Time series within fields such as finance and economics are often modelled using long memory processes. Alternative studies on the same data can suggest that series may actually contain a 'changepoint' (a point within the time series where the data generating process has changed). These models have been shown to have elements of similarity, such as within their spectrum. Without prior knowledge this leads to an ambiguity between these two models, meaning it is difficult to assess which model is most appropriate. We demonstrate that considering this problem in a time-varying environment using the time-varying spectrum removes this ambiguity. Using the wavelet spectrum, we then use a classification approach to determine the most appropriate model (long memory or changepoint). Simulation results are presented across a number of models followed by an application to stock cross-correlations and US inflation. The results indicate that the proposed classification outperforms an existing hypothesis testing approach on a number of models and performs comparatively across others.

Changepoint models are increasingly used to represent changes in the rate of warming in surface temperature records. On the opposite hand, a large body of literature has suggested long‐memory processes to characterize long‐term behavior in surface temperatures. While these two model representations provide different insights into the underlying mechanisms, they share similar spectrum properties that create “ambiguity” and challenge distinguishing between the two classes of models. This study aims to compare the two representations to explain temporal changes and variability in surface temperatures. To address this question, we extend a recently developed time‐varying spectral procedure and assess its accuracy through a synthetic series mimicking observed global monthly surface temperatures. We vary the length of the synthetic series to determine the number of observations needed to be able to accurately distinguish between changepoints and long‐memory models. We apply the approach to two gridded surface temperature data sets. Our findings unveil regions in the oceans where long‐memory is prevalent. These results imply that the presence of long‐memory in monthly sea surface temperatures may impact the significance of trends, and special attention should be given to the choice of model representing memory (short versus long) when assessing long‐term changes.

Life expectancy in the UK has increased since the 19th century. As of 2019, there are just under 12 million people in the UK aged 65 or over, with close to a quarter living by themselves. Thus, many families and carers are looking for new ways to improve the health and care of older people. Passive sensors such as infra-red motion and plug sensors have had success as a noninvasive way to help the older people. These provide a series of categorical sensor events throughout the day. Modeling this categorical dataset can help to understand and predict behavior. This article proposes a method to model the probability a sensor will trigger throughout the day for a household whilst accounting for the prior data and other sensors within the home. We present our results on a dataset from Howz, a company helping people to passively identify changes in their behavior over time.

Approximately one in five people will live to see their 100th birthday due to advancements in modern medicine and other factors. Over 65’s constitute 42% of elective admissions and 43% of emergency admissions to hospitals. Increasingly, people are turning to technology to help improve health and care of the elderly. There is mixed evidence of the success of wearables in older populations with a key barrier being adoption. In contrast, passive sensors such as infra-red motion and plug sensors have had more success. These passive sensors give us a sequence of categorical “trigger” events throughout the day. This paper proposes a method for detecting subtle changes in sequences while taking account of the natural day-to-day variability and differing numbers of “trigger” events per day.

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