Unbiased Estimation Of Autocovariance Function Of A Univariate Time Series With Unknown Mean And Its Application

This proposal refers to an unbiased estimator for the autocovariance function of time series,and we first focus on univariate time series with unknown mean.This estimator is a linear function of the usual sample autocovariances,and is obtained by using the demeaned sequence.In the method,we first stack the usual sample autocovariances into a vector,and its expectation just happens to be a linear combination of the population autocovariances.The weights of these linear combinations can be summarized into a matrix,and hence the name of A matrix.When the true autocovariance functions are zero or near to zero at large lags,we can obtain the exactly unbiased or nearly unbiased estimation of the rest.The A-matrix estimator is approximately equivalent to the commonly used sample autocovariance estimators.The simulation results obtained by previous researchers show that the A-matrix estimator can fully reduce the bias and keep MSE not increasing.This proposal gets the results of the A-matrix estimator when it is applied to real data,and we analyze the estimation effects of A-matrix estimator and discuss whether it can be promoted in practical applications.This paper selects several real data from January 2013 to December 2017,and uses the ARIMA model to construct the time series model.We use the A-matrix estimator to estimate the autocovariance function,and the estimation result is compared with the estimation results of two commonly used standard autocovariance function estimators.Based on the previous simulation results of A-matrix estimator,we can find that when there is no AR component in the time series model,that is,when the model is a MA model,and when the estimated step size is small,we can choose the A-matrix estimator to estimate the autocovariance function.In summary,the A-matrix estimator can be applied to practice on certain conditions.If it can be modified and perfected in the future study,we may get an unbiased estimator that can replace the commonly used standard estimators of the autocovariance function.This is of great significance for both the future time series research and the practical applications.The innovations of this paper are as follows:The A-matrix estimator has been proposed recently.It has not been used in real data.Only numerical simulation has been performed.In this paper,we apply the A-matrix estimator to real data,and obtain the estimation effects of the A-matrix estimator when it is applied to real data.