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The MAARTS (Merger and Acquisition Autoregressive Time-Series Models) package provides a comprehensive framework for analyzing M&A time-series data using autoregressive models. This vignette demonstrates the key features and functionality of the package.
# Install from local directory
install.packages("path/to/MAARTS", repos = NULL, type = "source")library(MAARTS)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zooThe package includes a sample M&A time-series dataset for demonstration:
data(ma_sample_data)
head(ma_sample_data)## Qtr1 Qtr2 Qtr3 Qtr4
## 2000 12.34568 13.21457 14.12346 13.87654
## 2001 14.54321 15.23457plot(ma_sample_data, type = "l", main = "Sample M&A Time-Series",
xlab = "Time", ylab = "M&A Activity")
Calculate comprehensive descriptive statistics:
desc_stats <- ma_descriptive_stats(ma_sample_data)
print(desc_stats)## Descriptive Statistics for M&A Time-Series
## ===========================================
## Sample Size: 200
## Mean: 49.917
## Sum: 9983.404
## Variance: 459.8718
## Standard Deviation: 21.4446
## Standard Error (Mean): 1.5164
## Minimum: 12.3457
## Maximum: 86.7654
## Range: 74.4198
## Q1 (25%): 31.5432
## Median (50%): 49.8888
## Q3 (75%): 68.3827
## IQR: 36.8395
## MAD: 27.5105
## Skewness: -0.0013
## Kurtosis: 1.8017
## Coeff. of Variation: 42.9605%
##
## Normality Diagnostic Tests
## --------------------------
## Shapiro-Wilk W: 0.9551 (p-value: 0) [Non-normal]
## Jarque-Bera X-sq: 11.9658 (p-value: 0.0025) [Non-normal]
## Anderson-Darling A: 2.1806 (p-value: 0) [Non-normal]
## Cramer-von Mises W-sq:0.2984 (p-value: 3e-04)
## Pearson chi-square: 23.89 (p-value: 0.0472)
## Shapiro-Francia W': 0.9601 (p-value: 1e-04)
## Overall Conclusion: Strong evidence against normality (all p-values < 0.05)Perform stationarity tests to ensure the time-series is suitable for AR modeling:
stationarity <- ma_stationarity_tests(ma_sample_data)## Warning in tseries::adf.test(ts_y, alternative = "stationary"): p-value smaller
## than printed p-value## Warning in tseries::pp.test(ts_y, alternative = "stationary"): p-value smaller
## than printed p-valueprint(stationarity)## Stationarity Tests for M&A Time-Series
## ======================================
##
## Augmented Dickey-Fuller (ADF) Test
## ----------------------------------
## Statistic: -7.0156
## P-value: 0.01
## Interpretation: Reject null: Series is stationary
##
## Phillips-Perron (PP) Test
## -------------------------
## Statistic: -235.4583
## P-value: 0.01
## Interpretation: Reject null: Series is stationary
##
## KPSS Test
## ---------
## Statistic: 4.0989
## Critical Values: 10%= 0.347 , 5%= 0.463 , 1%= 0.739
## Interpretation: Reject null: Series is non-stationary
##
## DF-GLS Test
## -----------
## Statistic: 0.2847
## Critical Values: 10%= -1.62 , 5%= -1.94 , 1%= -2.58
## Interpretation: Fail to reject null: Series is non-stationary
##
## Overall Summary: Moderate evidence for stationarity (ADF and PP support stationarity, KPSS disagrees)Examine autocorrelation structure to determine appropriate AR order:
acf_pacf <- ma_acf_pacf(ma_sample_data, plot = TRUE)
print(acf_pacf)## ACF and PACF Analysis for M&A Time-Series
## ==========================================
##
## Sample size: 200
## Max lag: 23.0103
## 95% significance bound: +/- 0.1386
##
## Significant ACF lags: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
## Significant PACF lags: 1
## Suggested AR order: 1Fit an AR model to the data:
ar_model <- ma_ar_fit(ma_sample_data, order = 2)
print(ar_model)## AR Model Fit for M&A Time-Series
## ================================
## Order: 2
## Method: OLS
## Sample Size: 200
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## [1,] 0.5050 0.05793 8.717 1.177e-15
## [2,] 0.4946 0.05829 8.486 5.102e-15
##
## Intercept: 49.917
## Variance of Prediction: 0.1444
##
## Information Criteria:
## AIC: 184.7332
## BIC: 194.598
## HQIC: 188.7261
##
## Model Stability:
## Stable: TRUE
## Persistence: 0.9996
## F-statistic: 302482.2
## F-pvalue: 0Generate forecasts with multiple confidence intervals:
forecast <- ma_forecast(ar_model, h = 12, confidence = c(0.80, 0.90, 0.95, 0.99))
print(forecast)## Forecast for M&A AR Time-Series
## ================================
## Forecast Horizon: 12
##
## Point Forecasts and Confidence Intervals:
## Period 1: 136.3167 (SE = 0.3800) CI_80% [135.8297, 136.8037] CI_90% [135.6917, 136.9418] CI_95% [135.5719, 137.0615] CI_99% [135.3379, 137.2955]
## Period 2: 161.6674 (SE = 0.4257) CI_80% [161.1219, 162.2130] CI_90% [160.9672, 162.3676] CI_95% [160.8331, 162.5018] CI_99% [160.5709, 162.7639]
## Period 3: 198.9781 (SE = 0.5122) CI_80% [198.3216, 199.6345] CI_90% [198.1356, 199.8206] CI_95% [197.9742, 199.9820] CI_99% [197.6587, 200.2974]
## Period 4: 230.3574 (SE = 0.5651) CI_80% [229.6332, 231.0817] CI_90% [229.4279, 231.2870] CI_95% [229.2498, 231.4650] CI_99% [228.9018, 231.8131]
## Period 5: 264.6576 (SE = 0.6227) CI_80% [263.8596, 265.4556] CI_90% [263.6334, 265.6818] CI_95% [263.4372, 265.8780] CI_99% [263.0537, 266.2615]
## Period 6: 297.4988 (SE = 0.6710) CI_80% [296.6389, 298.3588] CI_90% [296.3951, 298.6026] CI_95% [296.1837, 298.8140] CI_99% [295.7704, 299.2273]
## Period 7: 331.0481 (SE = 0.7181) CI_80% [330.1279, 331.9683] CI_90% [329.8670, 332.2292] CI_95% [329.6407, 332.4555] CI_99% [329.1985, 332.8977]
## Period 8: 364.2332 (SE = 0.7613) CI_80% [363.2577, 365.2088] CI_90% [362.9811, 365.4854] CI_95% [362.7412, 365.7253] CI_99% [362.2724, 366.1941]
## Period 9: 397.5847 (SE = 0.8025) CI_80% [396.5562, 398.6132] CI_90% [396.2647, 398.9048] CI_95% [396.0118, 399.1577] CI_99% [395.5175, 399.6519]
## Period 10: 430.8401 (SE = 0.8416) CI_80% [429.7616, 431.9186] CI_90% [429.4558, 432.2244] CI_95% [429.1907, 432.4896] CI_99% [428.6724, 433.0079]
## Period 11: 464.1292 (SE = 0.8790) CI_80% [463.0028, 465.2557] CI_90% [462.6835, 465.5750] CI_95% [462.4065, 465.8520] CI_99% [461.8652, 466.3933]
## Period 12: 497.3879 (SE = 0.9147) CI_80% [496.2156, 498.5602] CI_90% [495.8833, 498.8925] CI_95% [495.5950, 499.1807] CI_99% [495.0317, 499.7441]plot(forecast)
Check for residual autocorrelation:
diagnostics <- ma_diagnostic_tests(ar_model)
print(diagnostics)## Diagnostic Tests for M&A AR Model Residuals
## ============================================
##
## Number of residuals: 198
## Model order (fitdf): 2
##
## Ljung-Box Test
## --------------
## Lag 6: Q = 578.8614, df = 4, p-value = 0.0000 [Significant autocorrelation detected]
## Lag 12: Q = 1140.4877, df = 10, p-value = 0.0000 [Significant autocorrelation detected]
## Lag 18: Q = 1684.3114, df = 16, p-value = 0.0000 [Significant autocorrelation detected]
## Lag 24: Q = 2210.3785, df = 22, p-value = 0.0000 [Significant autocorrelation detected]
##
## Box-Pierce Test
## ---------------
## Lag 6: Q = 561.5396, df = 4, p-value = 0.0000 [Significant autocorrelation detected]
## Lag 12: Q = 1089.5213, df = 10, p-value = 0.0000 [Significant autocorrelation detected]
## Lag 18: Q = 1584.4539, df = 16, p-value = 0.0000 [Significant autocorrelation detected]
## Lag 24: Q = 2047.4461, df = 22, p-value = 0.0000 [Significant autocorrelation detected]Comprehensive residual analysis including normality and heteroscedasticity tests:
resid_diag <- ma_residual_diagnostics(ar_model, plot = FALSE)## Warning in nortest::cvm.test(data): p-value is smaller than 7.37e-10, cannot be
## computed more accuratelyprint(resid_diag)## Residual Diagnostics for M&A AR Model
## ======================================
##
## Residual Summary Statistics:
## Mean: 0
## Std Dev: 0.381
## Min: -0.475
## Max: 0.7677
## Skewness: 0.0567
## Kurtosis: 1.5363
##
## Normality Tests on Residuals:
## Shapiro-Wilk: p = 0 [ Non-normal ]
## Jarque-Bera: p = 1e-04 [ Non-normal ]
## Anderson-Darling: p = 0 [ Non-normal ]
## Conclusion: Strong evidence against normality (all p-values < 0.05)
##
## Heteroscedasticity Tests:
## Breusch-Pagan: stat = NA , p = NA [ Heteroscedasticity detected ]
## ARCH LM: stat = 192.9985 , p = 0 [ ARCH effects detected ]Analyze model stability and persistence:
stability <- ma_stability_analysis(ar_model)
print(stability)## Stability Analysis for M&A AR Model
## ====================================
##
## AR Order: 2
##
## Characteristic Roots:
## Root 1: 1.0003 + -0.0000i (modulus = 1.0003)
## Root 2: -2.0211 + 0.0000i (modulus = 2.0211)
##
## All roots outside unit circle: TRUE
## Model is: STABLE (stationary)
##
## Persistence (sum of AR coefficients): 0.9996
## Mean Reversion Speed: 4e-04
## Half-life of shocks: 2499.1 periods
## Long-run Mean: 120418.1Analyze shock transmission and dynamic effects:
irf <- ma_impulse_response(ar_model, n_periods = 20, plot = FALSE)
print(irf)## Impulse Response Function for M&A AR Model
## ============================================
##
## Periods computed: 20
## Long-run multiplier: 2412.365
## Innovation std dev: 0.38
##
## IRF values (first 10 periods):
## Period IRF Cumulative
## 0 1.000000 1.000000
## 1 0.504950 1.504950
## 2 0.749610 2.254560
## 3 0.628282 2.882842
## 4 0.688035 3.570876
## 5 0.658194 4.229070
## 6 0.672681 4.901751
## 7 0.665236 5.566987
## 8 0.668643 6.235630
## 9 0.666681 6.902311Compare multiple AR models using information criteria:
ar1 <- ma_ar_fit(ma_sample_data, order = 1)
ar2 <- ma_ar_fit(ma_sample_data, order = 2)
ar3 <- ma_ar_fit(ma_sample_data, order = 3)
comparison <- ma_model_comparison(ar1, ar2, ar3)
print(comparison)## Model Comparison for M&A AR Models
## ===================================
##
## Model Order AIC BIC HQIC LogLik Sigma2
## Model_1 1 240.0 246.5 242.6 -117.98 0.191639
## Model_2 2 184.7 194.6 188.7 -89.37 0.144398
## Model_3 3 -780.7 -767.5 -775.4 394.33 0.001069
##
## Best Model by AIC: Model_3
## Best Model by BIC: Model_3
## Best Model by HQIC: Model_3Detect structural breaks in the time-series:
breaks <- ma_structural_break(ma_sample_data)
print(breaks)## Structural Break Analysis for M&A Time-Series
## ===============================================
##
## Bai-Perron Multiple Breakpoint Analysis
## Estimated breakpoints: 34, 68, 101, 134, 167
##
## CUSUM Test
## Statistic: 0.2522
## P-value: 1
## Result: No structural instabilityIdentify cyclical components in the frequency domain:
spectral <- ma_spectral_analysis(ma_sample_data, plot = FALSE)
print(spectral)## Spectral Analysis for M&A Time-Series
## =====================================
##
## Sample Size: 200
## Dominant Frequency: 0.335
## Dominant Period: 2.99 observationsEvaluate estimator performance using simulation:
set.seed(123)
sim_results <- ma_monte_carlo_simulation(
true_coefficients = c(0.6, -0.2),
intercept = 10,
n = 100,
n_sim = 500,
sigma = 2
)
print(sim_results)## Monte Carlo Simulation Results for M&A AR Model
## =================================================
##
## Simulations: 500 / 500 (successful)
## Sample size: 100
## Confidence level: 95 %
##
## Parameter Estimation Performance:
## Parameter True Mean_Est Bias MSE RMSE Coverage
## AR1 0.6 0.5851 -0.014939 0.008932 0.0945 0.868
## AR2 -0.2 -0.2012 -0.001157 0.005661 0.0752 0.954Calculate forecast accuracy measures:
# Create actual vs predicted for demonstration
actual <- ma_sample_data[1:150]
predicted <- ma_sample_data[2:151]
accuracy <- ma_accuracy(actual, predicted)
print(accuracy)## Forecast Accuracy Measures
## ==========================
## MSE: 0.332109
## RMSE: 0.5763
## MAE: 0.5377
## MAPE: 1.6428%
## SMAPE: 1.6248%
## MASE: 0.9964
## Theil's U: 1.0679
## R-squared: 0.9987
## Observations: 150A complete analysis workflow:
# 1. Load and examine data
data(ma_sample_data)
plot(ma_sample_data, type = "l", main = "M&A Time-Series")
# 2. Descriptive statistics
desc_stats <- ma_descriptive_stats(ma_sample_data)
# 3. Check stationarity
stationarity <- ma_stationarity_tests(ma_sample_data)## Warning in tseries::adf.test(ts_y, alternative = "stationary"): p-value smaller
## than printed p-value## Warning in tseries::pp.test(ts_y, alternative = "stationary"): p-value smaller
## than printed p-value# 4. Examine ACF/PACF
acf_pacf <- ma_acf_pacf(ma_sample_data, plot = FALSE)
# 5. Fit models of different orders
models <- list()
for (p in 1:4) {
models[[p]] <- ma_ar_fit(ma_sample_data, order = p)
}
# 6. Compare models
comparison <- do.call(ma_model_comparison, models)
print(comparison)## Model Comparison for M&A AR Models
## ===================================
##
## Model Order AIC BIC HQIC LogLik Sigma2
## Model_1 1 240.0 246.5 242.6 -117.98 1.916e-01
## Model_2 2 184.7 194.6 188.7 -89.37 1.444e-01
## Model_3 3 -780.7 -767.5 -775.4 394.33 1.069e-03
## Model_4 4 -1374.4 -1358.0 -1367.8 692.20 5.012e-05
##
## Best Model by AIC: Model_4
## Best Model by BIC: Model_4
## Best Model by HQIC: Model_4# 7. Select best model
best_model <- models[[comparison$Order[1]]]
# 8. Forecast
forecast <- ma_forecast(best_model, h = 12)
# 9. Diagnostics
diagnostics <- ma_diagnostic_tests(best_model)
resid_diag <- ma_residual_diagnostics(best_model, plot = FALSE)## Warning in nortest::cvm.test(data): p-value is smaller than 7.37e-10, cannot be
## computed more accurately# 10. Stability analysis
stability <- ma_stability_analysis(best_model)
# 11. Impulse response
irf <- ma_impulse_response(best_model, n_periods = 20, plot = FALSE)
# Summary
cat("\n=== Analysis Summary ===\n")##
## === Analysis Summary ===cat("Best Model: AR", comparison$Order[1], "\n")## Best Model: AR 1cat("AIC:", round(comparison$AIC[1], 4), "\n")## AIC: 239.9612cat("BIC:", round(comparison$BIC[1], 4), "\n")## BIC: 246.5478cat("Stable:", stability$is_stable, "\n")## Stable: TRUEcat("Persistence:", round(stability$persistence, 4), "\n")## Persistence: 0.9995The MAARTS package provides a comprehensive toolkit for M&A time-series analysis. All major aspects of AR modeling are covered, from descriptive statistics and stationarity testing to forecasting and advanced diagnostic analysis.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.