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

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

The 6th Eurostat Colloquium on Modern Tools for Business Cycle Analysis:

“The Lessons from Global Economic Crisis” 26-29 Sep. 2010, Luxembourg

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

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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).

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By removing the moving holiday effect, the important features

• f 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.

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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.

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Procedures:

• 1. Seasonal Adjustment for Malaysia

(SEAM)

• 2. Regression-ARIMA (regARIMA) using

SEASABS package

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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)

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Step 1: Run X-12 ARIMA program and obtained “Final trend-cycle, (D12) ” and “Final Irregular, (D11)” Step 2: Estimate the True Irregular (without moving holiday effect) Based on the multiplicative assumption, the model is represented as, However, During the first run of X-12 ARIMA, the component was automatically removed. Estimate the moving holiday effect

• Fit a regression model to the component
• The estimated function (holiday effect) is then given as,

ε β β

t t t

h I + + =

1

h I

t t

β β ˆ ˆ ˆ

1 0 +

= I S T Y

t t t t

× × = ′ × × =

t t t t

I H E I

t

I

t

T

t

E

t

E

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is the dummy variable for the holiday effect assigned using 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 by dividing the irregular component ( ) by the estimated values of irregular component ( ). Step 4: Seasonally Adjusting the series The series is seasonally adjusted for moving holiday effect by multiplying with . is a new series free from moving holiday effects. SEAM was carried out using X-12 in SAS.

t

I

″ =

t t t

I I I ˆ

″ I t

t

h

t

T

″ × = ′

t t t

I T Y

′

t

Y

t

I ˆ

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• Regression-ARIMA

is part

• f

X-12 ARIMA modelling capabilities.

• RegArima procedure was carried out using

SEASABS (SEASonal Analysis, Australia Bureau

• f

Statistics Standards).

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• 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

• n

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.

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• 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).

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w n1

REG1

Case 1 : when the festival fall in the beginning of the month (1st - 15th),

in the respective festive month before the respective festive month 0 otherwise n1 no. of holidays fall in the festive mth. , n2 no. of holidays fall before the festive mth.

Case 2 : when the festival fall at the end of the month (16th – 31st)

in the respective festive month after the respective festive month 0 otherwise n1 no. of holidays fall in the festive mth. , n2 no. of holidays fall after the festive mth. w n1 w n2

Reg1 =

w n2

Reg1 = w = 8 for CNY w = 7 for Eid-ul Fitr w = 4 for Deepavali w = 8 for CNY w = 7 for Eid-ul Fitr w = 4 for Deepavali

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• REG1
• Example of REG1 using one dummy variable

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

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w n1

REG3

Case 1 : when the festival fall in the beginning of the month (1st - 15th), in the respective festive month before the respective festive month

• 1 after the respective festive month

0 otherwise Case 2 : when the festival fall at the end of the month (16th – 31st) in the respective festive month after the respective festive month

• 1 before the respective festive month

0 otherwise w n1 w n2

Reg3 =

w n2

Reg3 =

w=8 for CNY w=7 for Eid-ul Fitr w=4 for Deepavali n1 =no. of holidays fall in festive mth. n2 =no. of holidays fall before festive mth w=8 for CNY w=7 for Eid-ul Fitr w=4 for Deepavali n1 =no. of holidays fall in festive mth. n2 =no. of holidays fall after festive mth

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• REG3
• Example of REG3 using three dummy variables

Year

Month

Date of Festival Dummy Variable Chinese New Year Eid-ul Fitr Deepavali 1986 9 1986 10 0.25 1986 11 1-Nov 0.75 1986 12

• 1
• 1

1987 1 29-Jan 0.62 1987 2 0.38 1987 3 1987 4

• 1

1987 5 29-May 0.71 1987 6 0.29 1987 7 1987 8

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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

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Test for the Presence of Seasonality

ORIGINAL DATA SERIES STABLE SEASONALITY (test at 0.1%) MOVING SEASONALITY (test at 1%) ( * test at 5%) COMBINED TEST

F-value p-value Presence F-value p-value

Presence SEASONALITY 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

All series were found to have significant presence of seasonality effect.

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Test for Moving Holiday Effects

REGRESSOR TIME SERIES DATA TEST FOR MOVING HOLIDAY EFFECT (α=0.05) 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

The effects of moving holidays are significant at 5% level of significance.

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Test for Moving Holiday Effects

REGRESSOR TIME SERIES DATA TEST FOR MOVING HOLIDAY EFFECT (α=0.05) 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

The effects of moving holidays are significant at 5% level of significance.

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Test for Presence of Seasonality for Seasonally Adjusted Series

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Ranking the p-value of moving seasonality based on regressors

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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.

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To determine which procedure performs better in forecasting of trend for seasonally adjusted time series, ARIMA models were fitted to the data series. Based on Ljung-Box test, AIC and RMSE the best ARIMA models were then selected.

) (

2 ] [ p

n K −

α

χ

Data Series ARIMA Model Ljung-Box AIC MSE Best ARIMA Model d.f p-value IMPORT (5,1,1)(1,0,0)12 4 7.8 0.101 3989.94 704.30 (5,1,1)(1,0,0)12 (5,1,2)(1,0,0)12 4 4.6 0.329 3991.63 707.24 (5,1,2)(1,0,1)12 3 4.3 0.233 3992.88 704.74 EXPORT (3,1,0)(1,0,0)12 8 7.0 0.533 3942.52 786.05 (4,1,0)(1,0,0)12 7 7.5 0.381 3944.51 787.41 (5,1,0)(1,0,0)12 6 2.5 0.870 3941.88 779.27 (5,1,0)(1,0,0)12 OMP (4,1,0)(1,0,0)12 7 6.5 0.488 7396.24 421688.42 (4,1,0)(1,0,1)12 6 6.5 0.374 7397.83 422466.82 (5,1,0)(1,0,0)12 6 2.3 0.888 7377.45 419533.64 (5,1,0)(1,0,0)12

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To determine which procedure performs better, the evaluation of forecast accuracy is performed using out-of-sample evaluation. Based

• n RMSE and MAPE the best procedure was then selected.

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Summary of ranking based on RMSE and MAPE.

• The SEAM method has smaller total rank for REG1 and REG3.
• Overall conclusion, the SEAM method provides better forecasts of the underlying

trend as compared to RegARIMA method.

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• Most of the Malaysian economic time series data are

significantly affected by moving holiday effects.

• The application of the seasonal adjustment procedure using

SEAM and RegARIMA can significantly eliminate the presence

• f the moving holiday effects and able to seasonally adjust the

data series.

• Overall, SEAM performs better than RegARIMA in removing the

moving holiday effect and hence improved the forecast of trend values.

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