sign in sign up
<<
Home , Central bank, Currency in circulation

A of

Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for

Koziński, Witold; Świst, Tomasz

Article -term in circulation forecasting for purposes: The case of Poland

e-Finanse: Financial Internet Quarterly

Provided in Cooperation with: University of Information Technology and Management, Rzeszów

Suggested Citation: Koziński, Witold; Świst, Tomasz (2015) : Short-term forecasting for monetary policy purposes: The case of Poland, e-Finanse: Financial Internet Quarterly, ISSN 1734-039X, University of Information Technology and Management, Rzeszów, Vol. 11, Iss. 1, pp. 65-75, http://dx.doi.org/10.14636/1734-039X_11_1_007

This Version is available at: http://hdl.handle.net/10419/147121

Standard-Nutzungsbedingungen: Terms of use:

Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes.

Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Financial Internet Quarterly „e-Finanse” 2015, vol.11 / nr 1, s. 65 - 75 DOI: 10.14636/1734-039X_11_1_007

SHORT-TERM CURRENCY IN CIRCULATION FORECASTING FOR MONETARY POLICY PURPOSES – THE CASE OF POLAND

Witold Koziński1 Tomasz Świst2

Abstract One of the most significant factors which influences the level of banking sector liquidity is Currency in Circulation. Although the central is in charge of of the currency it can’t assess the demand for the currency, as that demand is generated by the customers of commercial . Therefore, the amount of Currency in Circulation has to be modelled and forecasted. This paper introduces ARIMA(2,1) and SARIMA(2,1)(5,0) models with dummy variables and discusses its applicability to the forecasting of Currency in Circulation. The forecasting performance of these models is compared. The results indicate that the performance of SARIMA(2,1)(5,0) is better and that both models might be applied for monetary policy purposes as supportive tools for banking sector liquidity forecasting.

JEL classification: C01, C53, E52 Keywords: Currency in Circulation, Banking Sector Liquidity, Monetary Policy

Received: 09.10.2014 Accepted: 12.06.2015

1 of Poland, [email protected]. 2 National , [email protected].

The authors wish to express sincere gratitude to Mr Krzysztof Senderowicz (Director of Domestic Operations Depart- ment, NBP), Mrs Agnieszka Strużyńska (Supervisor of OMOs Planning Division, NBP), Mr Michał Adam (Senior at Financial Markets Division, NBP) and other colleagues from the for creative discussion which led to improvement of this article. The opinions expressed in this paper are solely those of the authors and do not ne- cessarily reflect the views of the National Bank of Poland.

www.e-finanse.com University of Information Technology and Management in Rzeszów 65 Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

approach introduced by Harvey A., Koopman S. and Riani INTRODUCTION M. (1997). The forecasting performance of the models The gradual increments of short-term banking were assessed in the context of their impact on the sector liquidity in Poland since 2009 implied the need liquidity management of the . The presented to strengthen the liquidity management framework results suggest that two approaches are powerful and that by the National Bank of Poland and gave an apparent the ARIMA model has the best forecasting performance role to Open Operations (OMOs). In particular, over horizons of 5 days and more, while STS is the best it was necessary to update the existing daily liquidity for horizons of 1 to 4 days. The authors concluded that forecast techniques so that they could provide accurate the best forecasting performance could be achieved by information on short-term liquidity needs, which could combining the two approaches. be managed with the use of regular (as well as fine- In the Czech Republic, Hlaváček M., Michael tuning) OMOs. Koňák M. and Čada J. (2005) introduced a feedforward The main banking sector liquidity forecasting structured neural network model and discussed its horizon (of the daily liquidity forecasts) is the reserve applicability to the forecasting of Currency in Circulation. requirement maintenance period, which lasts from 4 The forecasting performance of the neural network model to 5 weeks. However, within each reserve maintenance was compared with an ARIMA model described by 71 period, the main operations are held on parameters. The results indicated that the performance a weekly basis (the NBP conducts them on Fridays), so of the neural network model was on average more the forecasting horizon of to five working days is at a accurate than ARIMA, however comparison of predictive similar level of importance. accuracy with the use of a Diebold-Mariano test didn’t The daily banking sector liquidity forecast is show a statistically significant difference. determined by the accuracy of its individual components. Dheerasinghe R. (2006) modelled Currency in While some items are under the ’s control, Circulation for Sri Lanka with the use of three methods. others are influenced by external factors, which are Three separate models were estimated with daily, weekly under direct control of the central bank in the short- and monthly time series, assembling tools for forecasting run. Those autonomous factors determine the change trends, seasonal patterns and cycles in separate individual in demand and supply of commercial that series. Trend and seasonal effects were identified by the central bank needs to balance by conducting open regressing on trend and seasonal dummies, while cyclical market operations. Especially important are currency in dynamics were captured by allowing for an ARMA effect circulation (with vault ) and government deposits in the regression disturbances. The author concluded (in domestic currency), whose movements increase that all three models fit the data well and give very small or decrease the amount of reserves estimation errors, which were less than 1% in all models and directly influence liquidity conditions. Whereas the tested in the post sample period. government is the most unpredictable item in Lang M., Kunovac D., Basač S. and Štaudinger Ž. liquidity forecasting, currency in circulation shows some (2008) described two time series models for forecasting periodic patterns. This facilitates forecasting the short- Currency in Circulation outside banks in Croatia, i.e. term movement of currency. Due to the importance regression (REG) and ARIMA models. Both models of currency in circulation for conducting monetary generated good short-term forecasts, completing each policy, many central banks have developed and applied other in the sense that the REG outperformed the econometric models for forecasting purposes. ARIMA model on the interval of up to 5 days ahead and One of the first papers describing the importance of on the other hand, the ARIMA model outperformed the modelling Currency in Circulation was the publication by first one in longer horizons. The authors stated that due Cabrero A., Camba-Mendez G., Hirsch A., Nieto F. (2002), to differences in the approach of those two models, in which modelling the daily series of in combination of forecasts would outperform them. circulation in the context of the liquidity management of In Turkey, daily changes of Currency in Circulation the Eurosystem was presented. The authors applied two has been modelled by Güler H. and Talasli A. (2010). approaches, the ARIMA-based approach proposed by The authors introduced the ARIMA-GARCH(1,1) based Bell W. and Hillmer S. (1983) and Structural Time Series approach to model seasonality in daily time series and

www.e-finanse.com 66 University of Information Technology and Management in Rzeszów Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

evaluated forecasting performance. The results show 2) the day effect in the month (denoted further as: that the forecasting performance of the model is better D1, … , D31), than the expert judgement both in the and short 3) the week effect in the month (denoted further run. Moreover the authors emphasized that the model as: W1, … , W5; where the 5th week is incomplete), has to be continuously revised to improve the quality of 4) the month effect in the year (denoted further the forecasts and adjusted whenever needed. as: JAN, … , DEC), 5) the of Easter (EAS) and Christmas (CHR), in here considered as a period of 5 working days Properties of Currency in Circulation Time Series in Poland before and 5 working days after the given calendar effect and The Currency in Circulation (CiC) is one of the major 6) “the long weekend at the beginning of May” autonomous factors in NBP’s (liabilities (LWM), the 1st and 3rd of May are holidays in Poland side), which plays one of the major roles in the context (Labour Day and Day, respectively). of banking sector liquidity management, both in term of As the series of CiC shows significant seasonality, its level as well as volatility. Due to the fact that CiC is out comprising daily, weekly, monthly, annual patterns and of direct control of the central bank its level and volatility some calendar effects like religious holidays, modelling can’t be strictly deterministic. This feature of CiC implies CiC time series becomes a complex issue. Table 1 the necessity of model calibration, which will allow us to presents descriptive statistics of CiC time series (including forecast future developments as accurately as possible. descriptive statistics on a daily basis). The accuracy of a forecast, for monetary policy purposes, The trading day effect is one of the most significant is measured by absolute deviation of the average level in and the shorter seasonal effects of CiC series. This effect a given reserve maintenance period. is the consequence of changing demand for CiC during From the operational realization of monetary policy the week. Typically, the level of CiC decreases on Monday the analysis considers CiC as the volume of all banknotes and this trend lasts till Wednesday. On Thursday and and notes in domestic currency including vault cash held Friday usually systematic increases are observed, then by commercial banks. When CiC is returned to the central there is an increased demand for CiC for the upcoming bank its level in the banking sector is decreasing and the weekend. According to the CiC series, the level of CiC level of banking sector liquidity is increasing and vice declines by 0,11% on Mondays, 0,24% on Tuesdays and versa. During the days of a year, increases and decreases 0,08% on Wednesdays and then increases by 0,30% and of CiC are the consequences of seasonal factors, such 0,32% on Thursdays and Fridays, on average (Figure as: 1 and Figure 2). Cumulative change in the level of CiC 1) the day effect in the week (denoted further as: during the week is usually above zero. MON, TUE, WEN, THE, FRI),

Table 1: Descriptive Statistics of Cash in Circulation for Poland (in PLN mln)

Source: National Bank of Poland

www.e-finanse.com University of Information Technology and Management in Rzeszów 67 Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

Figure 1: Trading Day Effect (in PLN mln) Figure 2: Trading Day Effect (in %)

Source: National Bank of Poland, averaged values, Source: National Bank of Poland, averaged values, no-weekend holidays included no-weekend holidays included

Intra-monthly seasonal effect of CiC is associated The consequences of the observed cyclical changes with the payment of salaries, which are paid in Poland in the following days of the month is the effect of the at the beginning of the month. On average, systematic week in the month, where in the two first weeks of the increases in the level of CiC from the 1st to the 14th day of month CiC increases and in the 3rd and 4th week usually the month are observed. Then, from the 15th to the 28th, declines. In the 5th week, which is per se incomplete, an opposite tendency takes place and after that, in the again increases are observed. latter part of the month, CiC increases again (Figure 3).

Figure 3: Intra-monthly Effect (in PLN mln)

Source: National Bank of Poland, averaged values, included no-weekend holidays

In the broader context, modelling of CiC should The absorption of CiC from the banking sector takes be focused on the month in the year effect. Particularly place in the next month – January is the month, in which noteworthy here is December, in which significant significant declines are observed. The characteristics increase in demand for CiC is observed before the of CiC changes in the consecutive months of a year are Christmas period, as shown in Figure 4. presented in Figure 5.

www.e-finanse.com 68 University of Information Technology and Management in Rzeszów Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

Figure 4: Christmas Effect (in PLN mln) Figure 5: Intra-yearly Effect (in PLN mln)

Source: National Bank of Poland, averaged values Source: National Bank of Poland, averaged values

The Data and the Performance of After such a procedure the final structure of econometric Econometric Models models were achieved - ARIMA(2,1) with 15 dummy The presented models are estimated on the basis of variables and SARIMA(2,1)(5,0) with 14 dummy their sample performance over the period 2 January 2006 variables, the details are presented in Table 6 and Table 7. – 31 December 2011 and covers 1565 observations. The For the operational purposes of monetary policy, identified seasonal patterns have been coded as dummy the daily changes of the CiC level are forecast for the variables. With the use of Akaike Information Criterion next Reserve Maintenance Period (RMP). RMP covers a (AIC) and Schwarz Information Criterion (SIC) the ARIMA period of about a calendar month and ranging from 28 and SARIMA models were chosen. The best results to 33 days (including Saturdays and Sundays, in which were obtained for ARIMA(2,3) with a constant and increases of CiC are zero). The exact scopes of RMPs SARIMA(2,3)(5,0) also with a constant (Tables 2 – 5). The the NBP publishes on the TM Reuters side dummy variables were added both to model ARIMA(2,3) and Bloomberg side . From the point of view with a constant and to SARIMA(2,3)(5,0) with a constant. of monetary policy purposes the most important is the In each step of approximation statistically insignificant average change of the CiC level in the given RMP. Thus, variables were rejected for p- greater than 5%. the evaluation criterion of models considers absolute After such a procedure the final structure of econometric average deviation of forecasts from average CiC in the models were achieved - ARIMA(2,1) with 15 dummy relevant RMPs in 2012 (testing sample). The results of variables were rejected for p-value greater than 5%. this analysis are presented in Table 8.

Table 2: AIC for ARIMA Table 3: SIC for ARIMA

Source: Own analysis based on the National Source: Own analysis based on the National Bank of Poland data Bank of Poland data Table 4: AIC for SARIMA Table 5: SIC for SARIMA

Source: Own analysis based on the National Source: Own analysis based on the National Bank of Poland data Bank of Poland data

www.e-finanse.com University of Information Technology and Management in Rzeszów 69 Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

Table 6: Structural form of ARIMA(2,1) Table 7: Structural form of SARIMA(2,1)(5,0) with dummies (p-value>0,05) with dummies (p-value>0,05)

Source: Own analysis based on the National Bank of Poland data Table 8: Comparative Analysis of Models’ Forecasts

Source: Own analysis based on the National Bank of Poland data www.e-finanse.com 70 University of Information Technology and Management in Rzeszów Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

absolute deviation accounted for less than 0,7% of the Conclusions average scale of Polish banking sector liquidity in the case Average absolute deviation for both models stood of both models. The analysis of the models’ performance at around PLN 600 million, which from the perspective shows their good predictive properties in situations of the Polish banking sector this (over) liquidity should where the demand for CiC generated by commercial be treated as a small value. Excluding June’s RMP with a banks as a result of their customers’ needs reflects the significant increase in the level of CiC at the beginning of repeatable and predictable behaviour of human beings. this period due to the sports event 2012 (it caused This paper shows that forecasting Currency in average absolute deviation in June’s RMP for over PLN Circulation with the use of ARIMA(2,1) and SARIMA(2,1) 1 600 millions) these values stood at around PLN 500 (5,0) models with dummy variables reflects repeatable million. behaviours of cash users and helps in managing liquidity The average issue of NBP bills (weighted by conditions. Moreover both models show good fitness maturity) in RMPs of 2012 amounted to PLN 94 559 measures. To sum up, these models might be applied for million (excluding fine-tuning operations, i.e. NBP bills monetary policy purposes as at least supportive tools for with maturity of less than 7 days). It means that average banking sector liquidity management and forecasting.

REFEREnces Bell, W., Hillmer S. (1983). Modeling Time Series with Calendar Variation, Journal of the American Statistical Association, Vol. 78, 526-534. Bindseil, U., Seitz F. (2001). The for Eurosystem Deposits. The First 18 Months, Working Paper Series No. 44. Bhattacharya, K., Joshi, H. (2000). Modelling Currency in Circulation in India, Reserved Press. Cabrero, A., Camba-Mendez, G., Hirsch A., Nieto, F. (2002). Modelling the Daily Banknotes in Circulation in the Context of the Liquidity Management of the European Central Bank, European Central Bank Working Paper Series No. 142. Diebold, F., Mariano, R. (1995). Comparing Predictive Accuracy, Journal of Business and , Vol. 13, No. 3, 253-263. Dheerasinghe, R. (2006). Modelling and Forecasting Currency in Circulation in Sri Lanka, Central Bank of Sri Lanka Staff Studies Vol. 36, 36-72. European Payment Council (2009). Single Euro Cash Area Framework. Güler, H., Talash, A. (2010). Modelling the Daily Currency in Circulation in Turkey, Central Bank of the Republic of Turkey, Central Bank Review, Vol. 10(1), 29-46. Harvey, A., Koopman, S., Riani, M., (1997). The Modeling and Seasonal Adjustment of Weekly Observations, Journal of Business and Economic Statistics, Vol. 15, No. 3, 354-368. Hlaváček, M., Koňák, M., Čada, J. (2005). The Application of Structured Feedforward Neural Networks to the Modelling of Daily Series of Currency in Circulation, Working Paper Series No. 11. Kearney, A. T. Inc., Schneider, F. (2009). The Shadow Economy in Europe. Using Payment Systems to Combat the Shadow Economy, Kearney Press. Lang, M., Kunovac, D., Basac, S., Staudinger, Z. (2008). Modelling of Currency Outside Banks in Croatia, Working Papers. National Bank of Poland (2013). Annual Report 2012. Banking Sector Liquidity. Monetary Policy Instruments of the National Bank of Poland, NBP Press. Simkawa, K. (2006). The Determinants of Currency in Circulation in Malawi, Press. Staverski, Z. (1998). Currency in Circulation, National Bank of Republic of Macedonia, Working Paper Series No. 1.

www.e-finanse.com University of Information Technology and Management in Rzeszów 71 Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

Appendix 1: Forecasts and actual CiC daily changes in the RMPs of 2012

www.e-finanse.com 72 University of Information Technology and Management in Rzeszów Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

www.e-finanse.com University of Information Technology and Management in Rzeszów 73 Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

www.e-finanse.com 74 University of Information Technology and Management in Rzeszów Witold Koziński, Tomasz Świst Short-term currency in circulation forecasting for monetary policy purposes – the case of Poland „e-Finanse” 2015, vol. 11/ nr 1

Appendix 2: Currency in Circulation in the years 2006 – 2012 (in PLN mln)

Source: National Bank of Poland (2013). Annual Report 2012. Banking Sector Liquidity. Monetary Policy Instruments of the National Bank of Poland, NBP Press, p. 16

www.e-finanse.com University of Information Technology and Management in Rzeszów 75