Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
| Hi-index | 0.00 |
Sample means are perhaps the most commonly used statistics in data analysis. When the data points are independent, behavior of sample means is governed by the Law of Large Numbers. When the data are serial correlated, theoretical results of stationary stochastic processes are often used to describe the behavior of sample means. How do the sample mean behave when data are nonstationary (or nearly so) is yet to be discussed. In this paper, I give the limiting distribution of sample means when the processes are either nonstationary or nearly nonstationary. I also discuss why the conventional formula fails to provide adequate inference for sample means when the processes are nearly nonstationary.