Graduation Year
2024
Document Type
Thesis
Degree
M.A.
Degree Name
Master of Arts (M.A.)
Degree Granting Department
Mathematics and Statistics
Major Professor
Jiwoong Kim, Ph.D.
Committee Member
Seung-Yeop Lee, Ph.D.
Committee Member
Lu Lu, Ph.D.
Keywords
Generalized linear model(GLM), Markov chain Monte Carlo(MCMC), Frequency domain, Spectral density, Recurrent Neural Network(RNN)
Abstract
This study presents a comparative analysis of contemporary applications of time series models, focusing on the Bayesian approach. In contrast to many nonparametric studies, the Bayesian approach circumvents the common issue of bandwidth selection by offering systematic estimation and avoiding ad hoc methods. Specifically, we delve into the Bayesian approach for estimating the autocovariance function of a time series model’s error term. Traditional time series models often make the unrealistic assumption of a constant error term. Furthermore, models such as autoregressive conditional heteroskedasticity (ARCH) and general autoregressive conditional heteroskedasticity (GARCH) address the limitation of constant variance by assuming an autoregressive error term. However, this may still fail to capture the actual error accurately. The Bayesian method overcomes these assumptions by leveraging actual sample data and employing the Markov Chain Monte Carlo (MCMC) method for parameter estimation. We elucidate the transformation of the time series error term into the frequency domain via spectral density. Spectral density, a population concept, is estimated using a periodogram with discrete Fourier transform. Utilizing sample data, we construct the periodogram in the frequency domain. Asymptotically, the periodogram follows an exponential distribution approximated by a mixture of five Gaussian distributions. This thesis thoroughly examines the Bayesian method and evaluates its efficacy using real-world time series data, such as exchange rates and stocks. Performance assessment involves comparing traditional time series autoregressive (AR) (1) models and machine learning recurrent neural network (RNN) models, which provide valuable reference points for analysis. The Bayesian model outperforms the AR model by effectively capturing and reflecting fluctuation patterns in the data. The Bayesian model's root mean squared error (RMSE) was consistently smaller than that of the AR(1) process. This indicates that the errors of the Bayesian method were smaller than those of AR(1), indicating superior performance of the Bayesian model compared to AR(1).
Scholar Commons Citation
Yang, Young Keun, "Comparative Analysis of Time Series Models on U.S. Stock and Exchange Rates: Bayesian Estimation of Time Series Error Term Model Versus Machine Learning Approaches" (2024). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/10265
