  Time series classification using novel techniques has experienced a recent
resurgence and growing interest from statisticians, subject-domain scientists,
and decision makers in business and industry. This is primarily due to the ever
increasing amount of big and complex data produced as a result of technological
advances. A motivating example is that of Google trends data, which exhibit
highly nonlinear behavior. Although a rich literature exists for addressing
this problem, existing approaches mostly rely on first and second order
properties of the time series, since they typically assume linearity of the
underlying process. Often, these are inadequate for effective classification of
nonlinear time series data such as Google Trends data. Given these
methodological deficiencies and the abundance of nonlinear time series that
persist among real-world phenomena, we introduce an approach that merges higher
order spectral analysis (HOSA) with deep convolutional neural networks (CNNs)
for classifying time series. The effectiveness of our approach is illustrated
using simulated data and two motivating industry examples that involve Google
trends data and electronic device energy consumption data.
