Methodological Advances and Empirical Applications in Official Time Series

The paper develops and applies a new method for computing a cost of living index (COLI) based on an estimated generalized constant-elasticity-of-substitution utility function (GCESUF) that has 4 main desirable features: (i) GCES/COLI is developed formally using economic reasoning, mathematics, and econometrics; (ii) GCESUF maps one-to-one to a translog utility function (TLUF) and, therefore, accounts similarly for consumer responses to changed prices and expenditures as a TLUF while generally being nonhomothetic; (iii) GCES/COLI accounts implicitly for changes in preferences for goods for any reasons, including changes in qualities of goods, so that hedonic adjustment of prices of goods for changes in qualities of goods is unnecessary and unwarranted; (iv) GCES/COLI is practically applicable to many goods, like the thousands of goods in the U.S. Consumer Price Index of Urban Consumers (CPIU). 

Time series data with non-integer seasonal periodicities (e.g., weekly series, which would have a seasonal period of approximately 52.18) present modelling challenges; standard seasonal differencing operators are designed for an even division of the year, and as such, may not adequately stabilize series that fall outside this paradigm.  We develop a non-integer differencing operator that can overcome this limitation.  We do so by first determining the specific frequencies for removal and then reverse engineering the differencing operator that can achieve this.  We examine the mathematical properties of our proposed differencing operator and demonstrate its effectiveness in signal extraction and seasonal adjustment for weekly time series via some practical applications. 

Weekly economic and administrative time series often contain localized calendar effects that are not well represented by smooth annual seasonality. We propose a dynamic holiday-loading model that separates the geometry of a recurring calendar effect from its year-specific magnitude. The geometry is represented by compactly supported loading functions that describe the timing, duration, and shape of each holiday response, while the corresponding annual intensities evolve across years through parsimonious stochastic models. The framework accommodates multiple calendar effects, including effects whose windows overlap in time, and reduces to a standard dynamic regression model once the loading functions are fixed. Estimation is based on a marginal Gaussian likelihood profiled over candidate loading windows. Simulation experiments are designed to evaluate bandwidth recovery for single and multiple holiday effects, sensitivity to kernel misspecification, and the impact of overlapping holiday windows. The method is applied to weekly U.S. Business Formation Statistics data, where it identifies distinct turn-of-year and Thanksgiving effects that are not captured by a smooth seasonal baseline. 

Respondents to the U.S. Decennial Census and related surveys are classified into hundreds of detailed occupation categories. The classification systems change periodically, creating breaks in time series. Researchers may want a unified occupation category set to extend for a long time period, to study the effects of technological change, for example. Standard crosswalks and unified category systems from IPUMS and other researchers accomplish this, but they reclassify the data coarsely, based only on the original occupation category. In theory they could make more use of particular "dual-coded" data sets in which specialists have applied multiple category systems based on more of the respondent attributes, such as their industry of work, age, income, and geographic location. Modern machine learning tools can do this on a large scale to impute occupations to millions of observations. Meyer and Asher (2021) applied random forest methods to accomplish this on an experimental scale. We extend the methods of Meyer and Asher (2021) to cover employed persons in the Population Census and Current Population Survey from 1970 to 2024, assigning best-matching 1990 Census occupations on the basis of several variables. We compare the assignments to earlier systems (e.g. IPUMS's occ1990) to see what changes the new method induced, and test the resulting distributions of occupations for how well they match known trends and how much the resulting occupation categories jump in size or attributes when the classification systems changed. 

We explore different parameterization of spectral matrices of multiple time series. with given. marginal spectral densities. Such spectral copula models are useful in multiple time series modeling when marginal. univariate specification is available for some or all of the coordinate processes. The models. involve. parameterizing the coherence.s and novel. parameterization of. the matrix function honoring the natural constraints are investigated. Estimation under the new parameterization is. also investigated and the benefits illustrated with numerical examples.