Plan your calendar free and make sure you have plenty of party clothes in your closet, because chances are you’ll be invited to several weddings this year around summer. We’re talking about the famous catch-up weddings, weddings that have been postponed to the following year due to corona restrictions.

How do we know this? Using a time series analysis, we made a prediction of the expected number of marriages in 2020 and early 2021. However, the actual number of marriages that have taken place is lower. We suspect that these marriages have been postponed because of corona restrictions, which have prevented a large celebration for the past 1.5 years.

The CBS has been registering the daily number of marriages and registered partnerships in the Netherlands for more than 25 years. A number of trends are clearly visible in this data. Friday is, as expected, the most popular day to get married. Monday is still relatively often married, free of charge, making this day more popular than Tuesday and Wednesday.

**Number of marriages per day per year**

In addition, each year there is a distinct wedding season from May to June and late August to September. During this period, the number of weddings rises to as many as 400 per day. In the off-season, ‘only’ 100 to 150 ‘yeses’ are said each day.

It is also notable that marriages are declining in popularity. Since the year 2010 there is a downward trend in the number of marriages to see. Presumably, more and more Dutch people will opt for a registered partnership instead of marriage. The number of registered partnerships, on the other hand, shows an upward trend. Since 2010, the number of registered partnerships has more than doubled.

**Number of marriage ceremonies and registered partnerships as of 2010**

We all remember Maxima’s tearful wedding on 02-02-2002. The royal couple is not the only one with a preference for special wedding dates. Beautiful dates that fall within the wedding season and on weekends guarantee full wedding venues. For example, Friday 08-08-2008 was the most popular wedding day of the past 25 years with almost 3,000 weddings. Thursday 09-09-1999 also went into the books as popular with over 2,500 weddings. With over 1,500 more weddings on Friday 10-09-1999, this is the most popular wedding week of the past 25 years.

**Number of marriage closings per week from 1996**

For many people, a dream wedding includes the presence of family and friends. Due to the corona measures from March 2020, this picture fell apart for wedding couples. We ourselves were curious how much impact these measures would have on the number of weddings. The strong trends we saw in the data gave us confidence that by using a statistical model we could make a good prediction for the expected number of weddings in 2020 and 2021. By contrasting this with the actual weddings performed, we have an indication of the number of weddings that have been delayed and will hopefully be caught up in 2022.

To make a prediction of the number of expected marriages, we use statistical models. Based on past results, we try to make a statement for the future. Many standard statistical prediction methods assume that the data points (number of marriages on a day) are mutually independent. However, in the case of a time series, there is dependence between the data points. This is also called autocorrelation: a new data point is often a delayed copy of an earlier point. For example, the proportion of marriages on a Monday is relatively low, and more people get married just before or after the summer. Because this dependency between data points exists in the data, methods that take it into account are needed. In this case, a time series model is a good method to model and make predictions.

Before we can start creating the model, we need to make sure that there are no more outliers in the data. Outliers include “nice” dates such as 20-05-2005 where the number of marriages is more than 3x higher than usual for the season. A week before or after, we do not expect so many marriages and therefore 20-05-2005 will distort our prediction and it is better to remove this outlier. As explained earlier, the number of marriage closings shows a trend throughout the year, but also within a week. Since this becomes very complex to model, we decided to calculate the total number of marriage closings per week and use this to estimate a statistical model.

There are several types of time series models, the most well-known being ARIMA. ARIMA stands for AutoRegressive Integrated Moving Average. This model looks at the value prior to the current data point (last week, the week before, etc.) and the deviation from the expected number. It also looks at whether there is a trend, for example, that over a long period of time fewer and fewer people are getting married.

A time series model tries to build the number of marriages from a trend and any noise. The data analyst’s job is to determine how many weeks you look back to predict this week.

The data must meet a number of conditions to use this model. We break down the number of marriages per week into a trend, seasonal effect, and any noise to control for these conditions.

**Breakdown of marriages by trend, seasonal effect and residual**

Following the total numbers, the second graph shows a predominantly decreasing trend in recent years. The next graph shows a clear seasonal pattern with the length of 1 year and the last graph shows the noise. This noise does not appear to contain a pattern and is uniformly distributed, meaning that the data is stationary. This is necessary to apply statistical models such as ARIMA. In addition to looking at these graphs, we perform two tests to confirm that the data is stationary.

Now that it is confirmed that the data is stationary, we can estimate an ARIMA model on the data. For this, we only use the data through 2018, so that we can use the model for the year 2019 to make a prediction of the expected number of marriages.

**Actual and predicted marriages with ARIMA**

The chart above shows these actual numbers and our 2019 forecast based on the ARIMA model. The percentage deviation between the forecast and actual numbers in 2019, the Mean Average Percentage Error (MAPE), is a measure of the accuracy of our forecast. With a MAPE of 12.4%, the forecast deviates from the actual numbers by an average of 12.4% and therefore we are not yet convinced that ARIMA is the best fit for our data.

Besides ARIMA, there are several other techniques that we can apply. The algorithm whose predictions have the smallest deviation (the lowest MAPE), is then the best choice. We will use this algorithm to predict how many marriages we would have expected in 2020 and 2021 (if there had been no corona). The algorithms we are trying in addition to ARIMA are; NBEATS, Prophet and Exponential Smoothing.

- Prophet is a technique developed by Facebook and takes into account a trend, seasonal effect and possibly holidays.
- NBEATS, Neural Basis Expansion Analysis for Interpretable Time Series, is a deep learning model that takes previous and future points into account.
- Exponential Smoothing is a technique that handles a trend and seasonal effects well. Like ARIMA, Exponential Smoothing looks at the number of marriages in the previous weeks, with data points that are further in the past given a lower weight and counted less heavily than data points closer in time.

More explanation of the models can be found here: NBEATS, Prophet and Exponential Smoothing.

All techniques have their strengths and weaknesses. Applying them all to predict marriages, we see that Exponential Smoothing works best for our data. This model only has a MAPE of 8.6% per week on the number of predicted marriage closings for 2019. Where as the other models have a variance between 9.6% and 12.4%.

The graph below shows the actual number of marriage closings along with the predictions and MAPE of the different techniques.

**Predictions and actual marriage closings 2019**

The 8.6% deviation is mainly in the September period where the number of marriage closings is higher than all the different models predicted based on the number of marriage closings in recent years. This high number is partly caused by several ‘nice dates’ in this month; Monday 9-9-2019 and Thursday 19-9-2019. We could not have predicted these outliers. As can be read here, a MAPE below 10% means that the model is very accurate.

We are satisfied with the Exponential Smoothing model and this gives us enough confidence to make a forecast of the expected number of marriage closings for 2020 and 2021 as well. Let’s call this the number of intended marriages. However, due to the outbreak of the pandemic and the associated measures, we know that the number of marriages has been different from the number of intended marriages.

The charts below show our forecast and the actual number of marriage closings by month through September 2021.

The graphs show that the actual number of marriages in the period March to August 2020 was lower than predicted, this is a difference of 28%. During this period there were severe restrictions due to corona on group sizes. We therefore expect this to be the explanation for this decrease. In 2021, we also see fewer marriages than predicted in a period with strict measures. In the period July to September, there were fewer restrictions on group sizes and the number of marriages is actually higher than predicted. Some delayed marriages are expected to have caught up during this period.

Over the entire period from March 2020 through September 2021, there were almost 7,000 fewer marriages than we expected. This is 13% of the total expected number of marriages. In doing so, we suspect that a portion of the 100,000 weddings that were performed continued in a scaled-down form without a major celebration. If all persons, who postponed their marriage because of the coronation measures or celebrated in a slimmed-down form, still catch up in 2022, we are going to have a great year of celebration! For example, 22-02-2022 can be quite a bang date and also Friday 9 and 16 September will guarantee many weddings. Therefore, our advice: make sure there are enough party outfits in the closet!

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