In this paper, we have developed a Fama - French five factor model (FF5 model) from Fama & French (2015) by using concept of timevarying coefficient. For a data set, we have used monthly data form Kenneth R. French home page, it include Japan portfolios (classified by using size and book-to-market) and 5 factors from July 1990 to April 2020. The first analysis, we used Augmented Dickey-Fuller test (ADF test) for the stationary test, from the result, all Japan portfolios and 5 factors are stationary. Next analysis, we estimated a coefficient of Fama - French five factor model by using a generalized additive model with a thin-plate spline to create the time-varying coefficient Fama - French five factor model (TV-FF5 model). The benefit of this study is TV-FF5 model which can capture a different effect at different times of 5 factors but the traditional FF5 model can’t do it. From the result, we can show a time-varying coefficient in all factors and in all portfolios, for time-varying coefficients of Rm-Rf, SMB, and HML are significant for all Japan portfolios, time-varying coefficients of RMW are positively significant for SM, and SH portfolio and time-varying coefficients of CMA are significant for SM, SH, and BM portfolio.

In this paper, we propose the new time-varying coefficient GARCH-in-Mean model. The benefit of our model is to allow the risk-return parameter in the mean equation to vary over time. At the end of 2019 to the beginning of 2020, the world witnessed two shocking events: COVID-19 pandemic and 2020 oil price war. So, we decide to use the daily data from December 2, 2019 to May 29, 2020, which cover these two major events. The purpose of this study is to find the dynamic movement between risk and return in four major oil markets: Brent, West Texas Intermediate, Dubai, and Singapore Exchange, during COVID-19 pandemic and 2020 oil price war. For the European oil market, our model found a significant and positive risk-return relationship in Brent during March 26-April 21, 2020. For the North America oil market, our model found a significant positive risk return relationship in West Texas Intermediate (WTI) during March 12-May 8, 2020. For the Middle East oil market, we found a significant and positive risk-return relationship in Dubai during March 12-April 14, 2020. Lastly, for the South East Asia oil market, we found a significant positive risk return relationship in Singapore Exchange (SGX) from March 9-May 29, 2020.

In financial economics studies, the autoregressive model has been a workhorse for a long time. However, the model has a fixed value on every parameter and requires the stationarity assumptions. Time-varying coefficient autoregressive model that we use in this paper offers some desirable benefits over the traditional model such as the parameters are allowed to be varied over-time and can be applies to nonstationary financial data. This paper provides the Monte Carlo simulation studies which show that the model can capture the dynamic movement of parameters very well, even though, there are some sudden changes or jumps. For the daily data from January 1, 2015 to February 12, 2020, our paper provides the empirical studies that Thailand, Taiwan and Tokyo Stock market Index can be explained very well by the time-varying coefficient autoregressive model with lag order one while South Korea’s stock index can be explained by the model with lag order three. We show that the model can unveil the non-linear shape of the estimated mean. We employ GJR-GARCH in the condition variance equation and found the evidences that the negative shocks have more impact on market’s volatility than the positive shock in the case of South Korea and Tokyo.