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Ratio Transformation for Stationary Time Series with Special Application in Consumer Price Index in Qatar. By: Adil Yousif , Hind Alrkeb , Doha Alhashmi Department of Mathematics and Statistics Qatar University Doha, Qatar. Abstract.
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AdilYousif, Hind Alrkeb, Doha Alhashmi
Department of Mathematics and Statistics
This article was intended to perform a comprehensive time series analysis for Consumer Price Index (CPI) in Qatar. The data was obtained from the Statistics Authority in Qatar. For the period between: (2002-2009) a quarterly data was analyzed using several time series techniques such as Exponential Trend method, Holts’ Trend method, and ARIMA. These methods were used to examine trends and built a forecast model. Ratio transformation technique was used to obtain a stationary time series and found to be efficient with small size of data.
Despite the small size of the data the analysis indicated that ARIMA model is more adequate forecast one.
Key words: Time series, index, CPI, ARIMA, Ratio Transformation
The GDP has increased rapidly during the last period. It reached 268 billion Qatari Riyals (73.4 billion US Dollar) in 2009 as per the estimation of Statistics Authority.
The growth rates of the GDP during last three years were 34%, 13%, and 15% in the years 2006, 2007 and 2008 respectively.
As Qatar’s economy is in the booming phase, the prices level increased rapidly during last years as a result of expanding in the Building & Construction sector. This expansion caused inflation in rent rates, and hence affected the prices level in Qatar
Both exponential trend method and Holts’ Double Exponential Smoothing were used and the last outperformed the first when their MADs are compared.
Figure  shows the fitted values versus actual values and one year ahead of forecast together with their 95% prediction interval for the Holt’s exponential model.
It appears that there is an increasing trend in the Household variable with a MAD (1.21962).
The one year a head forecasts of this model are displayed in table 
Also from the table  it can be noticed that Ljung-Box test has a p –value associated with for lags K = 12 and K = 24 are both greater than 0.05. Hence, it can be concluded that model is adequate. Moreover since =0.4095 < 1 then the third difference data is stationary.
Modified Box-Pierce (Ljung-Box) Chi-Square statistic