Pre-treatment practices for Seasonal Adjustment Including Calendar Adjustment

1. Pre-treatment practices forSeasonal Adjustment Including Calendar Adjustment Necmettin Alpay KOÇAK UNECE Workshop on Short-Term Statistics (STS) and Seasonal Adjustment 14 – 17 March 2011 Astana, Kazakhstan 1 4.1.2020

2. Introduction • Seasonal adjustment is a statistical procedure with the target of removing the seasonal (and calendar) component from a time series. • The idea behind is that a series is composed by unobserved components such as trend, cycle, seasonality, irregular • The seasonal component disturbs short-term analysis, so it is removed from the original series to facilitate the monitoring and interpretation of the economy by analysts 2 4.1.2020

3. First step: the graph of the series Each series must be plotted against time to detect visually whether or not a seasonal component is present (but in some case it is not sufficient!) Example: Industrial production index - Total, Kazakhstan : Period: 2000M1-2010M10 3 4.1.2020

4. First step: the graph of the series Seasonal graphs are a special form of line graph in which you plot separate line graphs for each season in a regular frequency monthly or quarterly data. Example: Industrial production index - Total, Kazakhstan : Period: 2000M1-2010M10

5. Theunobserved components

6. Decomposition scheme • A time series yt can be decomposed in Yt = TCt +St+εt • A time series yt can also be decomposed in Yt = TCt×St×εt log(Yt)=log(TCt)+log(St)+log(εt) The Additive model Multiplicative model

7. The REG-ARIMA model • The REG-ARIMA model is a convenient way to represent a timeseries with deterministic and stochastic effects. Given theobserved time series zt , it is expressed as, zt = ytβ+xt Φ(B)δ(B)xt=θ(B)at • where • β is a vector of regression coefficients • yt denotes n regression variables • B is the backshift operator (Bkyt = yt-k ) • Φ(B), δ(B), and θ(B) are finite polynomials in B • at is assumed a normal independentlyidentically distributed(NIID)(0,σa2) white-noiseinnovation

8. The regression variables • The regression variables capture thedeterministic components ofthe series. In TS, these can be of different type: • Calendar effects • Trading day effect • Easter effect • Leap-year effect • Holidays • Intervention variables generated by the program • Regression variables entered by the user • Outliers

9. The ARIMA model • Model-based-pre-adjustment identifies and fits an ARIMA model on the linearized series (cleaned from deterministic effects). The ARIMA model is composed of three components: • the stationary AR component (polynomial Φ(B)) • the non-stationary AR component (polynomial δ(B)) • the invertible MA component (polynomial θ(B)) • For seasonal time series, the polynomials are given by: • Φ(B) = (1+ Φ1B + … + ΦpBp)(1+ Φ1Bs + …+ ΦPBs×P) • δ(B) = (1-B)d(1-Bs)D • θ(B) = (1+ θ1B + … + θpBp)(1+ θ1Bs + …+ θPBs×P) • A seasonal ARIMA model is identied by the order of itspolynomials: (p;d;q)(P;D;Q)

10. TRAMO / Reg-ARIMA • Program for estimation, forecasting, and interpolation ofregression models with missing observations and ARIMAerrors, with possibly several types of outliers • The program is aimed at monthly or lower frequency data(quarterly, semester, 4-month, bimonth, semester, year) • Performs a pretesting to decide between a log transformationand no transformation

11. TRAMO / Reg-ARIMA • Identifies the ARIMA model through anAutomatic ModelIdentification (AMI) procedure • Interpolates missing values • Detects outliers • Estimates the REG-Arima model • Computes forecasts

12. Automatic model identication • The ARIMA model can be automatically identified by theprogram • Two steps • Obtains the order of differencing • max order ∆2 ∆s • Obtains the multiplicative stationary ARMA model • 0<=(p;q)<=3 • 0 <=(ps;qs )<=1 • Chosen with the BIC criterion, favors balanced model (similarorders of AR and MA parts) • Otherwise, it can be input by the user (parameters P,D,Q, BP,BD, BQ) • It works jointly with the Automatic Outlier Detection andCorrection (AODC)

13. Outliers • They represent the effect on the time series of some special events(new regulation, major political or economical reform, strike,natural disaster). Three possible forms of outliers: • Additive outliers (AO) • Level Shift (LS) • Transitory Changes (TC)

14. Outliers

15. Calendar effects • Calendar adjustment removes those non-seasonal calendar effectsfrom the series, for which there is statistical evidence and aneconomic explanation. Four possibilities in TS: • Trading days (working/non-working, 6 regressors)) • National and moving holidays ((provided by the user)) • Leap-year (TS versus X-12-ARIMA) • Easter • A pre-testing on the presence of theseeffects. • If trading days are significant, adding the holidays variableimproves significantly the results!

16. Examples of calendar effects

17. Trading/Working Day Adjustment • Aims at a series independent of the length and the composition in days • Length of month, number of working days and weekend days, composition of working days (Monday/Friday) • Working or trading-day adjustment is recommended for series with such effects • If effects not present –Regressors should not be applied • Compile, maintain and update national calendars! • A historical list of public holidays including information on compensation holidays

18. Correction for Moving Holidays • Occur irregularly in the course of the year • Correct for detected moving holidays in series • Not removed by standard filters • If effects not present –Regressors should not be applied • These effects may be partly seasonal: • The Catholic Easter, for example, falls more often in April than in March • Since the seasonal part is captured by seasonal adjustment filters, it should not be removed during the calendar adjustment

19. An illustrative example for national calendar regressor

20. Original vs. Linearized series