Time Series Analysis Using Gaussian Process

The Gaussian process (GP) regression model is applied for prediction of time series.The autoregressive model is used instead of time-driven model. We firstly introduce thesingle step prediction using GP and then extend it to multi-step prediction of time series.The connection between stationarity of kernel function of GP and that of time series underinvestigation is found that the GP with the stationary kernel function produces poor predic-tion results for non-stationary time series. The conventional GP model has to be modifiedto fit the non-GP time series, e.g. the famous autoregressive conditional heteroskedasticity(ARCH) series. A novel exponential ARCH model based on GP is introduced to investigatethe volatility of data. Numerical experiments show good performance of this model. Finallywe present a novel probabilistic method employing GP prior to deal with speech enhance-ment as well as voice activity detection. The computer simulations show better or at leastcomparative performance than conventional methods.