (MM-ARE), and general AR(p) models with OLS and Bayesian estimation

• Descriptive statistics: Mean, variance, standard deviation, skewness, kurtosis, coefficient of variation

• Normality tests: Shapiro-Wilk, Jarque-Bera, Anderson-Darling, Cramer-von Mises, Pearson chi-square, Shapiro-Francia

• Stationarity tests: ADF, Phillips-Perron, KPSS, DF-GLS (Elliott-Rothenberg-Stock)

• Autocorrelation analysis: ACF, PACF with significance bounds

• Forecasting: Multi-step ahead forecasts with confidence intervals at 80\

• Model diagnostics: Ljung-Box, Box-Pierce

• Accuracy measures: MSE, MAE, MASE, RMSE, SMAPE, MAPE, Theil's U, R-squared

• Residual diagnostics: Normality tests, Breusch-Pagan, ARCH LM

• Model stability: Characteristic roots, persistence, half-life, mean reversion

• Impulse response: IRF, cumulative IRF, dynamic multipliers

• Information criteria: AIC, BIC, HQIC, log-likelihood

• Structural breaks: Chow test, Bai-Perron, CUSUM

• Spectral analysis: Periodogram and spectral density estimation

• Monte Carlo simulation: Bias, MSE, coverage probability assessment

Details

A comprehensive R package for analyzing Merger and Acquisition (M&A) time-series data using specialized Autoregressive (AR) models.

Models

The package implements three specialized M&A time-series models:

M-ARS

Merged Autoregressive Spline model with linear spline trend around merger knot points. See ma_ars_model.

MM-AR

Multiple-Merger Autoregressive model for simultaneous treatment of multiple merger events. See ma_multiple_merger_ar.

MM-ARE

Multiple-Merger Autoregressive with Explanatory series, extending MM-AR with exogenous predictor variables. See ma_multiple_merger_ar.

Author(s)

Maintainer: Shikhar Tyagi shikhar1093tyagi@gmail.com (ORCID)

Authors:

• Mohd Mudassir mudassir94stats@gmail.com

• Vrijesh Tripathi vrijesh.tripathi@uwi.edu

Examples

# Load sample M&A time-series data
data(ma_sample_data)

# Descriptive statistics
desc_stats <- ma_descriptive_stats(ma_sample_data)

# Stationarity tests
stationarity <- ma_stationarity_tests(ma_sample_data)

# Fit AR model
ar_model <- ma_ar_fit(ma_sample_data, order = 2)

# Forecast with confidence intervals
fc <- ma_forecast(ar_model, h = 12, confidence = c(0.80, 0.90, 0.95, 0.99))

# Fit M-ARS model
mars_model <- ma_ars_model(ma_sample_data, order = 2, merger_times = 50)

Forecast Accuracy Measures for M&A Time-Series

Description

Computes comprehensive forecast accuracy measures including MSE, MAE, RMSE, MAPE, SMAPE, MASE, and Theil's U statistic.

Usage

ma_accuracy(actual, predicted)

Arguments

Value

An object of class ma_accuracy

Examples

actual <- c(1, 2, 3, 4, 5)
predicted <- c(1.1, 2.2, 2.9, 4.1, 5.2)
accuracy <- ma_accuracy(actual, predicted)

ACF and PACF Analysis for M&A Time-Series

Description

Computes autocorrelation and partial autocorrelation functions with significance bounds and optional plotting.

Usage

ma_acf_pacf(data, lag_max = NULL, plot = TRUE)

Arguments

Value

An object of class ma_acf_pacf

Examples

data(ma_sample_data)
acf_result <- ma_acf_pacf(ma_sample_data, plot = FALSE)

ACF Plot using ggplot2

Description

ACF Plot using ggplot2

Usage

ma_acf_plot(
  y,
  lag_max = 20,
  confidence_level = 0.95,
  title = "Autocorrelation Function"
)

Arguments

Value

A ggplot object showing the autocorrelation function with significance bounds.

AR Model Estimation for M&A Time-Series

Description

Fit an Autoregressive model to M&A time-series data with comprehensive diagnostics.

Usage

ma_ar_fit(data, order = NULL, method = "OLS")

Arguments

Value

A list containing model fit, parameters, and diagnostics

Examples

data(ma_sample_data)
ar_model <- ma_ar_fit(ma_sample_data, order = 2)

Merger and Acquisition AR with Spline (M-ARS) Model

Description

Fits an AR model with spline function to account for non-linear trends around merger events.

Usage

ma_ars_model(
  y,
  merger_times,
  order = 1,
  knots_before = 1,
  knots_after = 1,
  method = "OLS",
  spline_degree = 1
)

Arguments

Value

List containing model parameters, fitted values, residuals, and diagnostic information

Examples

y <- rnorm(100)
result <- ma_ars_model(y, merger_times = c(50), order = 2)

Bayesian Estimation with Loss Functions

Description

Internal function for Bayesian estimation using Normal-Inverse-Gamma conjugate prior.

Usage

ma_bayesian_estimation(Y, X, method)

Arguments

Value

List containing estimation results

Descriptive Statistics for M&A Time-Series

Description

Computes comprehensive descriptive statistics for M&A time-series data, including measures of central tendency, dispersion, shape, and distribution.

Usage

ma_descriptive_stats(data, include_tests = TRUE)

Arguments

Value

A list of class ma_descriptive_stats containing the descriptive statistics.

Examples

data(ma_sample_data)
stats <- ma_descriptive_stats(ma_sample_data)
print(stats)

Diagnostic Tests for M&A AR Models

Description

Performs Ljung-Box and Box-Pierce tests for residual autocorrelation.

Usage

ma_diagnostic_tests(model, lag = NULL)

Arguments

Value

An object of class ma_diagnostic_tests

Examples

data(ma_sample_data)
ar_model <- ma_ar_fit(ma_sample_data, order = 2)
diagnostics <- ma_diagnostic_tests(ar_model)

Forecasting for M&A AR Models

Description

Generates forecasts with confidence intervals at multiple levels (80%, 90%, 95%, 99%). Supports both standard AR models (ma_ar_fit) and M&A AR models (ma_ar_model).

Usage

ma_forecast(model, h = 10, confidence = c(0.8, 0.9, 0.95, 0.99))

Arguments

Value

An object of class ma_forecast

Examples

data(ma_sample_data)
ar_model <- ma_ar_fit(ma_sample_data, order = 2)
fc <- ma_forecast(ar_model, h = 12)

Forecast Plot using ggplot2

Description

Forecast Plot using ggplot2

Usage

ma_forecast_plot(
  forecast_result,
  historical_data = NULL,
  title = "Forecast with Confidence Intervals"
)

Arguments

Value

A ggplot object showing historical data with forecasts and confidence bands.

Histogram Plot using ggplot2

Description

Histogram Plot using ggplot2

Usage

ma_histogram_plot(y, bins = 30, title = "Histogram with Density")

Arguments

Value

A ggplot object showing a histogram with an overlaid normal density curve.

Impulse Response Function for M&A AR Models

Description

Computes impulse response functions (IRF), dynamic multipliers, and cumulative impulse responses to analyze shock transmission in M&A AR models.

Usage

ma_impulse_response(model, n_periods = 20, plot = TRUE)

Arguments

Value

An object of class ma_impulse_response

Examples

data(ma_sample_data)
ar_model <- ma_ar_fit(ma_sample_data, order = 2)
irf <- ma_impulse_response(ar_model, n_periods = 20, plot = FALSE)

Model Comparison for M&A AR Models

Description

Compares multiple AR models using information criteria (AIC, BIC, HQIC), log-likelihood values, and accuracy measures.

Usage

ma_model_comparison(..., model_names = NULL)

Arguments

Value

An object of class ma_model_comparison

Examples

data(ma_sample_data)
ar1 <- ma_ar_fit(ma_sample_data, order = 1)
ar2 <- ma_ar_fit(ma_sample_data, order = 2)
comparison <- ma_model_comparison(ar1, ar2)

Monte Carlo Simulation for M&A AR Models

Description

Performs Monte Carlo simulation to evaluate estimator performance. Assesses bias, MSE, RMSE, and coverage probability of confidence intervals.

Usage

ma_monte_carlo_simulation(
  true_coefficients,
  n = 200,
  n_sim = 1000,
  intercept = 0,
  sigma = 1,
  confidence_level = 0.95
)

Arguments

Value

An object of class ma_monte_carlo_simulation

Examples

sim <- ma_monte_carlo_simulation(true_coefficients = c(0.6, -0.2),
                                  n = 100, n_sim = 100)

Multiple Merger AR Model with Explanatory Series

Description

Fits an AR model accounting for multiple merger events with explanatory series.

Usage

ma_multiple_merger_ar(
  y,
  x_explanatory = list(),
  merger_times = numeric(0),
  order = 1,
  method = "OLS"
)

Arguments

Value

List containing model parameters, fitted values, residuals, and diagnostic information

Examples

y <- rnorm(100)
x <- list(x1 = rnorm(100), x2 = rnorm(100))
result <- ma_multiple_merger_ar(y, x, merger_times = c(30, 70), order = 2)

Normality Tests for M&A Time-Series

Description

Performs comprehensive normality tests including Shapiro-Wilk, Jarque-Bera, Anderson-Darling, Cramer-von Mises, Pearson chi-square, and Shapiro-Francia tests.

Usage

ma_normality_tests(data)

Arguments

Value

A list containing the individual test statistics, p-values, and an overall interpretation.

Examples

y <- rnorm(100)
tests <- ma_normality_tests(y)

PACF Plot using ggplot2

Description

PACF Plot using ggplot2

Usage

ma_pacf_plot(
  y,
  lag_max = 20,
  confidence_level = 0.95,
  title = "Partial Autocorrelation Function"
)

Arguments

Value

A ggplot object showing the partial autocorrelation function with significance bounds.

Normal Q-Q Plot using ggplot2

Description

Normal Q-Q Plot using ggplot2

Usage

ma_qq_plot(model, title = "Normal Q-Q Plot")

Arguments

Value

A ggplot object showing a Q-Q plot of residuals against normal quantiles.

Residual Diagnostics for M&A AR Models

Description

Performs comprehensive residual diagnostics including normality tests, heteroscedasticity tests (Breusch-Pagan, ARCH LM), and graphical diagnostics.

Usage

ma_residual_diagnostics(model, plot = TRUE, lags = c(6, 12, 18))

Arguments

Value

An object of class ma_residual_diagnostics

Examples

data(ma_sample_data)
ar_model <- ma_ar_fit(ma_sample_data, order = 2)
diag <- ma_residual_diagnostics(ar_model, plot = FALSE)

Residual Plot using ggplot2

Description

Residual Plot using ggplot2

Usage

ma_residual_plot(model)

Arguments

Value

A ggplot object showing residuals over time.

Sample M&A Time-Series Data

Description

A simulated dataset representing Merger and Acquisition activity over time. This data follows an AR(2) process with parameters phi1 = 0.6, phi2 = -0.2, intercept = 10, and sigma = 2, typical of M&A time-series dynamics.

Usage

ma_sample_data

Format

A time-series object (ts) of length 200 representing quarterly M&A activity from 2000 Q1 to 2049 Q4.

Source

Simulated data for demonstration purposes.

Examples

data(ma_sample_data)
plot(ma_sample_data, type = "l", main = "Sample M&A Time-Series")
ma_descriptive_stats(ma_sample_data)

Spectral Analysis for M&A Time-Series

Description

Performs spectral analysis to identify cyclical components in M&A activity using periodogram and spectral density estimation.

Usage

ma_spectral_analysis(data, plot = TRUE)

Arguments

Value

An object of class ma_spectral_analysis

Examples

data(ma_sample_data)
spectral <- ma_spectral_analysis(ma_sample_data, plot = FALSE)

Stability Analysis for M&A AR Models

Description

Evaluates the stability and stationarity conditions of AR models through characteristic root analysis, persistence measures, and half-life calculation.

Usage

ma_stability_analysis(model)

Arguments

Value

An object of class ma_stability_analysis

Examples

data(ma_sample_data)
ar_model <- ma_ar_fit(ma_sample_data, order = 2)
stability <- ma_stability_analysis(ar_model)

Internal function to conclude stationarity

Description

Internal function to conclude stationarity

Usage

ma_stationarity_conclusion(adf_p, pp_p, kpss_stat, kpss_cval5pct)

Stationarity Tests for M&A Time-Series

Description

Performs comprehensive stationarity and unit root tests on time-series data, including Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), KPSS, and DF-GLS tests.

Usage

ma_stationarity_tests(data, lag = NULL, trend = "drift")

Arguments

Value

An object of class ma_stationarity_tests containing test statistics, critical values, and p-values.

Examples

data(ma_sample_data)
stationarity <- ma_stationarity_tests(ma_sample_data)
print(stationarity)

Structural Break Analysis for M&A Time-Series

Description

Performs structural break analysis using Chow test, Bai-Perron multiple breakpoint tests, and CUSUM tests to detect changes in M&A dynamics.

Usage

ma_structural_break(data, model = NULL, break_point = NULL, max_breaks = 5)

Arguments

Value

An object of class ma_structural_break

Examples

y <- c(rnorm(50), rnorm(50, mean = 2))
breaks <- ma_structural_break(y, break_point = 50)

Plot method for ma_forecast

Description

Plot method for ma_forecast

Usage

## S3 method for class 'ma_forecast'
plot(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of producing a forecast plot with confidence bands.

Print method for ma_accuracy

Description

Print method for ma_accuracy

Usage

## S3 method for class 'ma_accuracy'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing a summary of forecast accuracy measures to the console.

Print method for ma_acf_pacf

Description

Print method for ma_acf_pacf

Usage

## S3 method for class 'ma_acf_pacf'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing ACF/PACF analysis results to the console.

Print method for ma_ar_fit

Description

Print method for ma_ar_fit

Usage

## S3 method for class 'ma_ar_fit'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing model coefficients, information criteria, and stability diagnostics to the console.

Print method for ma_ar_model

Description

Print method for ma_ar_model

Usage

## S3 method for class 'ma_ar_model'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing model type, AR coefficients, and coefficient summary to the console.

Print method for ma_descriptive_stats

Description

Print method for ma_descriptive_stats

Usage

## S3 method for class 'ma_descriptive_stats'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing descriptive statistics and normality test results to the console.

Print method for ma_diagnostic_tests

Description

Print method for ma_diagnostic_tests

Usage

## S3 method for class 'ma_diagnostic_tests'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing Ljung-Box and Box-Pierce test results to the console.

Print method for ma_forecast

Description

Print method for ma_forecast

Usage

## S3 method for class 'ma_forecast'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing point forecasts and confidence intervals to the console.

Print method for ma_impulse_response

Description

Print method for ma_impulse_response

Usage

## S3 method for class 'ma_impulse_response'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing impulse response function values and cumulative responses to the console.

Print method for ma_model_comparison

Description

Print method for ma_model_comparison

Usage

## S3 method for class 'ma_model_comparison'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing a model comparison table with information criteria to the console.

Print method for ma_monte_carlo_simulation

Description

Print method for ma_monte_carlo_simulation

Usage

## S3 method for class 'ma_monte_carlo_simulation'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing Monte Carlo simulation results including bias, MSE, and coverage probabilities to the console.

Print method for ma_residual_diagnostics

Description

Print method for ma_residual_diagnostics

Usage

## S3 method for class 'ma_residual_diagnostics'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing residual summary statistics, normality tests, and heteroscedasticity test results to the console.

Print method for ma_spectral_analysis

Description

Print method for ma_spectral_analysis

Usage

## S3 method for class 'ma_spectral_analysis'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing dominant frequency, period, and spectral density summary to the console.

Print method for ma_stability_analysis

Description

Print method for ma_stability_analysis

Usage

## S3 method for class 'ma_stability_analysis'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing characteristic roots, persistence, half-life, and stability status to the console.

Print method for ma_stationarity_tests

Description

Print method for ma_stationarity_tests

Usage

## S3 method for class 'ma_stationarity_tests'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing ADF, Phillips-Perron, KPSS, and DF-GLS test results to the console.

Print method for ma_structural_break

Description

Print method for ma_structural_break

Usage

## S3 method for class 'ma_structural_break'
print(x, ...)

Arguments

Value

The input object x, invisibly. Called for its side effect of printing structural break test results to the console.