MLPs without a skip layer are inherently stationary models, therefore, their forecasting performance is expected to be poor when applied to nonstaionary data, that is data in which the trend or variability in the data changes over time. If a skip layer is included, then the NN model accommodates for nonstationarity. However, nonstaionary models can show unstable and explosive behavior. In other words, it is recommended to include a skip layer in the neural network design in order to model time series data in which your input variables are the lag values of the response variable over time.
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I know Prof. Bala Bhaskaran & Dr. Rajan Saxena. I met them many times in conferences in Hyderabad and Faculty meets. I worked in ICFAI Business School Hyderabad for 4 years as a Professor - Statistics & Business Intelligence. My students at IBS Hyderabad are still in touch with me.
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