From ‘ABCD’ to STSMs – New Thinking about Banknote Demand Forecasting
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This article was first published in the June issue of Cash & Payment News and is republished with the editor’s authorisation.
With the publication of the IMF paperSee Banknote paper. More ‘Measurement and Use of CashMoney in physical form such as banknotes and coins. More by Half the World’s Population’ and the CashEssentials’ rebuttal, a new paper about demand forecasting by the Banca d’Italia (BdI) is timely and adds to the discussion.
The Eurosystem Research Network on Cash (EURECA) was set up in response to changing cash usage in Europe and the need to research and understand better cash-related data, whether paymentA transfer of funds which discharges an obligation on the part of a payer vis-à-vis a payee. More diaries, circulation data or something else. The first project of EURECA looked at better forecasting cash demand. The report, written by BdI, is the joint work of the NCBs of France, Germany, Italy and Spain, who account for 80% of banknotes issued in the EurosystemThe Eurosystem comprises the European Central Bank and the national central banks of those countries that have adopted the euro. More.
The benchmark model, as it is known, for the Eurosystem has been forecast based on ARIMAX models of banknotes issued nationally by denominationEach individual value in a series of banknotes or coins. More. These NCBs have developed Structural Time Series Models (STSMs) as an additional forecasting tool and used it on their data. They found that, for most denominations, the results were more accurate than the benchmark model, albeit with the caveat that the projection period used was only 12 months long.
The Problem
BanknoteA banknote (or ‘bill’ as it is often referred to in the US) is a type of negotiable promissory note, issued by a bank or other licensed authority, payable to the bearer on demand. More production requirements are calculated using two approaches to gain robust results: (i) bottom-up based on national forecasts provided by the national central banksIn general, the expression refers to the central banks of different countries. More and (ii) top-down using a centralised euroThe name of the European single currency adopted by the European Council at the meeting held in Madrid on 15-16 December 1995. See ECU. More area forecast made by the European Central Bank. This approach combines national expertise with a euro-area-wide perspective.
However, the national forecasts of the bottom-up approach are not harmonised. Each national central bank of the Eurosystem can decide which forecasting models to choose and how to evaluate them.
At the launch of the euro, what was known as the ABCD model was used for forecasting based on the difference between withdrawals from and lodgements to NCBs and the quantity of fit banknoteA used banknote that the central bank deems fit to be returned into circulation. More retrievable through sortingProcess of fitness sorting of banknotes by their condition of use. Through this process, used banknotes are classified as fit or unfit to return into the circulation. See Processing of banknotes. More activities. The NCBs looked at the cointegration relationships with relevant macroeconomic variables. During the 2009 economic crisis, the ABCD model could not fully reflect developments that affected cash demand.
In 2019 the ABCD-2 model was adopted by the ECB. This uses a small basket of models to arrive at a forecast. In France, Germany and Spain, the NCBs use ARIMA models. BdI derives its forecast of banknotes in circulation from combining the predictions of withdrawals and lodgements generated by a basket of models, which also includes ARIMA models and exponential smoothing.
All of the models fall within traditional time-series econometric techniques such as exponential smoothing, ARIMA, VAR and SUR. See definitions below.
The four NCBs have found that the traditional framework and benchmark models have not coped well with shocks – such as the global financial crisis of 2008, the European sovereign debt crisis, or the COVID pandemic of 2020-21 – or regulatory interventions, such as the decision to stop issuing the €500 banknote on 4 May 2016. Within each country, there have also been national shocks that the benchmark model has struggled to cope with.
Another driver of the need for better forecasting is the ‘cash paradox’, fewer cash transactions but ever more notes in circulation.
In addition, NCBs face a particular forecasting problem caused by the nature of the euro and the Eurosystem. The euro is slightly different from most other currencies because of foreign demand for the euro, which leads to the export of euros outside the eurozone and the flow of notes between countries within the monetary union. For countries with large numbers of tourists, this is particularly relevant.
STSM solution
The STSM approach is a classical decomposition of the time series into trends and seasonal, cycle and irregular components augmented with regression variables. It was used to forecast net issuanceThe value or units of banknotes (or coins) issued by a central bank over a period, minus the equivalent withdrawn from circulation during the same period. A positive net issuance expresses an increase in circulation during the period. More for each country and denomination.
Each component is separately modelled by an appropriate dynamic stochastic process which usually depends on normally distributed disturbances. The trend component characterises long-term developments in the economy. Mid-term dynamics can be modelled directly by the cycle component.
All dynamics in the time series data are analysed simultaneously. Missing data and time-varying regression coefficients are easily handled in state-space frameworks.
The state-space form provides the key to the statistical treatment of STSMs. It enables maximum likelihood estimators (MLE) of the unknown parameters in a Gaussian model to be computed via the Kalman filter and the prediction error decomposition. Once estimates of these parameters have been obtained, it provides algorithms for estimating the unobserved components and predicting future observations. An advantage of STSMs and Kalman filtering techniques is that various explanatory variables, dummies, and missing observations can be easily included in the model.
An essential benefit of the STSM forecasts is that they originate from realistic model representations of the macroeconomic time series rather than black-box methods.
Performance of STSM forecasting
According to the forecast accuracy measures employed, the STSMs outperform the benchmark models for each denomination in Spain. In France and Italy, STSMs do a better job at forecasting banknotes in circulation for all but the €50 denomination and in Germany for four out of six denominations (€10, €20, €50 and €200).
Although the statistical informative value of this comparison is limited by the 12-month projection period, on balance STSMs, seem to be a promising extension to time series models currently employed, at least for France, Germany, Italy and Spain. Inevitably this report concludes that further exercises of this kind are needed to assess the robustness of this finding.
Definitions
EXPONENTIAL SMOOTHING: A rule-of-thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average, the past observations are weighted equally, exponential functions assign exponentially decreasing weights over time. It makes some determination based on prior assumptions by the user, such as seasonality and is often used to analyse time-series data. (WIKIPEDIA)
ARIMA: Auto Regressive Integrated Moving Average model is a generalization of an autoregressive moving average (ARMA) model. Both models are fitted to time series data to comprehend the data better or forecast upcoming series points. ARIMA models are applied in some cases where data show evidence of non-stationarity in the sense of mean (but not variance/autocovariance), where an initial differencing step (corresponding to the “integrated” part of the model) can be applied one or more times to eliminate the non-stationarity of the mean function (i.e., the trend). (WIKIPEDIA)
ARIMAX: An Autoregressive Integrated Moving Average with Explanatory Variable (ARIMAX) model can be viewed as a multiple regression model with one or more autoregressive (AR) terms and one or more moving average (MA) terms. This method is suitable for forecasting when data is stationary/non-stationary and multivariate with any data pattern, i.e., level/trend/seasonality/cyclicity. (SMARTEN.COM)
VAR: Vector autoregression (VAR) is a statistical model that captures the relationship between multiple quantities as they changeThis is the action by which certain banknotes and/or coins are exchanged for the same amount in banknotes/coins of a different face value, or unit value. See Exchange. More over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregressive model by allowing for multivariate time series. VAR models are often used in economics and the natural sciences. (WIKIPEDIA)
SUR: Seemingly Unrelated Regressions (SUR) is a generalization of a linear regression model that consists of several regression equations, each having its dependent variable and potentially different sets of exogenous explanatory variables. Each equation is a valid linear regression and can be estimated separately, so the system is seemingly unrelated.
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