1. USING DEMETRA+ IN DAILY WORK SAUG – Luxembourg, 16 October 2012 Enrico INFANTE, Eurostat Unit B1: Quality, Methodology and Research

2. 2 Summary Price Series –Price Volatility Analysis Production Series –Seasonal Adjustment –SARIMA Forecasts –Current vs. Concurrent Adjustment –Direct vs. Indirect approach IB test –In the future… SAUG – Luxembourg, 16 October 2012 Enrico Infante

3. 3 The study is conducted on Italian food and agricultural data SAUG – Luxembourg, 16 October 2012 Enrico Infante Price Volatility Analysis PRICE SERIES Price Volatility Analysis

4. 4 How many series? Sector Price Volatility Analysis Milk1 Butchering10 Agro-food48 Ichthyic12 Total71 SAUG – Luxembourg, 16 October 2012 Enrico Infante Price Volatility Analysis

5. 5 The basic idea is to check whether the price of a determined product in a determined period is outside the expected trend. The procedure follows three main steps: 1.Model the series without the last three observations using a SARIMA(p,d,q)(P,D,Q) 2.Using the model identified during step 1 to produce forecast intervals for the three observations not considered in step 1 3.Check whether the price observed is inside or outside the forecast interval If the price observed is outside the interval, then there is high volatility SAUG – Luxembourg, 16 October 2012 Enrico Infante

6. 6 The procedure is the follow SAUG – Luxembourg, 16 October 2012 Enrico Infante Price Series SARIMA model without 3 obs. Forecast intervals Detect the volatility degree Price Volatility Analysis

7. 7 Example: Parmigiano Reggiano and Grana Padano There is low volatility for the "Grana Padano", as the observed price is in the forecasted interval There is high volatility for the "Parmigiano Reggiano", as the observed price is not within the forecasted interval SAUG – Luxembourg, 16 October 2012 Enrico Infante Price Volatility Analysis

8. 8 Special cases (e.g. fruit) In some cases (typically for the fruit series) there are data just for a certain period of the year. In these cases the available data are considered consecutive, and no seasonal and/or calendar effects are considered SAUG – Luxembourg, 16 October 2012 Enrico Infante Price Volatility Analysis

9. 9 The study is conducted on Italian food and agricultural data SAUG – Luxembourg, 16 October 2012 Enrico Infante Seasonal Adjustment Forecast Direct/Indirect approach Current/Concurrent Adjustment PRODUCTION SERIES Seasonal Adjustment

10. 10 How many series? SectorSA and Forecast Milk5 Butchering21 Ichthyic1 Import/Export Agro-food99 Import/Export Ichthyic20 Total145 SAUG – Luxembourg, 16 October 2012 Enrico Infante Seasonal Adjustment

11. 11 Seasonal Adjustment The series are seasonally adjusted following the ESS guidelines A knowledge of the sectors is a key part for modelling outliers, calendar effects, etc. The series are modelled using the TRAMO/SEATS modules of Demetra+ The models detected from the automatic procedure (RSA4) are modified, when necessary, in order to get better results If necessary, the earliest years are removed from the model SAUG – Luxembourg, 16 October 2012 Enrico Infante

12. 12 SARIMA Forecasts The study focuses on the forecasts of the series The first step is to identify the SARIMA model  Demetra+ forecasts The forecasts are sometimes "adjusted" basing on qualitative information Example: Milk The total milk produced in Italy is more or less the same amount for every production year (from April to March). So the values obtained from Demetra+ are adjusted in order to get the same total (10883,073) SAUG – Luxembourg, 16 October 2012 Enrico Infante

13. 13 Current vs. Concurrent Adjustment The way in which Seasonal Adjustment is carried out has implications for the revisions of seasonally adjusted data There are monthly series that are updated every quarter, so each quarter there are 3 new observations Usually there are no revisions on the series, and even if there are some, they are very small SAUG – Luxembourg, 16 October 2012 Enrico Infante

14. 14 Current vs. Concurrent Adjustment A partial Concurrent Adjustment strategy is chosen, with an update of the parameters coefficient and outliers in the last year SAUG – Luxembourg, 16 October 2012 Enrico Infante The main issue arises when the chosen model does not produce good forecasts, even if the model seems to be good. In that case the model is re-estimated in order to get better results in terms of forecasts

15. 15 Direct vs. Indirect approach Some series are aggregated at different levels In order to decide which approach to follow, an a priori test has been used The main advantage of using an a priori test is that the choice is made on statistical bases without running any seasonal adjustment procedure The test used is the so-called IB test, that is in line with the ESS guidelines on Seasonal Adjustment: when the series composing the aggregate have common similar seasonal patterns, a Direct approach would be used The test is performed using R scripts SAUG – Luxembourg, 16 October 2012 Enrico Infante

16. 16 Direct vs. Indirect approach – IB test The basic idea of the IB test is stated in Infante and Buono (2012)Infante and Buono (2012) The classic test for moving seasonality is based on a 2-way ANOVA test, where the two factors are the time frequency (usually months or quarters) and the years. This test is based on a 3-way ANOVA model, where the three factors are the time frequency, the years and the series The variables tested are the de-trended series, where the trend is determined by applying a Hodrick-Prescott filter for each series The notation SI is kept for remarking the fact that it is a de-trended series SAUG – Luxembourg, 16 October 2012 Enrico Infante

17. 17 Direct vs. Indirect approach – IB test The model is: Where: a i, i=1,…,M, represents the numerical contribution due to the effect of the i-th time frequency (usually M=12 or M=4) b j, j=1,…,N, represents the numerical contribution due to the effect of the j-th year c k, k=1,…,S, represents the numerical contribution due to the effect of the k-th series of the aggregate The residual component term e ijk (assumed to be normally distributed with zero mean, constant variance and zero covariance) represents the effect on the values of the SI of the whole set of factors not explicitly taken into account in the model SAUG – Luxembourg, 16 October 2012 Enrico Infante

18. 18 Direct vs. Indirect approach – IB test The test is based on the decomposition of the variance of the observations: Between time frequencies variance Between years variance Between series variance Residual variance SAUG – Luxembourg, 16 October 2012 Enrico Infante

19. 19 Direct vs. Indirect approach – IB test The table for the ANOVA test VARMeandfSum of Squares SAUG – Luxembourg, 16 October 2012 Enrico Infante

20. 20 Direct vs. Indirect approach – IB test The null hypothesis is made by taking into consideration that there is no change in seasonality over the series The test statistic is the ratio of the between series variance and the residual variance, and it follows a Fisher-Snedecor distribution with (S-1) and (MNS-1)-(M-1)-(N-1)-(S-1) degrees of freedom Rejecting the null hypothesis is to say that the pure Direct Approach should be avoided, and an Indirect Approach should be considered SAUG – Luxembourg, 16 October 2012 Enrico Infante

21. 21 Direct vs. Indirect approach – IB test An example: butchering pork SAUG – Luxembourg, 16 October 2012 Enrico Infante

22. 22 Direct vs. Indirect approach – IB test An example: butchering pork SAUG – Luxembourg, 16 October 2012 Enrico Infante VARMean Squaredf Months4.818.439.36611 Years1.135.483.53310 Series141.362.592.2582 Residual1.054.706.450384 There is no evidence of common seasonal patterns between the series at 5 per cent level An Indirect approach is recommended

23. 23 In the future… From Demetra+ to Jdemetra+!!! SAUG – Luxembourg, 16 October 2012 Enrico Infante

24. 24 In the future… SAUG – Luxembourg, 16 October 2012 Enrico Infante Assessment for residual seasonality Additive aggregate What if the aggregation function is different? Test a priori Java code (older version) R code

25. 25 Questions Many thanks for your attention!!! SAUG – Luxembourg, 16 October 2012 Enrico Infante Your questions and comments are very welcome!