A Parameter Estimation of Fractional Order Multivariate Grey Model with Time-delay Based on Adaptive Dynamic Cat Swarm Optimization

In order to reduce the time-delay impact of different factors on some grey systems, we firstly add multiple time delay values in the multivariate grey model and promote it to fractional order for getting better prediction accuracy. As the parameters involved are large and complex, we utilize grey correlation analysis to estimate the time-delay values and adaptive dynamic cat swarm optimization(ADCSO) to estimate the other parameters of the model. The main method is organized as follow. Firstly, use the data of the total domestic tourism revenue and consumption levels of urban and rural residents in China from 2006 to 2014 to train the model to obtain the parameters and then use the data of 2015 to 2017 to test the accuracy of the grey model. Secondly, simulate and analyze the four multivariate grey models: integer order models with and without time-delay, and fractional order models with and without time-delay. The comparison results show that the models with time-delay perform much better than those without time-delay, and the fractional-order models can produce more accurate prediction values than integral-order models under the same condition.