Monitoring a very frequently administered educational test with a relatively short history of stable operation imposes a number of challenges. Test scores usually vary by season, and the frequency of administration of such educational tests is also seasonal. Although it is important to react to unreasonable changes in the distributions of test scores in a timely fashion, it is not a simple matter to ascertain what sort of distribution is really unusual. Many commonly used approaches for seasonal adjustment are designed for time series with evenly spaced observations that span many years and, therefore, are inappropriate for data from such educational tests. Harmonic regression, a seasonal-adjustment method, can be useful in monitoring scale stability when the number of years available is limited and when the observations are unevenly spaced. Additional forms of adjustments can be included to account for variability in test scores due to different sources of population variations. To illustrate, real data are considered from an international language assessment.

Maintaining a stable score scale over time is critical for all standardized educational assessments. Traditional quality control tools and approaches for assessing scale drift either require special equating designs, or may be too time-consuming to be considered on a regular basis with an operational test that has a short time window between an administration and its score reporting. Thus, the traditional methods are not sufficient to catch unusual testing outcomes in a timely manner. This paper presents a new approach for score monitoring and assessment of scale drift. It involves quality control charts, model-based approaches, and time series techniques to accommodate the following needs of monitoring scale scores: continuous monitoring, adjustment of customary variations, identification of abrupt shifts, and assessment of autocorrelation. Performance of the methodologies is evaluated using manipulated data based on real responses from 71 administrations of a large-scale high-stakes language assessment.

Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits nonzero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

A seasonal commodity is one that either (1) is not available during certain seasons or (2) is always available but its prices or quantities fluctuate with the season or time of year. The existence of type-1 seasonal commodities in consumer preference functions means that the usual economic approach to index number theory cannot be applied to construct a short-term month-to-month or quarter-to-quarter consumer price index. We postulate various separability assumptions on intertemporal preferences that can be used to justify various seasonal index number formulas. One of our approaches leads to an index number solution to the problem of seasonal adjustment.

This paper studies the problems of measuring economic growth under conditions of high inflation. Traditional bilateral index number theory implicitly assumes that variations in the price of a commodity within a period can be ignored. To justify this assumption under conditions of high inflation, the accounting period must be shortened to a quarter, a month, or possibly a week. However, once the accounting period is less than a year, the problem of seasonal commodities is encountered; i.e., in some subannual periods, many seasonal commodities will be unavailable and hence the usual bilateral index number theory cannot be applied. The paper systematically reviews the problems of index number construction when there are seasonal commodities and high inflation. Various index number formulas are justified from the viewpoint of the economic approach to index number theory by making separability assumptions on consumers' intertemporal preferences. We find that accurate economic measurement under conditions of high inflation is very complex.