Modeling Time Series with Asymmetric Volatility and Long Memory

Time series modeling of the price of agricultural commodities has immense importance in the Indian agricultural landscape. Volatility is an intrinsic property of time series. If positive and negative shocks of the same scale have differing effects on it, it is said to be asymmetric. The volatility of any time series is said to have long-term persistence if, for any given time epoch, it is significantly influenced by its distant past counterpart. The fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroscedastic (FIEGARCH) model may be used to capture asymmetric volatility in any time series with long-term persistence. This paper uses the modal price series of onion for Delhi, Lasalgaon, and Bengaluru markets and S&P 500 index (close) data for empirical illustration. The GARCH, EGARCH, FIGARCH, and FIEGARCH models have been applied to the selected data sets. Significant asymmetric and long term persistence volatility in the selected time series has been found. It has been observed that the FIEGARCH model outperformed the other models in capturing volatility for all the selected time series.