The 6 th Eurostat Colloquium on Modern Tools for Business Cycle - PowerPoint PPT Presentation

The 6 th Eurostat Colloquium on Modern Tools for Business Cycle Analysis: “ The Lessons from Global Economic Crisis ” 26-29 Sep. 2010, Luxembourg Norhayati Shuja’ ’ Norhayati Shuja Department of Statistics, Malaysia Department of Statistics, Malaysia Mohd. Alias Lazim Mohd. Alias Lazim Yap Bee Wah Yap Bee Wah Universiti Teknologi MARA, Malaysia Universiti Teknologi MARA, Malaysia

� Introduction � Research Objective � Methodology � Data Analysis & Results � Evaluating Models’ Forecast Performance � Conclusion 2

� Certain kinds of economic activities and their associated time series are affected significantly by holidays ( Findley & Soukop, 2000 ) � These holidays tend to affect or influence the economic activities for the periods in the vicinity of the holiday dates. � Incidentally, there are some holidays whose event dates are not fixed at any specific location within a year period but move from one point to the next. � The impact of these festival holidays on the time series data need to be taken into account when performing seasonal adjustment so as to avoid misleading interpretations on the seasonally adjusted and trend estimates ( Zhang et al., 2001 ). 3

� By removing the moving holiday effect, the important features of economic series such as direction, turning points and consistency between other economic indicators can be easily identified ( Ashley, 2001 ). � In the context of Malaysia, the economic time series data are affected by the major religious festivals, i.e, the Eid-ul Fitr of the Muslims, the Chinese New Year of the Chinese and the Deepavali of the Indians. � The dates of these festivals are determined by the respective religious calendar and do not fall on fixed date of the Gregorian calendar. � Due to the importance of eliminating the effect of moving holiday from time series data, we explore a different procedure for eliminating non-fixed seasonal effect with the aim of achieving more reliable methods in improving trend-cycle forecast. 4

The research objective of this study is: � to explore and to develop a different procedure that can be used to eliminate the non-fixed seasonal effects on Malaysian economic time series data with the aim of achieving more reliable methods in improving trend-cycle forecast. 5

Procedures: 1. Seasonal Adjustment for Malaysia (SEAM) 2. Regression-ARIMA (regARIMA) using SEASABS package 6

The five data series selected are : 1. Monthly Total Imports (IMPORT) 2. Monthly Total Exports (EXPORT) 3. Monthly Sales Value of Own Manufactured Products (Ex-Factory) (OMP) 4. Monthly Production of Palm Oil (PALM) 5. Monthly Manufacture & Assembly of Motor Vehicle (1600 cc & below) (VEHICLE) 7

Step 1: Run X-12 ARIMA program and obtained “Final trend-cycle, T t (D12) ” and “Final Irregular, (D11)” I t Step 2: Estimate the True Irregular (without moving holiday effect) Based on the multiplicative assumption, the model is represented as, = × × Y T S I t t t t E ′ t However, = × × I E H I t t t t E During the first run of X-12 ARIMA, the component was t automatically removed. Estimate the moving holiday effect - Fit a regression model to the component = β + β + ε I h t t t 0 1 - The estimated function (holiday effect) is then given as, ˆ ˆ = 0 + ˆ β β h I t t 1 8

h is the dummy variable for the holiday effect assigned using t REG1 and REG3 (will be explained under Regressor) Step 3: Removing the ‘Moving Holiday’ component The process of removing the ‘moving holiday effect’, is done I by dividing the irregular component ( ) by the estimated t ˆ values of irregular component ( ). I t I ″ t = I t ˆ I t Step 4: Seasonally Adjusting the series The series is seasonally adjusted for moving holiday effect by ″ T multiplying with . I t t ′ ″ = × Y T I t t t ′ Y is a new series free from moving holiday effects. t SEAM was carried out using X-12 in SAS . 9

� Regression-ARIMA is part of X-12 ARIMA modelling capabilities. � RegArima procedure was carried out using SEASABS (SEASonal Analysis, Australia Bureau of Statistics Standards). 10

� The numbers of holidays taken before, during and after the festivals were used to construct the regressors. � To determine the number of holidays, a sample survey was conducted on 350 individuals primarily to collect information on the number of holidays taken to celebrate the festivals. The results as shown below; Festival Before During After TOTAL 1. Eid-ul Fitr 2 2 3 7 2. Chinese New Year 2 2 4 8 3. Deepavali 1 1 2 4 Note: “ During ” refer to the number of public holiday for respective festival. 11

� Two regressors were proposed; REG1 and REG3. 1. REG1 using one dummy variable (Eid-ul Fitr, Chinese New Year and Deepavali are combined). 3. REG3 using three dummy variables (Eid-ul Fitr, Chinese New Year and Deepavali are separated into three different dummy variables). 12

REG1 Case 1 : when the festival fall in the beginning of the month (1 st - 15 th ), n 1 in the respective festive month w = 8 for CNY w w = 7 for Eid-ul Fitr Reg1 = n 2 before the respective festive month w = 4 for Deepavali w 0 otherwise n 1 no. of holidays fall in the festive mth. , n 2 no. of holidays fall before the festive mth. Case 2 : when the festival fall at the end of the month (16 th – 31 st ) n 1 in the respective festive month w w = 8 for CNY Reg1 = w = 7 for Eid-ul Fitr n 2 after the respective festive month w = 4 for Deepavali w 0 otherwise 13 n 1 no. of holidays fall in the festive mth. , n 2 no. of holidays fall after the festive mth.

� REG1 � Example of REG1 using one dummy variable Dummy Year Month Date of Festival Ratio Variable 1986 9 0.00 1986 10 1/4 0.25 1986 11 0.75 1-Nov 3/4 1986 12 0.00 1987 1 0.62 29-Jan 5/8 1987 2 3/8 0.38 1987 3 0.00 1987 4 0.00 1987 5 0.71 29-May 5/7 1987 6 2/7 0.29 1987 7 0.00 1987 8 0.00 14

REG3 Case 1 : when the festival fall in the beginning of the month (1 st - 15 th ), n 1 in the respective festive month w w =8 for CNY n 2 w =7 for Eid-ul Fitr before the respective festive month w =4 for Deepavali w Reg3 = n 1 =no. of holidays fall in festive mth. -1 after the respective festive month n 2 =no. of holidays fall before festive mth 0 otherwise Case 2 : when the festival fall at the end of the month (16 th – 31 st ) n 1 in the respective festive month w w =8 for CNY n 2 w =7 for Eid-ul Fitr after the respective festive month w =4 for Deepavali w Reg3 = n 1 =no. of holidays fall in festive mth. -1 before the respective festive month n 2 =no. of holidays fall after festive mth 15 0 otherwise

� REG3 � Example of REG3 using three dummy variables Dummy Variable Date of Year Month Chinese New Eid-ul Festival Deepavali Year Fitr 1986 9 0 0 0 1986 10 0 0 0.25 1986 11 1-Nov 0 0 0.75 1986 12 -1 0 -1 1987 1 29-Jan 0.62 0 0 1987 2 0.38 0 0 1987 3 0 0 0 1987 4 0 -1 0 1987 5 29-May 0 0.71 0 1987 6 0 0.29 0 1987 7 0 0 0 16 1987 8 0 0 0

Step 1 : Test for Seasonality Effect Step 2 : Test for the Presence of Individual Festival Effect (REG1 & REG3) Step 3 : Test for Moving Holiday Effect Step 4 : Apply SEAM & Reg-ARIMA Step 5 : Test the Seasonally Adjusted Data for the Presence of Seasonality Step 6 : Compare the Performance of SEAM and Reg-ARIMA in Removing Holiday Effect Step 7 : Forecast using ARIMA Models Step 8 : Compare Forecast Performance of SEAM and Reg- ARIMA 17

Test for the Presence of Seasonality All series were found to have significant presence of seasonality effect. STABLE SEASONALITY MOVING SEASONALITY COMBINED (test at 0.1%) (test at 1%) ( * test at 5%) TEST ORIGINAL DATA SERIES SEASONALITY F-value p-value Presence F-value p-value Presence PRESENCE 1 IMPORT 12.452 0.00 YES 3.719 0.00 YES YES 2 EXPORT 16.391 0.00 YES 4.972 0.00 YES YES 3 OMP 3.523 0.00 YES 5.161 0.001 YES YES 4 PALM 19.283 0.00 YES 9.341 0.0002 YES YES 5 VEHICLE 11.371 0.99 YES 1.889 0.00 YES YES 18

Test for Moving Holiday Effects The effects of moving holidays are significant at 5% level of significance. TEST FOR MOVING HOLIDAY EFFECT TIME SERIES ( α =0.05) REGRESSOR DATA F-value p-value Presence REG1 IMPORT 28.677 0.000 YES EXPORT 44.492 0.000 YES OMP 26.204 0.000 YES PALM 16.724 0.000 YES VEHICLE 24.628 0.000 YES 19

Test for Moving Holiday Effects The effects of moving holidays are significant at 5% level of significance. TEST FOR MOVING HOLIDAY EFFECT TIME SERIES ( α =0.05) REGRESSOR DATA F-value p-value Presence REG3 IMPORT 13.881 0.000 YES EXPORT 23.993 0.000 YES OMP 14.356 0.000 YES PALM 12.678 0.000 YES VEHICLE 12.865 0.000 YES 20

Test for Presence of Seasonality for Seasonally Adjusted Series 21

Ranking the p-value of moving seasonality based on regressors 22

Summary of Total Rank for SEAM and RegARIMA • The smallest total rank value will be considered as the more effective procedure. • Conclusion, the SEAM method is more effective than the RegARIMA in removing the moving holiday effect. 23