Determinism and non-linear behaviour in log-return and conditional volatility time series of the stock market index is examined for twenty-six countries. For this goal, the principal statistical techniques used in this study are a robust estimator of correlation dimension, a normalized non-linear prediction error, and pseudo-periodic surrogate data method. The proposed approach indicates, first, the stochastic behaviour of all log-return time series. Second, the inability of local linear, ARMA, or state- dependent noise models (such as ARCH, GARCH, and EGARCH) to describe its structure for the frontier, emerging, and developed markets. The same stochastic behaviour of conditional volatility time series, estimated by the stochastic volatility model with moving average innovations, is detected. This finding proves the efficiency of the stochastic volatility model compared with some analysed types of GARCH models for all studied markets.

JEL Classification: C12, C52, D53, E44

对26个国家/地区的股票指数的对数收益率和条件波动率时间序列中的确定性和非线性行为进行了检验。为此，本研究中使用的主要统计技术是相关维数的鲁棒估计器，归一化非线性预测误差和伪周期替代数据方法。所提出的方法首先表明了所有对数-返回时间序列的随机行为。其次，局部线性，ARMA或状态相关的噪声模型（例如ARCH，GARCH和EGARCH）无法描述前沿，新兴和发达市场的结构。可以检测到条件波动率时间序列的相同随机行为，该波动率是由随机波动率模型和移动平均创新估计的。

JEL分类： C12，C52，D53，E44