Prediction of asynchronous impulsive noise volatility for indoor powerline communication systems using GARCH models

In this paper we will discuss the estimation of powerline communication (PLC) asynchronous impulsive noise volatility by studying the conditional variance of the noise time series residuals. In our approach, we use the Generalized Autoregressive Conditional Heteroskedastic (GARCH) models on the basis that in our observations, the noise time series residuals indicates heteroskedasticity. By performing an ordinary least squares (OLS) regression of the noise data, the empirical results show that the conditional variance process is highly persistent in the residuals. The variance of the error terms are not uniform, in fact, the error terms are larger at some portions of the data than at other time instances. Thus, PLC impulsive noise often exhibit volatility clustering where the noise time series is comprised of periods of high volatility followed by periods of high volatility and periods of low volatility followed by periods of low volatility. The burstiness of PLC impulsive noise is therefore not spread randomly across the time period, but instead has a degree of autocorrelation. This provides evidence of time-varying conditional second order moment of the noise time series. Based on these properties, the noise time series data is said to suffer from heteroskedasticity. Numerical results provide evidence that the proposed model is capable of providing an accurate stochastic representation of the impulsive noise in the 1-30MHz frequency band. The parameter estimates of the model indicates a high degree of persistence in conditional volatility of impulsive noise which is a strong evidence of explosive volatility.