Record linkage proposals involve a significant amount of initial analysis and discussion to develop a formal project contract. Information is provided to Statistics Canada so that project feasibility can be assessed before the formal record linkage application for approval can begin. To facilitate the experience through all project steps, applicants are encouraged to familiarize themselves with the requirements for approval, understand their data sources and what is needed for record linkage, as well as giving thought early on about desired outputs and data access protocols.

Here are some questions to consider before starting a record linkage project at Statistics Canada:

The purpose of the SDLE program is to facilitate pan-Canadian social and economic statistical research. It is a record linkage environment that:

• increases the relevance of existing Statistics Canada surveys without collecting new data (including maintaining the relevance of completed longitudinal surveys);
• substantially increases the use of administrative data;
• generates new information without additional data collection;
• maintains the highest privacy and data security standards; and
• promotes a standardized approach to record linkage processes and methods.

How it works

The SDLE is a highly secure environment that facilitates the creation of linked population data files for social analysis. It is not a large integrated data base.

At the core of the SDLE is a Derived Record Depository (DRD), essentially a national dynamic relational data base containing only basic personal identifiers. The DRD is created by linking selected Statistics Canada source index files^{Defintion 4} for the purpose of producing a list of unique individuals. These files are brought into the environment, processed and linked only once to the DRD. Each individual in the DRD is assigned an SDLE identifier. Some of the source index files used to build the DRD include tax records, vital statistics registration records (births and deaths), and immigrant data. Updates to these data files are linked to the DRD on an ongoing basis.

Only basic personal identifiers are stored in the DRD. Examples of personal identifiers stored in the DRD include surnames, given names, date of birth, sex, insurance numbers, parents' names, marital status, addresses (including postal codes), telephone numbers, immigration date, emigration date and date of death.

The paired SDLE identifiers and source index file record IDs resulting from the record linkage are stored in a Key Registry^{Defintion 2}. All source index files are linked to the DRD either probabilistically using a generalized software tool (G-Link) or deterministically using SAS scripts.

Deterministic record linkage involves matching records based on unique identifiers shared by both files. On the other hand, probabilistic record linkage works with non-unique identifiers (e.g. names, sex, date of birth and postal code) and estimates the likelihood that records are referring to the same entity.

Once a study requiring linked data has been defined and approved, the associated record IDs (extracted from the Key Registry) are used to find the individual records in the source data files^{Defintion 3}. Selected variables from these sources can then be integrated into a linked analysis file. This approach provides a virtual linkage environment that eliminates the need to build a large integrated data base.

Figure 1. Social Data Linkage Environment overview diagram

This bar graph shows Statistics Canada's budgetary authorities and expenditures, in thousands of dollars, as of June 30, 2014 and 2015:

• As at June 30, 2014
  • Net budgetary authorities: $379,555
  • Vote netting authority: $120,000
  • Total authority: $499,555
  • Net expenditures for the period ending June 30: $121,613
  • Year-to-date revenues spent from vote netting authority for the period ending June 30: $12,951
  • Total expenditures: $134,564

• As at June 30, 2015
  • Net budgetary authorities: $525,095
  • Vote netting authority: $120,000
  • Total authority: $645,095
  • Net expenditures for the period ending June 30: $127,586
  • Year-to-date revenues spent from vote netting authority for the period ending June 30: $5,955
  • Total expenditures: $133,541

Behind the data provides simple explanations of concepts found in Statistics Canada's The Daily. For more detailed information on methods, please consult the Standards, data sources and methods section.

• Canadian Economic News
• Population projections at Statistics Canada—Frequently asked questions
• Advance indicators—Frequently asked questions
• Seasonally adjusted data—Frequently asked questions
• The Integrated Business Statistics Program
• Real-time data tables
• Trend-cycle estimates—Frequently asked questions
• Variance and bias
• Field Crop Reporting Series
• Age-standardized Rates
• Bank of Canada's preferred measures of core inflation
• 2015 Canadian Community Health Survey—Nutrition – Questions and answers
• Other visuals

By Susie Fortier, Steve Matthews and Guy Gellatly, Statistics Canada

Statistics Canada releases graphical information on trend-cycle movements for several monthly economic indicators. Estimates of the trend-cycle are presented along with the seasonally adjusted data in selected charts in The Daily. The inclusion of trend-cycle information is intended to support the analysis and interpretation of the seasonally adjusted data.

This reference document provides information on trend-cycle data. It outlines basic concepts and definitions and discusses selected issues related to the use and interpretation of trend-cycle estimates. The document includes a specific example using data on monthly retail sales. Detailed information on the computation of the trend-cycle is also provided.

1. 1. What is the trend-cycle of a time series?

   Trend-cycle data represent a smoothed version of a seasonally adjusted time series. They provide information on longer-term movements, including changes in direction underlying the series.

   The trend-cycle is the combination of two distinct components:

   • The trend provides information on longer-term movements in the seasonally adjusted data series over several years.
   • The cycle is a sequence of smoother fluctuations around the longer-term trend in part characterized by alternating periods of expansion and contraction.

   Changes in trend-cycle data reflect the influence of factors that condition long-run movements in the economic indicator over time, along with fluctuations in economic activity associated with the business cycle. These two components, the trend and the cycle, are often paired together because of the difficulty involved in estimating them individually.

2. 2. What is the difference between a seasonally adjusted series and its trend-cycle?

   A seasonally adjusted data series is a series that has been modified to eliminate the effect of seasonal and calendar influences in order to facilitate comparisons of underlying conditions from period to period. Seasonally adjusted data series can also be defined as the combination of the trend-cycle and the irregular component of a time series.

   In much the same way as a seasonally adjusted series represents the raw series with seasonal and calendar effects removed, the trend-cycle estimates represent the seasonally adjusted series with the irregular component removed. As its name suggests, the irregular component is the part of the time series that is not in line with the usual or expected pattern of the series. This irregular component is not part of the trend-cycle, nor is it related to current seasonal factors or calendar effects.

   The irregular component of a time series can represent unanticipated economic events or shocks (for example, strikes, disruptions, natural disasters, unseasonable weather, etc.) or can simply arise from noise in the measurement of the unadjusted data. In some cases, this irregular component can make large contributions to the period-to-period movements in a seasonally adjusted time series.

   By removing this irregular component from seasonally adjusted data, the trend-cycle data can yield a better picture of longer-term movements in the time series. In this sense, the trend-cycle can be interpreted as a smoothed version of the seasonally adjusted series.

3. 3. What can we learn from trend-cycles?

   Trend-cycle data provide information on longer-term movements in a seasonally adjusted time series, including changes in the direction of the data. These smoothed data make it easier to identify periods of positive change (growth) or negative change (decline) in the time series, as the noise of the irregular component has been removed. This allows for a more accurate identification of turning points in the data.

   For example, the accompanying graph presents data on monthly retail sales in Canada from July 2010 to July 2015. Two data lines are shown: the seasonally adjusted time series and the trend-cycle estimates. The trend-cycle estimates for the most recent reference months are more subject to revision than the estimates for previous periods, and are presented as a dotted line (see question 5).

   While the seasonally adjusted data can be used to examine basic changes in the direction of the time series, it is easier to see the longer term movement in these data from the trend-cycle line. The trend-cycle estimates show that retail sales trended upward at a relatively constant rate during 2010 and 2011, and then slowed in 2012. Growth resumed from late 2012 until mid-2014, before sales trended downward in late 2014. Trend-cycle data for early 2015 indicated a return to growth. Estimates for this most recent period are based on a preliminary estimation of the trend-cycle and should be interpreted with caution as they are subject to revision as noted above.

   Figure 1 — Retail sales

   

   Trend-cycle data are particularly useful when the irregular component makes large contributions to the month-to-month movements in a seasonally adjusted time series. In these cases, graphical information on the trend-cycle helps to interpret the movements in the seasonally adjusted series.

4. 4. Why are trend-cycle data revised?

   Existing estimates of the trend-cycle are revised with each release of new seasonally adjusted data. As new seasonally adjusted data becomes available, the trend-cycle data for previous months can be better estimated. If the trend-cycle data were not revised along with the seasonally adjusted series, the resulting trend-cycle data could contain series breaks, and would likely be inconsistent with the seasonally adjusted series in terms of levels, period-to-period movements, or both. It is necessary to revise the trend-cycle data to maintain their analytical value.

5. 5. Why is the trend-cycle line dotted for the most recent reference months?

   The trend-cycle line that is published graphically is dotted in the most recent reference periods, as these periods are more likely to be subject to revisions. This is done to signal that the trend-cycle data in this period is a preliminary estimate, and subject to change as new data becomes available. New data make it possible to more accurately estimate the various components that make up the time series. These revisions can change the location of economic turning points, as well as reverse movements between individual months. These types of revisions are more likely to occur in the most recent reference months.

6. 6. Can the trend-cycle be interpreted as a means of forecasting data for future reference periods?

   The trend-cycle should not be viewed as a way to forecast the underlying seasonally adjusted data. These estimates are based solely on the historical values of the seasonally adjusted series and do not take into account any other information that could be used to project data for future reference periods. Furthermore, since the trend-cycle is subject to revision when additional reference periods are added to the series, the shape of the trend-cycle in the most recent reference periods should be viewed as a preliminary estimate.

7. 7. What methods can be used to estimate the trend-cycle series?

   There is no unique method that is recommended to estimate the trend-cycle that underlies a time series. A variety of methods have been developed in the literature, ranging from very simple to highly complex. Some methods introduce restrictions on the shape of the trend (for example a linear trend of several years), others are based on explicit models that estimate a trend-cycle component, and others, still, are based on variations of moving averages, where the mean of the data is calculated from successive sub spans or intervals of the data.

   Since the trend-cycle can also be interpreted as a smoothed version of the seasonally adjusted series, a straightforward way of estimating the trend-cycle is by averaging the last three or six months of the data. While this may yield additional insight into the long-term movement in the series, some measure of caution is warranted as this approach does not take the place of more formal trend-cycle estimation techniques. It can be shown that indicators of the economic cycle derived from this simplified method tend to shift in time and may be artificially dampened.

8. 8. How does Statistics Canada estimate the trend-cycle series?

   Statistics Canada uses a weighted moving average of the data to compute the trend-cycle. This method is based on the Cascade Linear Filter of Dagum and Luati (2008). This weighted average is computed using the previous six months, the current month and (for older estimates) up to six of the subsequent months in the series. In real time, for the most recent reference month in the series, only data for the six previous months and current month are used, as data for subsequent months are not yet known. As these data become available, the trend-cycle estimates will be revised.

   This specific weighted moving average method was selected after an empirical analysis of different alternatives. The estimate of the trend-cycle obtained with the selected method exhibits good statistical properties, as it provides smooth results with limited revisions, and has a low incidence of falsely identifying turning points. As well, it is a linear process and will preserve additive relationship in the data. This implies, for example, that the trend-cycle plotted on employment for men and women separately will sum up to the plotted trend-cycle line for both sexes. The method is easy to replicate as the weights used in the calculation of the weighted average are available.

9. 9. How does the trend-cycle method work in a more technical sense?

   The trend-cycle is estimated by applying moving averages weighted according to the cascade linear filter to the seasonally adjusted series. In general, the moving average used to calculate the trend-cycle for a specific reference month is a weighted average of up to 13 consecutive months, which are centered on the reference month, where possible.

   For more information on the calculation of trend-cycle estimates, please consult Details on calculation of trend-cycle estimates at Statistics Canada.

10. 10. How can I learn more about this topic?

    The following references provide more information on the topic of seasonal adjustment, including trend-cycle estimation.

    Dagum, E. B. and Luati, A. 2008. "A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation," Econometric Reviews. 28:1-3, 40-59.

    Statistics Canada. 2014. "Seasonally Adjusted Data — Frequently asked questions," Behind the data.

    Statistics Canada. 2009. "Seasonal adjustment and trend-cycle estimation," Statistics Canada Quality Guidelines. 5th edition. Catalogue no. 12-539-X.