Autocorrelation for time series with linear trend

The autocorrelation function (ACF) is a fundamental concept in time series analysis including financial forecasting. In this note, we investigate the properties of the sample ACF for a time series with linear trend. In particular, we show that the sample ACF of the time series approaches 1 for all lags as the number of time steps increases. The theoretical results are supported by numerical experiments. Our result helps researchers better understand the ACF patterns and make correct ARMA selection.