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Insolvency Statistics Seasonal Adjustment Review April 2024

Updated 30 April 2024

1. Background

Seasonal adjustment is the estimation and removal of effects on a time series that are a result of the time of year, such as the calendar month or Easter. Accounting for these effects makes it possible to analyse the underlying trend in the data.

A common example is retail sales, which peak as a result of the Christmas shopping period. However, this rapid increase in sales does not indicate a sustained upwards trend. Seasonal adjustment removes the effect estimated to be as a result only of Christmas, leaving the actual story in the data to be assessed.

If a data series is seasonal but is not adjusted to account for this, it is difficult to determine whether changes between different time periods result from calendar effects or are actually a change in the underlying trend.

The purpose of this annual review was to determine which of the data series included in the Insolvency Service’s monthly publications, the Company and Individual Insolvency Statistics, should be adjusted to account for seasonality.

2. Scope of the review

Prior to this review, two company insolvency time series were seasonally adjusted:

• Creditors’ voluntary liquidations (CVLs)
• Administrations

Eight individual insolvency time series were seasonally adjusted:

• Total bankruptcy Orders
• Bankruptcy orders – Creditor petitions
• Bankruptcy orders – Debtor petitions
• Consumer bankruptcy
• Trader bankruptcy
• Total Bankruptcy orders resulting in an Income Payments Order or Agreement
• Individual voluntary arrangements (IVAs)
• Debt relief orders (DROs)

These series were reviewed to determine whether it was still appropriate to apply seasonal adjustment and, if so, whether the model being used was still applicable.

Previous quarterly reviews found no consistent seasonality in the compulsory liquidation series, but the monthly series was considered for seasonal adjustment in this review.

Data series for Scotland and Northern Ireland were outside the scope of this review.

The data used in this review can be found in the long-run CSV files for the company and individual Insolvency Statistics.

The revisions policy for seasonally adjusted series is set out in a separate document on our website. Changes to the revisions policy were not considered as part of this review, but the Statistics Team would welcome comments and feedback on this approach.

3. Analysis

The data series published by the Insolvency Service contain monthly and quarterly data. They are series of differing lengths. Numbers for compulsory and creditors’ voluntary liquidations exist as far back as Q1 1960, compared to IVAs from 1987 and administrations from 1993. For the purposes of seasonal adjustment, monthly data since January 2000 has been used where possible, that is 291 full months of data at the time of this review. A few time series have a different start date. Accurate information relating to employment status in bankruptcy is only available starting from 2007, so the Consumer bankruptcy and Trader bankruptcy series start from January 2007. DROs were introduced in April 2009, so the series for seasonal adjustment starts at this time.

The Insolvency Service constrains the seasonally adjusted series to match the annual calendar year totals in the original data. While this may distort the seasonally adjusted totals, it is a common approach and doing so aids interpretation of the data. The seasonally adjusted numbers for bankruptcies were derived by adding the adjusted creditor and debtor series. Total individual insolvency numbers were derived by adding the seasonally adjusted IVA, DRO and bankruptcy series.

For each series, the following have been reviewed:

• Tests for the presence of seasonality
• regARIMA model, which considers the ARIMA model, as well as features (prior adjustments) such as outliers, level shifts, temporary changes, seasonal breaks as well as Easter and trading day effects
• The optimal choice of filters for the seasonal moving average and trend moving averages

The analysis was carried out using X13-ARIMA-SEATS, as implemented in the ‘seasonal’ package in R. This is the recommended programme for seasonal adjustment for National Statistics, and the pick model function was used to avoid over fitting.

Detailed comments on each series are given in the following sections.

4. Summary of outcomes

For all of the series where significant seasonality was detected, the seasonality was multiplicative and therefore a log transformation was applied to the data.

For all such series, the pick model function selected the ARIMA model (0,1,1)(0,1,1), a 3x5 seasonal moving average and a 13-term Henderson moving average to account for the trend. The only exception was for compulsory liquidations, where a 23-term Henderson moving average was selected.

Series	Decomposition	Model	Priors	Seasonal moving average	Trend moving average
Compulsory liquidations	Multiplicative	Log(0,1,1)(0,1,1)	Weekday, Easter[1]	3x5	23-term
Creditors’ voluntary liquidations	Multiplicative	Log(0,1,1)(0,1,1)	Weekday, Easter[8]	3x5	13-term
Administrations	Multiplicative	Log(0,1,1)(0,1,1)	Weekday	3x5	13-term
Receiverships	Seasonality not tested due to very small number of cases
Company voluntary arrangements	Seasonality not tested due to very small number of cases
Bankruptcy - Creditor Petitions	Multiplicative	Log(0,1,1)(0,1,1)	Trading day, Easter[8]	3x5	13-term
Bankruptcy - Debtor Petitions	Multiplicative	Log(0,1,1)(0,1,1)	Trading day, Easter[1]	3x5	13-term
Consumer bankruptcies	Multiplicative	Log(0,1,1)(0,1,1)	Trading day, Easter[1]	3x5	13-term
Trader bankruptcies	Multiplicative	Log(0,1,1)(0,1,1)	Trading day	3x5	13-term
Bankruptcies resulting in an Income Payments Order or Agreement	Seasonality not tested due to very small number of cases
Individual voluntary arrangements	Multiplicative	Log(0,1,1)(0,1,1)	Weekday	3x5	13-term
Debt relief orders	Multiplicative	Log(0,1,1)(0,1,1)	Trading day, Easter[8]	3x5	13-term

Easter[n] means an Easter effect of n days. Weekday means a trading day effect that only occurs for weekdays

4.1 Compulsory Liquidations

Previous quarterly reviews found no identifiable seasonality in the compulsory liquidation series. However, this review found that the monthly series demonstrated significant seasonality. The model selected a 23-term Henderson moving average as opposed to the 13-term moving average that was selected for the other series.

Prior adjustments that were identified for the series included additive outliers for May and June 2020 and a level shift in September 2020, which corresponded to lower numbers during the coronavirus pandemic. A level shift was also detected for January 2022, when compulsory liquidations started to increase following the dip in the pandemic.

4.2 Creditors’ Voluntary Liquidations

Similar to the previous quarterly reviews, the monthly series demonstrated significant seasonality.

Prior adjustments that were identified for the series included weekday trading effects and an Easter effect of eight days. Temporary changes were identified for June 2020 and January 2021, during the coronavirus pandemic.

The adjustment review for CVLs uses numbers after bulk insolvencies are removed. Bulk insolvencies were a large number of connected personal services companies entering liquidation, primarily between 2016 and 2019, following changes to claimable expense rules. See the Company Statistics Methodology and Quality Document for more information.

4.3 Administrations

In previous quarterly reviews, with the exception of 2019, the administrations times series demonstrated significant seasonality. This review found that the monthly series again demonstrated significant seasonality.

Prior adjustments that were identified for the series included weekday trading effects and multiple additive outliers for August 2000, October 2001, November 2006, October 2008 (when 728 managed service companies entered administration on the same day in September 2008) and December 2020.

4.4 Receiverships

Due to the very small numbers of receiverships, we did not test for seasonality in the data.

4.5 Company Voluntary Arrangements

Due to the very small numbers of company voluntary arrangements, we did not test for seasonality in the data.

4.6 Bankruptcy Orders - Creditor Petitions

Similar to the previous reviews, the series demonstrated significant seasonality.

Prior adjustments that were identified for the series included trading day effects and an Easter effect of eight days. A temporary change was identified for April 2020, that corresponded to lower numbers at start of the coronavirus pandemic.

4.7 Bankruptcy Orders - Debtor Petitions

Similar to the previous quarterly reviews, the monthly series demonstrated significant seasonality.

Prior adjustments that were identified for the series included trading day effects and an Easter effect of one day. An additive outlier was identified for May 2011. As with creditor petitions, a level shift was detected for April 2020 that corresponds to lower numbers at the start of the coronavirus pandemic.

4.8 Consumer Bankruptcy Orders

Similar to the previous quarterly reviews, the monthly series demonstrated significant seasonality.

Prior adjustments that were identified for the series included trading day effects and an Easter effect of one day. An Additive outlier was detected for May 2011. A level shift and an additive outlier were detected for April and June 2020 respectively, which corresponded with lower numbers at the start of the coronavirus pandemic.

4.9 Sole Trader Bankruptcy Orders

Similar to the previous quarterly reviews, the monthly series demonstrated significant seasonality.

Prior adjustments that were identified for the series included trading day effects and multiple outliers. A level shift and additive outlier were detected for April and May 2020 respectively, which corresponded with lower numbers during the start of the pandemic. A temporary change was detected for September 2020, which saw higher numbers than earlier in the pandemic. An additive outlier for December 2020 corresponded to a decline in numbers back to levels seen during the early part of the pandemic.

4.10 Total Bankruptcy Orders resulting in an Income Payments Order or Agreement

Numbers of IPOs and IPAs are now provided only by the date of order or agreement, not by the date of bankruptcy order as in the discontinued quarterly statistics publication. Monthly numbers of IPOs and IPAs are small, so we have not tested for seasonality in the data.

4.11 Individual Voluntary Arrangements (IVAs)

Similar to the previous quarterly reviews, the monthly series demonstrated significant seasonality.

Prior adjustments that were identified for the series included weekday trading effects and multiple outliers. An additive outlier was detected for March 2020, corresponding with lower numbers at the start of the coronavirus pandemic. An additive outlier was also detected for May 2020 when numbers increased because of a large number of delayed registrations from IVAs agreed before the start of the coronavirus pandemic. A level shift was detected for October 2020 when IVA numbers returned close to pre-pandemic levels.

4.12 Debt relief orders (DROs)

Similar to the previous quarterly reviews, the monthly series demonstrated significant seasonality.

Prior adjustments that were identified for the series included trading effects, an Easter effect of eight days and multiple outliers. An additive outlier and temporary change were detected for April 2009 corresponding with the introduction of DROs. An additive outlier for September 2015 and and a level shift for July 2021 both corresponded with increases of eligibility limits of debt, assets and income for DROs. A level shift in April 2020 corresponded with lower numbers at the start of the coronavirus pandemic. Another level shift in March 2023 corresponded with the introduction of DRO hubs.