## Saturday, January 16, 2016

### Seasonal adjustment with Indian data: how big are the gains and how to do it

by Rudrani Bhattacharya, Radhika Pandey, Ila Patnaik, Ajay Shah.

In India, we usually focus on year on year growth rates of macroeconomic series to monitor the economy. Structural change in the economy, and the rise of modern business cycle fluctuations (Shah, 2008; Ghate et. al. 2013), have given a surge of interest in monitoring macroeconomic data on the part of both economic agents and policy makers.

The analysis of macroeconomic data using year-on-year growth rate suffers from serious problems. Each value for the year-on-year growth of a monthly series is the sum of twelve previous month-on-month changes. When we compare June 2015 to June 2014, we are looking back at the entire year and not at June 2015 or May 2015. To know what is happening in May 2015 or June 2015, we need to look at month-on-month changes. However, most of the time, these are obscured by seasonality.

Seasonal adjustment removes the seasonality, permits the computation of point-on-point growth rates, and thus allows us to know what is going on in the economy in the latest data. As an example, Bhattacharya et. al., 2008, show how our understanding of inflation in India is improved by using seasonally adjusted data, and how this could have improved the conduct of monetary policy.

In most advanced countries, the statistical system publishes seasonally adjusted data series, in addition to the raw "non-seasonally adjusted" data. In India, the growing need for seasonally adjusted data has not yet been met by the Statistical System. Some statistical software packages (e.g. Eviews) are available which permit a certain black box usage, and have started getting used in this fashion, mostly by economists in financial firms.

In a recent paper (Bhattacharya et. al, 2016) we show the complete steps of the seasonal adjustment process for four monthly time-series: the Index of Industrial Production, Exports, the Consumer Price Index and the Wholesale Price Index. This involves calendar adjustment, correction for outliers, model selection and conducting diagnostic tests.

Further, it involves testing for festival effects and other features that may occur in certain months of a year. We find that Diwali has a significant effect on the IIP. In the jargon of seasonal adjustment, Diwali is referred to as a moving holiday'' since in some years it falls in the month of October and in some years in November. The Diwali month is a month of festivities with fewer working days but enhanced purchases prior to Diwali. The paper finds a significant negative impact of Diwali on IIP.

We examine the importance of the choice of direct' versus indirect' seasonal adjustment for some composite series. If a time series is a sum of component series, each component series can be seasonally adjusted and summed to get an indirect adjustment' for the aggregate series. On the other hand, we can apply the seasonal adjustment procedure directly to the aggregate series to obtain direct seasonal adjustment'. We compare the direct and indirect adjustment of IIP (following the use-based classification) and find that direct adjustment removes noise better compared to indirect adjustment.

A key question in India, given the rapid pace of structural change, is the wise choice of data span. There is a trade-off between the need for a longer time series in order to get a better estimate of the time-series model, and the necessity to avoid modeling a time series containing a structural break. A very long series will have data which will not relate to the pattern of the current series. On the other extreme, a short series may be highly unstable and be subject to frequent revisions. The length of the series may be shortened owing to changes in methodologies, definitions, moving to new statistical classifications, the use of new sources of information. This issue is particularly relevant for India as recently a number of series have undergone revisions due to changes in statistical methodology. We show that seasonal adjustment of a short series is unreliable. A ten year time span is appropriate to arrive at stable model parameters and reliable diagnostics as well as to retain the current pattern of the series.

How do we know that a seasonal adjustment procedure is adding value? We propose the following metric: The standard deviation of the month-on-month change. The standard deviation of the month-on-month change of the raw data is likely to be artificially elevated owing to the presence of seasonality. A good seasonal adjustment procedure should do well at reducing this standard deviation. E.g. a seasonal adjustment procedure that does not understand that Diwali is an India-specific holiday will suffer from a strong whiplash across the month containing Diwali, which will yield an elevated value for the standard deviation of the month-on-month change.

 IIP Raw series 73.26 SA using Eviews 26.79 SA with our approach (optimal span, outlier adjustment, trading day effect) 25.73 SA after adjusting for diwali effect 23.23 SA with full capabilities 23.12 Exports Raw series 132.53 SA using Eviews 89.40 SA with our approach (optimal span, outlier adjustment, trading day effect) 78.01 CPI Raw series 9.22 SA using Eviews Fails SA with our approach (optimal span, outlier adjustment, trading day effect) 7.28

The Table above shows the improvements obtained for three series: the IIP, Exports and CPI.

For the IIP, the raw series has a standard deviation of the point-on-point change of 73.26%. If Eviews is used as a black box, a sharp gain is obtained, and the volatility drops to 25.73. Our procedures add value, getting the standard deviation down to 23.12.

For the exports series, the raw data has a standard deviation of the point-on-point change of 132.53%. This drops to 89.4% using Eviews as a black box, and improves further to 78.01% using the steps described in the paper.

In the case of the CPI, the raw series has a standard deviation of point-on-point changes of 9.22%. Eviews as a black box is unable to process this series. Our best procedures get the standard deviation down to 7.28%.

The main finding of this paper is that the use of black box seasonal adjustment, e.g. by Eviews, yields a substantial reduction in the standard deviation of the point-on-point series. When a blackbox can do seasonal adjustment, it is better to do this when compared with using the year-on-year changes. However, careful analysis of seasonality is a superior approach: it works reliably for all series and it yields improved reductions in the variance of the point-on-point series.

### References

Rudrani Bhattacharya, Radhika Pandey, Ila Patnaik and Ajay Shah. Seasonal adjustment of Indian macroeconomic time-series. NIPFP Working Paper, January 2016.

Rudrani Bhattacharya, Ila Patnaik, Ajay Shah. Early warnings of inflation in India, Economic and Political Weekly, November 2008.

Chetan Ghate, Radhika Pandey and Ila Patnaik. Has India Emerged? Business Cycle Facts from a Transitioning Economy. Structural Change and Economic Dynamics, Volume 24, Page 157-172, March 2013.

Ajay Shah. New issues in macroeconomic policy Chapter 2, page 26--54 in Business Standard India edited by T. N. Ninan, Business Standard Books, 2008.

#### 1 comment:

1. For last two months (Oct2015 and Nov2015 releases) the IIP growth figure suffered significant seasonal (Diwali effect) effect which increased sudden volatility in the growth trend. A consistent release of proper seasonally adjusted data is important and required. Other wise, users will keep using black boxes (like EViews etc.) to generate seasonally adjusted data to get some meaningful understanding from non-seasonally adjusted data.

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