Browsing by Subject "Dynamic linear model"

Financial stock market data, for various reasons, frequently contain missing values. One reason for this is that, because the markets close for holidays, daily stock prices are not always observed. This creates gaps in information, making it difficult to predict the following day’s stock prices. In this situation, information during the holiday can be “borrowed” from other countries’ stock market, since global stock prices tend to show similar movements and are in fact highly correlated. The main goal of this study is to combine stock index data from various markets around the world and develop an algorithm to impute the missing values in individual stock index using “information-sharing” between different time series. To develop imputation algorithm that accommodate time series-specific features, we take multiple imputation approach using dynamic linear model for time-series and panel data. This algorithm assumes ignorable missing data mechanism, as which missingness due to holiday. The posterior distributions of parameters, including missing values, is simulated using Monte Carlo Markov Chain (MCMC) methods and estimates from sets of draws are then combined using Rubin’s combination rule, rendering final inference of the data set. Specifically, we use the Gibbs sampler and Forward Filtering and Backward Sampling (FFBS) to simulate joint posterior distribution and posterior predictive distribution of latent variables and other parameters. A simulation study is conducted to check the validity and the performance of the algorithm using two error-based measurements: Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE). We compared the overall trend of imputed time series with complete data set, and inspected the in-sample predictability of the algorithm using Last Value Carried Forward (LVCF) method as a bench mark. The algorithm is applied to real stock price index data from US, Japan, Hong Kong, UK and Germany. From both of the simulation and the application, we concluded that the imputation algorithm performs well enough to achieve our original goal, predicting the stock price for the opening price after a holiday, outperforming the benchmark method. We believe this multiple imputation algorithm can be used in many applications that deal with time series with missing values such as financial and economic data and biomedical data.

This dissertation explores how consumers learn from repeated experiences with a product offering. It develops a new Bayesian consumer learning model, the unstable learning model. This model expands on existing models that explore learning when quality is stable, by considering when quality is changing. Further, the dissertation examines situations in which consumers may act as if quality is changing when it is stable or vice versa. This examination proceeds in two essays.

The first essay uses two experiments to examine how consumers learn when product quality is stable or changing. By collecting repeated measures of expectation data and experiences, more information enables estimation to discriminate between stable and unstable learning. The key conclusions are that (1) most consumers act as if quality is unstable, even when it is stable, and (2) consumers respond to the environment they face, adjusting their learning in the correct direction. These conclusions have important implications for the formation and value of brand equity.

Based on the conclusions of this first essay, the second essay develops a choice model of consumer learning when consumers believe quality is changing, even though it is not. A Monte Carlo experiment tests the efficacy of this model versus the standard model. The key conclusion is that both models perform similarly well when the model assumptions match the way consumers actually learn, but with a mismatch the existing model is biased, while the new model continues to perform well. These biases could lead to suboptimal branding decisions.