Long memory in consumer sentiment and consumer dollar purchasing power in the United States from 1978 to 2025

Among the available macroeconomic series, consumer expectations and price levels are two of the most closely tracked and studied series. Despite their high frequency, there is a wide range of descriptions of their time-series properties in the applied literature. This study uses the monthly values of the University of Michigan Index of Consumer Sentiment and the purchasing power of the consumer dollar, the latter series being the inverse of the CPI of all items for urban consumers, between January 1978 and March 2025. Inflation and general consumer confidence indicators are maintained as context series. The empirical strategy is designed to be unitary rather than a typical multivariate study. To produce the integer-order classification, the Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin procedures are augmented for explicit deterministic specifications, after which the order of persistence is estimated as a fractional differencing parameter for which the memory of each series resides along a continuum, rather than being categorized as stationary or non-stationary. Among the variables, the indices of consumer sentiment, purchasing power, and consumer confidence are first-order integrated, whereas inflation is level stationary. All three fractional estimates indicated values of consumer sentiment, purchasing power, and consumer confidence slightly below (or slightly above) 1, suggesting that their processes are non-stationary and can slowly recover toward their means rather than being permanently affected by shocks. The consumer price index is not easily differentiated from unit roots. This implies that purchasing power is the most mean-reverting among the mean-reverting series, contrary to most expectations, which hold that mean-reverting data have the longest memory. Each series was specifically characterized through the results. There is no relationship between the estimated sentiment levels and affordability conditions, nor is one asserted in this study.