Code For Data Path C:\Users\Documents\Ba3dx6113.txt Install

Code For 2data Path Cusers Documentsm Ba3dx6113txtinstall

Code for #2: data_path critical value lines, then: # 1. Conclude serial correlations # 2. Conclude ARCH effects # ACF & PACF of squared residuals - first lag removed par(mfcol = c(2, 1)) acf(ba.log.res^2, 25, xlim = c(1, 25), ylim = c(-0.2, 0.2)) pacf(ba.log.res^2, 25, ylim = c(-0.2, 0.2)) par(mfcol = c(1, 1)) #====================================== # Q3B #====================================== # Build a GARCH model with Gaussian innovations for the log return series # Perform model checking and write down the fitted model ba.log.m1 pnorm(ba.log.m2.tratio); ba.log.m2.pv #====================================== # Q3E #====================================== # Fit a GARCH-M model to the monthly log returns # Write down the fitted model # Is the risk premium statistically significant? ba.log.m3 pnorm(0.65823, lower.tail = F); ba.log.m3.pv #====================================== # Q3F #====================================== # Fit a TGARCH(1,1) model to the monthly log returns # Write down the fitted model # Is the leverage effect statistically significant? ba.log.m4 0 ba.log.m4.tratio

Paper For Above instruction

The provided script offers a comprehensive framework for analyzing financial return series, specifically focusing on the monthly returns of Boeing as captured in the dataset "m-ba3dx6113.txt." This analysis incorporates data handling, exploratory data analysis, and advanced volatility modeling, notably GARCH family models, which are pivotal in understanding and predicting financial market volatility. The sequence of steps reflects a methodical approach to time series econometrics, emphasizing model adequacy, residual diagnostics, and the significance of risk factors within the returns. This paper explicates each segment of the code, contextualizes the methodological choices, and discusses their implications in financial econometrics.

Introduction

Financial return series often exhibit characteristics such as volatility clustering, leptokurtosis, and leverage effects. Consequently, financial econometric modeling has increasingly relied on GARCH and its variants to capture the time-varying volatility inherent in these series. This script applies these models to the logarithmic returns of Boeing's stock prices, deploying a methodical strategy that begins with data importation and preprocessing, followed by exploratory analysis, hypothesis testing for serial correlation and ARCH effects, and culminates in the estimation of several sophisticated GARCH models with different innovation distributions.

Data Handling and Preliminary Analysis

The dataset is read into R using read.table(), with the working directory set accordingly. Returns are computed as the natural logarithm of the adjusted closing prices plus one, to stabilize variance and normalize the data. The summary statistics via basicStats() reveal properties like mean, variance, skewness, and kurtosis, elucidating the distribution’s shape. Plotting the series provides visual insights, such as volatility clustering or trends, which are common in financial time series. The ACF and PACF plots serve to identify initial autocorrelation patterns, guiding model specification.

Testing for Serial Correlation and ARCH Effects

An initial t-test evaluates whether the mean of the log returns differs from zero, a common hypothesis in finance reflecting the Efficient Market Hypothesis. Autocorrelation checks through ACF and Ljung-Box tests identify serial dependence. The analysis proceeds to testing for ARCH effects, crucial for GARCH modeling, by examining the squared residuals’ autocorrelations. Significant autocorrelations in squared returns suggest volatility clustering, justifying the use of GARCH models.

GARCH Model Estimation and Diagnostics

The script fits a basic Gaussian GARCH(1,1) model, reflects on residual diagnostics including QQ-plots and Shapiro-Wilk tests for normality, and examines residual autocorrelations. Such diagnostics assess whether the model adequately captures the data's volatility dynamics or whether alternative residual distributions might be warranted. Notably, residuals often deviate from normality in financial returns, prompting the use of non-normal innovations, such as skewed Student-t, which better accommodate heavy tails and asymmetry.

Advanced GARCH Variants and Model Comparison

The analysis progresses to fit GARCH models with skew-Student-t innovations, capturing both heavy tails and skewness characteristic of financial returns. Further, the model’s adequacy is re-evaluated via residual diagnostics. A significant skewness (or lack thereof) informs on the distributional assumptions about the innovations. The script also implements GARCH-M (volatility-in-mean) models to test whether higher volatility levels are associated with higher expected returns, capturing the risk-return tradeoff.

Leverage Effects with TGARCH

The final model fitted is the Threshold GARCH (TGARCH), allowing asymmetry in volatility responses to positive and negative shocks. This model captures the leverage effect often seen in equity returns, where negative information tends to increase volatility more than positive news. The significance of the leverage effect is tested via the gamma parameter, with inference based on t-statistics and p-values, confirming whether asymmetry improves volatility modeling.

Discussion and Implications

The empirical findings underscore the importance of flexible volatility models in capturing the complex behavior of financial returns. The rejection or acceptance of normality assumptions, presence of ARCH effects, and significance of skewness and leverage inform risk management strategies, derivative pricing, and portfolio optimization. Moreover, acknowledging deviations from normality and the existence of asymmetric volatility responses enhances the predictive accuracy of econometric models, thereby offering more robust tools for financial analysts and policymakers.

Conclusion

This analysis exemplifies the application of advanced econometric models to real-world financial data, emphasizing the necessity of thorough diagnostics and multiple model specifications. The progression from basic GARCH to asymmetric and distributionally flexible models reflects the evolving understanding of market volatility. Future research may incorporate leverage effects in multivariate frameworks or explore regime-switching models to better adapt to changing market conditions, further refining the modeling of financial risks.

References

• Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
• Bera, A., & Higgins, M. (1993). ARCH models: properties, estimation, and forecasting. Journal of Economic Surveys, 7(4), 305–366.
• Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (1988). A Generalized Autoregressive Conditional Heteroskedasticity Model with Time-Varying Variance Estimation. Journal of Econometrics, 44(1-2), 47–78.
• Franses, P. H. (1998). Modelling Financial Time Series. Cambridge University Press.
• Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.
• Jondeau, E., & Rockinger, M. (2003). Conditional volatility, skewness, and kurtosis: applications to the French CAC 40 index. Journal of Economic Dynamics & Control, 27(6), 891–918.
• Nelson, D. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347–370.
• Tsay, R. S. (2010). Analysis of Financial Time Series. Wiley Series in Probability and Statistics.
• Zhang, G., Pincus, M., & Serletis, A. (2002). Stock market volatility and the return–volatility relation. The Quarterly Review of Economics and Finance, 42(2), 339–352.
• Engle, R. F. (2002). Dynamic Conditional Correlation: A Further Generalization of the GARCH Model. Journal of Business & Economic Statistics, 20(3), 339–350.