Measuring Trends and Cycles in Homeless Shelter Stays

The causes of homelessness are many and complex. Some are to be found in the personal vulnerabilities of people experiencing homelessness. These include problems of mental health, issues of substance abuse, adverse childhood experiences, relationship breakups and exogenous health events affecting oneself or family members. Still other causes are to be found in the conditions of housing and labour markets, in degrees of prejudice and in seasonality. These many causes mean that a complicated interaction of multiple data-generating processes, which differ in their period, frequencies and degree of randomness, produce data on the number of people experiencing homelessness.

In recognition of the difficulty of modelling the myriad behaviours and choices that lie behind many time series data, methods of time series decomposition that rely on few assumptions about underlying data-generating processes have been used to identify basic characteristics of key variables. In their introduction of the application of time series decomposition to macroeconomic data, Hodrick and Prescott (1997) emphasized that the method relied only on a limited amount of knowledge that is well supported by economic theory. In their application of time series decomposition to understanding trends and cycles in GDP data, they relied only on the maintained hypothesis of economic growth theory that the trend in GDP data varies smoothly over time.

This paper investigates the feasibility of using the Hodrick-Prescott (HP) filter to identify trends and cycles in monthly data describing the use of homeless shelters in Calgary, Alberta. In this application, descriptions of how and why people experience homelessness that are well supported in the literature are relied upon to identify trends and cycles in that measure.