The article presents the seasonal factors of 80 selected economic/financial time series comprising monetary, banking, price statistics, production data, service sector indicators, merchandise trade and alternate modes of payment. This article finds that most of the production-related variables seasonally peak around March and price-related variables record a seasonal trough around the same time. The seasonal variations in the prices of food products and primary articles have become accentuated over the last decade. As regards payment modes, instruments related to bulk transactions tend to peak during March, whereas, in the case of retail payment, seasonality peaks during festivals.

Introduction

Seasonal variations recurring weekly, monthly or quarterly constitute a behavioural component in economic series and therefore can be predictable. It is intertwined with other time series components, viz., trend, cyclical variations and random fluctuations. The presence of seasonality tends to obscure the true underlying characteristics of the economic variable and its data generating process as well as the inter-relationships between variables. At the same time, correctly understanding seasonal variations helps to accurately foresee behavioural changes. In this context, identification and segregation of seasonal factors of an economic variable is a first step to appropriately use the information for the purposes of modelling and forecasting.

Measuring seasonality and undertaking seasonal adjustments has been established as the best practice while modeling time series data. The cross country experience reveals that the USA measures GDP growth in terms of quarter-on-quarter annualised rates of change after adjusting for seasonality. The Inflation Report of the Bank of England generally uses seasonally adjusted data. The Quarterly Financial Report of Bank of Canada publishes assessment of seasonal demand for bank notes. The International Monetary Fund (2016) has advised member countries to report seasonally adjusted broad money data in their ‘Standardised Report Form for Money Aggregates’ in its International Financial and Monetary Statistics.

The Reserve Bank has been publishing monthly seasonal factors for important macroeconomic variables since 1980. This article carries forward this endeavor by computing and updating seasonal factors upto 2019-20. The rest of the article is organised as follows. A review of the literature relating to evolution of methodology and global usage of seasonal factors is presented in Section II. The economic variables selected for study and choice of technique for extracting seasonal factors are explained in Section III. Section IV brings out the seasonality patters for various groups of macroeconomic variables based on average monthly seasonal factors in light of data upto 2017-18. Section V presents the results on temporal shifts in seasonality patterns followed by empirical evaluation of seasonal variation. Section VI concludes the article with some policy perspective.

II. Review of the Literature

In literature, time series are assumed to be composed of orthogonal components, viz., trend, seasonal, cyclical and irregular components. In an additive model, the time series is represented as the sum of the four components mentioned above, whereas in a multiplicative model the time series is the product of the components. Seasonality is the yearly or monthly predictable variation of the time series over and above trend and cycle. Seasonality plays a key role in short-term analysis of macro-economic factors and aids in effective decision-making.

The literature refers to unmasking relevant short and long-term movements of economic time series by accounting for the behavioural nature of seasonality (Manna, et al., 2003; HCSO, 2017). Estimates of seasonal factors are observed to have improved the trend-based forecasts of economic variables (Lembke, 2015). Seasonal adjustment has been employed along with various smoothening and filtering techniques to extract the persistent component in economic variables, notably core inflation (Samanta, et al., 2000). The use of non-parametric singular spectrum analysis for extraction of seasonality has been discussed in the context of Global Positioning System (GPS) signal extraction (Chen, et al, 2013) and other related fields.

The literature on estimation of seasonal factors has a long history, starting from ratio-to-moving-average method (Macaulay, 1931), further refined as Census Methods by the US Census Bureau in 1954-55. Extensive research on the explicit functional specification of seasonal and trend/cycle components led to development of various versions of seasonal adjustment methods. The X-11 method (US Census Bureau, 1965) provided functional flexibility such as multiplicative as well as additive representation of components, treatment for extreme values and various tests for seasonality (Shiskin, et al., 1967). A major limitation of X-11 method, which is based on moving average or linear smoothing filter, however, was the lack of reliability of estimates for the most recent year because of inability to apply symmetric weights to end points as against central observations. This led to frequent revisions of estimates of most recent observations as more data points get added (Dagum, 1980).

Statistics Canada’s X-11-ARIMA method incorporated an Autoregressive Integrated Moving Average (ARIMA) model into the X-11 method to extrapolate original time series data for one year at both ends of the series. This helped to deal with the ‘end points’ problem and to obtain robust estimates of seasonal factors in a scenario when seasonality is moving rapidly in a stochastic way. The US Census Bureau developed X-12-ARIMA as an enhanced version of X-11 and added a feature called RegARIMA, which has an option of built-in or user-defined regressors that enable estimation of stock trading day and holiday effects as well as disruptions in the series such as sudden changes in levels (US Census Bureau, 2011).

US Census Bureau’s latest X-13 ARIMA-SEATS (Signal Extraction in ARIMA Time Series) is an enhanced version of the X-11 variant with two additional options, viz., TRAMO (Time series Regression with ARIMA Noise, Missing Values and Outliers) for automatic model selection and Seasonal Extraction in ARIMA Time Series (SEATS) for conducting the seasonal adjustment procedure (Gomez, et al., 1996; 2001a; 2001b; US Census Bureau, 2011).

III. Data and Methodology

In line with the best country practices and upholding standards set in the past in the Reserve Bank, the macroeconomic indicators covered here are monetary, banking, price statistics, production data, service sector indicators and merchandise trade. In recognition of the rapid proliferation of alternate modes of payment in India, viz., real time gross settlements (RTGS), paper clearing, retail electronic clearing (REC) and card payment, they are also subjected to seasonality analyses. Specifically, 80 monthly macroeconomic variables disaggregated by sector include 14 monetary and banking indicators, 21 categories of indices relating to consumer prices, nine relating to wholesale prices, 23 on industrial production, six on service sector indicators, three on merchandise trade and four series on alternative payment indicators. Seasonal factors are mostly derived from time series dating back to April 1994 (Annex Table 1).

Seasonal factors have been estimated under multiplicative model by using the X13-ARIMA-SEATS software of the US Census Bureau, after configuring it to suit Indian conditions, e.g., incorporating Diwali and Indian trading day effects.

Seasonal adjustment can be done in two ways; i) direct approach - applying the seasonal adjustment procedure directly to the aggregate series; and ii) indirect approach – first seasonally adjusting each components of the composite series and then summing (aggregating) the components to get seasonally adjusted composite (Manna et al., 2003). The article follows the direct approach.

IV. Analysis of Results

All the macroeconomic variables considered here exhibit different seasonality (Annex Tables 2 and 3)¹. Of the 14 major monetary and banking indicators, 11 recorded seasonal peaks during March or April (around the financial year closure), whereas seasonal troughs for the majority of these series can be located either in August or in December. For example, bank loans registered a seasonal peak in March, whereas banks’ investments register a seasonal trough in the same month. Demand deposits of scheduled commercial banks (SCBs) exhibited the highest seasonal variation (average seasonal factor (SF) range² at 9.3) followed by reserve money (average SF range at 6.0) and cash in hand and balances with RBI (SCBs) (average SF range at 5.8). On the other hand, time deposits of SCBs, exhibited the smallest seasonal variation (average SF range at 1.3) indicating preference to banks’ deposits as a savings avenue for fixed return and low risk (Annex Table 4).

Turning to prices, the Consumer Price Index (CPI) headline experiences seasonal upside pressure between July and November, which is largely due to the prices of food and beverages. CPI-food is driven by the seasonal patterns of prices of vegetables. Prices of fruits peak during the summer (April - August) and those of vegetables around the monsoon (July - November) due to lower availability and persistent demand (Chart 1).

CPI-vegetables showed the highest seasonal variation (nine-year average SF range at 23.0). Among vegetables, prices of tomatoes, onions and potatoes recorded average SF range of 65.6, 40.4 and 35.6, respectively. Seasonal variation in fruits prices was found to be lower (average SF range of 6.3) than those of vegetables. Further, seasonal variations in the prices of cereals and products were found to be lower (average SF range at 0.7) than that of pulses and products (average SF range at 3.2), where mismatches between supply and demand were persistent, possibly caused by production uncertainty and diet shifts linked to the economic development. On the other hand, CPI - non-alcoholic beverages exhibited the smallest seasonal variation (average SF range at 0.3), which could be attributed to rising awareness about healthy lifestyle and wellness among consumers. Seasonality in the aggregate CPI series [CPI-Combined, CPI for Industrial Workers (CPI-IW), CPI for Agricultural Labourers (CPI-AL) and CPI for Rural Labourers (CPI-RL)] is low while it is pronounced in some of the components, mainly food items (Annex Table 4).

Seasonal troughs in WPI series were concentrated in only two months (March and December) relative to the distribution of seasonal peaks. Seasonal fluctuations in the WPI-all commodities were largely driven by prices of primary articles, especially food, which have a seasonal pattern similar to CPI-food and beverages. Prices of fuel and power recorded the highest seasonal variation (average SF range at 19.4) and among manufactured products group, manufacture of food products showed the lowest seasonal variation (average SF range at 2.2) (Annex Table 4).

As regards seasonality in output, industrial production is highly seasonal. The index of industrial production (IIP) showed an average SF range of 13.0. Among the major sectors, mining had the highest seasonal variation (average SF range at 30.8); under the use-based classification, capital goods had the highest seasonal fluctuation (average SF range at 35.1). Seasonal peaks in the IIP series mostly occurred in March, the last month of the financial year, which could be due to achieving annual targets; seasonal troughs, on the other hand, were scattered. A seasonal moderation in cement production was observed between July to November, which is the monsoon season in major parts of India. Fertiliser production registered a seasonal decline between February to June, which is the harvesting time of rabi crops and a lean season for agricultural activity.

Four of the six services sector indicators recorded seasonal peaks in March. Only in the case of domestic and international passenger traffic, the seasonal peak coincided with the holiday seasons in May and January, respectively.

The seasonal peaks for merchandise exports remained unchanged in March, coinciding with the peak in the industrial production while non-oil non-gold imports also remained unchanged in December, but the peak in imports shifted to October from March earlier (Chart 2 & Annex Table 2).

The analysis of alternate payment modes shows that RTGS, paper clearing and retail electronic clearance recorded high seasonal variations and peak during March, indicating heightened usage of online transfers on annual financial year closing, whereas the seasonal peak of usage of card payments mode was found to be during October, consumption – demand around the festival season. The seasonal troughs, on the other hand, were found to be distributed over February, September and November (Chart 3 and Annex table 2).

V. Has Seasonality Changed?

A simple way of identifying change in seasonality patterns in 2019-20 would be to compare the outcomes for 2019-20 with the average seasonal factors for the last five years (2014-15 to 2018-19). Out of the 80 selected series, the peak and the trough for 41 series remained unchanged whereas four series recorded shifts in both peaks and troughs (Chart 4 and Annex table 5). This change in seasonality was noticed mainly in the case of CPI. The seasonal peak in CPI-all commodities advanced to November in 2019-20 from October earlier, mainly reflecting change in the prices of vegetables. Seasonal peaks in the prices of CPI-food and beverages also shifted to November from August earlier which got aligned with the seasonal peak in the prices of food articles in the wholesale market. Further, greater convergence in the seasonal peaks of the components of industrial production was found in 2019-20.

In order to explore ‘moving seasonality’- changes in seasonal factors over time - detecting the presence of secular trend is critical. A downward (upward) trend in the seasonal fluctuation of a series shows decline (increase) in seasonal variation over time.

While in majority of the cases, seasonal variation/ fluctuations (difference between the maximum and the minimum monthly seasonal factors) in 2019-20 remained similar to the previous five years’ average (Chart 5), empirical evidence indicates that seasonal fluctuations moderated for 35 series over a longer time horizon of last 10 years (Annex table 6). On the other hand, seasonality became more pronounced in another 22 series.

Seasonal fluctuations in monetary and banking aggregates either moderated or remained broadly unchanged during last 10 years, arguably reflecting better availability of banking services. Though seasonal fluctuation in general IIP remained unchanged, mining, manufacturing and electricity recorded rise in seasonal variation. The mining activity, especially coal, is adversely affected due to rain and slowdown in railway transport during the monsoon season. Hence, supposedly the higher production during active season to meet rising demand for coal and other minerals explains the rise in seasonal fluctuation over time. Seasonal variation moderated for the majority of CPI-combined elements; retail prices of tomatoes, meat and fish exhibited higher seasonality while potato and onion prices showed lower seasonality. In the wholesale market, WPI-all commodities showed more seasonal variation mainly due to prices of chemicals and chemical products (Chart 6).

VI. Conclusion

Seasonal adjustment has a crucial role to play in an accurate reading of the economy and in making policy decisions. It is observed that the heightened seasonal demand for currency in circulation around financial year-end and beginning of agricultural season, viz., March and June gives a cue for efficient currency management in the country, similarly, the knowledge of seasonal pattern in banks’ deposits can be used in managing the banks’ resources optimally.

Driven by the prices of vegetables, CPI headline inflation exhibited price pressures during the monsoon season. The seasonal peak for general retail prices got advanced to November in 2019-20 from October, aligning with the wholesale market. This calls for efficient supply chain management during such periods.

Majority of categories of industrial production peak in March whereas the production of consumer non-durables peak in December. The seasonal peak in the manufacture of textiles had advanced to December, the winter season in the country, from August earlier. Imports and exports experience a peak during March. Further, bank credit peaks in March, apparently to cater to the year-end pressure of target achievements. Well strategizing credit availability by banks and credit institutions, keeping in mind the demand around festivals, will provide stimulus to the productive activities.

References:

Bank of Canada, (2018). Quarterly Financial Report. June 30, Bank of Canada.

Bank of England, (2019). Inflation Report. February, Bank of England.

Dagum, E. B., (1980). The X-11-ARIMA Seasonal Adjustment Method. Statistics Canada.

Deutsche Bundesbank, (2018). Monthly Report. Vol. 70, No.9, Deutsche Bundesbank, September.

Gomez, V. and Maravall, A., (1996). Programs TRAMO and SEATS: Instructions for the User. Bank of Spain.

Gomez, V. and Maravall, A., (2001a). Automatic modeling methods for univariate series. In D. Pena, G. C. Tiao, and R. S. Tsay (Eds.), A Course in Time Series Analysis. New York, NY: J. Wiley and Sons.

Gomez, V. and Maravall, A., (2001b). Seasonal adjustment and signal extraction in economic time series. In D. Pena, G. C. Tiao, and R. S. Tsay (Eds.), A Course in Time Series Analysis. New York, NY: J. Wiley and Sons.

HCSO (2007). Seasonal Adjustments – Methods and Practices. Budapest, July, Hungarian Central Statistics Office.

IMF, (2016). Monetary and Financial Statistics Manual and Compilation Guide. International Monetary Fund.

Lembke, Ron (2015). Forecasting with Seasonality. Retrieved from http://business.unr.edu/faculty/ronlembke/handouts/Seasonality%20Final17.pdf.

Macaulay, F. R. (1931). The Smoothing of Time Series. National Bureau of Economic Research, Inc.

Manna, M., Peronaci, R., (2003). Seasonal Adjustment. European Central Bank.

Reserve Bank of India (2017). Monthly Seasonal Factors of Selected Economic Time Series. 2016-17, Reserve Bank of India Bulletin, September, Vol. LXXI, No. 9.

Samanta, G.P. and Bhattarjee, M., (2000). Are Seasonal Adjustment and HP-Filter Useful in Estimating Core Inflation in India? International Journal of Development Banking, Vol. 18, No. 2, July, pp. 61-75.

Shiskin, J., Young, A.H. and Musgrave, J.C., (1967). The X-11 Variant of Census Method II Seasonal Adjustment Programme. Technical Paper No. 15, Bureau of the Census, U.S. Department of Commerce.

US Census Bureau (1965). Estimating Trading-Day Seasonal Variation in Monthly Economic Time Series. US Bureau of the Census Technical Paper No. 12.

U.S. Census Bureau (2011). X-12-ARIMA Reference Manual, Version 0.3. Time Series Research Staff, Statistical Research Division (https://www.census.gov/ts/x12a/v03/x12adocV03.pdf).

U.S. Census Bureau (2017). X-13-ARIMA-SEATS Reference Manual, Version 1.1. Time Series Research Staff, Center for Statistical Research and Methodology (https://www.census.gov/ts/x13as/docX13AS.pdf).

Annex

* Prepared by Srijashree Sardar, Kashyap Gupta and Jugnu Ansari of the Modeling and Forecasting Division, Department of Statistics and Information Management. The views expressed are those of the authors and do not represent the views of the Reserve Bank of India.

¹ In case data are available for less than ten years, average for the corresponding period is taken.

² Range, a measure of dispersion, is calculated as the difference between maximum and minimum of monthly seasonal factors. Higher value of range indicates higher seasonality in the variable yielding to heightened activities/prices during a particular period of a year. ‘Average seasonal factor range’ is the range of average seasonal factors for the last ten years.