A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Application

In this paper, we propose a quick and efficient method to examine whether a time series ${X}_t$ possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting ${X}_t$ with a linear model. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of the variable being examined. Another advantage of our proposed test is that there is no over-rejection problem which exists in some famous nonlinearity tests. Our proposed test can also be used to test whether the hypothesized model, including linear and nonlinear, to the variable being examined is appropriate as long as the residuals of the model being used can be estimated. Our simulation study shows that our proposed test is stable and powerful. We apply our proposed statistic to test whether there is any nonlinear feature in the sunspot data. The conclusion drawn from our proposed test is consistent with those from other well-established tests.