GARCH及糢糊模型於配適與預測財務性時間序列之比較

Abstract

本篇論文著重於探討臺灣股市的非線性現象, 其中有幾點是我們有興趣想 瞭解的: (1) 股市日報酬率資料是否呈現隨機分佈? (2) GARCH或糢糊模 型何者可以解釋股市的結構? (3) GARCH、AR以及糢糊模型在短期預測股 市日報酬率上的比較。其中我們使用BDS統計值來偵測非線性結構的存在, 並嘗試以GARCH及模糊模型來配適及預測臺灣股市的日報酬率。從結果中 發現股市資料並非以隨機分佈的方式存在,同時GARCH及模糊模型均能部分 解釋股市資料,但是模糊模型在預測方面明顯優於GARCH模型。 This thesis studies the stock returns behavior of an attractively emerging East Asian stock market--Taiwan Stock Market in order to construct a realistic model which can generate the stock returns: (1)distribution of stock returns-- do they follow a normal distribution, or can they be modeled as linear white-noise processes? (2) stochastic or structural character of stock returns--or specifically, can a Generalized Autoregressive Conditional Heteroskedastic (GARCH) or a deterministic chaos model adequately explain the generating of the process of stock returns? (3) the forecasting performance of various models--we evaluate Autoregressive (AR), GARCH, and fuzzy models and decide which one is better. In Taiwan Stock Market, whether there exists chaotic structure in the behavior of daily stock returns is examined empirically by using the correlation dimension technique and performing the BDS test. For most of the data, the estimated correlation dimensions are not close to the embedding dimension and are higher for the residuals than the original data. This implies no evidence of low-dimension deterministic chaos for the daily stock returns. Although the GARCH model do remove some of the serial dependence and reduce the observed leptokurtosis fairly for certain cases, the results of the BDS test suggests that the GARCH model cannot precisely model the distribution of the daily stock returns in Taiwan Stock Markets. While, for almost half of the cases the standardized residuals from the fuzzy model are more close to an identical, distributed process than that from the GARCH model. Thus, using the fuzzy model, we may have a good chance to fit the daily stock returns better in the sense that the BDS test statistics are lower. However, for the stock returns of all cases, the fuzzy model does not appear to out-perform the GARCH model. Post-sample forecasts suggest that certain gain in forecasting accuracy can be realized by using the fuzzy model.