Calendar variation model based on ARIMAX for forecasting sales data with Ramadhan effect

Many economics and business data are compiled each month and are available as monthly time series. Such time series may be subjected to two kinds of calendar effects, namely trading day and holiday effects. The objective of this research is to develop a calendar variation model based on ARIMAX method for forecasting sales data with Ramadhan effect. In most Islamic countries, the trade activities frequently contain calendar variation pattern due to the consumption to certain products usually follows lunar calendar, instead of following common solar calendar. Firstly, this research focuses on the development of model building procedure to find the best calendar variation model. In this ARIMAX method, the deterministic and stochastic trends are examined. The procedure for fitting the ARIMAX model consists of only modeling calendar variation effect, its error, and adaptively combining the calendar variation effect and ARIMA model. This procedure is applied in modeling and forecasting of sales data, i.e. the monthly sales of Moslem boys’ clothes in Indonesia. The results show that the proposed model yields better forecast at out-sample data compared to the Decomposition method and Seasonal ARIMA, and Neural Networks.

[1]  Dany Pfeffermann,et al.  Festival and Working Days Prior Adjustments in Economic Time Series , 1982 .

[2]  Richard H. Thaler,et al.  Seasonal Movements in Security Prices II: Weekend, Holiday, Turn of the Month, and Intraday Effects , 1987 .

[3]  Lei Gao,et al.  Calendar Effects in Chinese Stock Market , 2005 .

[4]  A. Speight,et al.  Intraday periodicity, calendar and announcement effects in Euro exchange rate volatility , 2010 .

[5]  John L. Thompson,et al.  The Asian crisis and calendar effects on stock returns in Thailand , 2005, Eur. J. Oper. Res..

[6]  Chris Brooks,et al.  Seasonality in Southeast Asian stock markets: some new evidence on day-of-the-week effects , 2001, Applied Economics Letters.

[7]  David Michayluk,et al.  The persistent holiday effect: additional evidence , 1998 .

[8]  R. Ariel,et al.  High Stock Returns before Holidays: Existence and Evidence on Possible Causes , 1990 .

[9]  P. Alagidede.  Month-of-the-year and pre-holiday seasonality in African stock markets , 2008 .

[10]  T. Mills,et al.  Calendar effects in the London Stock Exchange FT-SE indices , 1995 .

[11]  William S. Cleveland,et al.  Calendar Effects in Monthly Time Series: Modeling and Adjustment , 1982 .

[12]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[13]  Lon-Mu Liu,et al.  Identification of time series models in the presence of calendar variation , 1986 .

[14]  Osamah M. Al-Khazali,et al.  Calendar anomaly in the Greek stock market: Stochastic dominance analysis , 2008 .

[15]  Chris Chatfield,et al.  Time series forecasting with neural networks: a comparative study using the air line data , 2008 .

[16]  E. Balaban.  Day of the week effects: new evidence from an emerging stock market , 1995 .

[17]  P. Alagidede.  Day of the week seasonality in African stock markets , 2008 .

[18]  Allan Timmermann,et al.  Dangers of data mining: the case of calendar effects in stock returns , 2001 .

[19]  Steven C. Hillmer,et al.  Modeling Time Series with Calendar Variation , 1983 .

[20]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[21]  R. C. Vergin,et al.  Revisiting the Holiday Effect: is it on holiday? , 1999 .

[22]  A. Abraham,et al.  Seasonality in stock returns and volatility: The Ramadan effect , 2005 .

[23]  Steven C. Hillmer.  Forecasting Time Series with Trading Day Variation , 1982 .

[24]  William S. Cleveland,et al.  Calendar Effects in Monthly Time Series: Detection by Spectrum Analysis and Graphical Methods , 1980 .