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We propose a covariance stationarity test for an otherwise dependent andpossibly globally non-stationary time series. We work in a generalized versionof the new setting in Jin, Wang and Wang (2015), who exploit Walsh (1923)functions in order to compare sub-sample covariances with the full samplecounterpart. They impose strict stationarity under the null, only considerlinear processes under either hypothesis in order to achieve a parametricestimator for an inverted high dimensional asymptotic covariance matrix, and donot consider any other orthonormal basis. Conversely, we work with a generalorthonormal basis under mild conditions that include Haar wavelet and Walshfunctions; and we allow for linear or nonlinear processes with possibly non-iidinnovations. This is important in macroeconomics and finance where nonlinearfeedback and random volatility occur in many settings. We completely sidestepasymptotic covariance matrix estimation and inversion by bootstrapping amax-correlation difference statistic, where the maximum is taken over thecorrelation lag $h$ and basis generated sub-sample counter $k$ (the number ofsystematic samples). We achieve a higher feasible rate of increase for themaximum lag and counter $\mathcal{H}_{T}$ and $\mathcal{K}_{T}$. Of particularnote, our test is capable of detecting breaks in variance, and distant, or verymild, deviations from stationarity.

A Global Wavelet Based Bootstrapped Test of Covariance Stationarity