# THE SHIFT INVARIANT DISCRETE WAVELET TRANSFORM (SIDWT) WITH INFLATION TIME SERIES APPLICATION

**Abstract**

Analysis of time series used in many areas, one of which is in the field economy. In this research using time series on inflation using Shift Invariant Discrete Wavelet Transform (SIDWT).Time series decomposition using transformation wavelet namely SIDWT with Haar filter and D4. Results of the transformation, coefficient of drag coefficient wavelet and scale that is used for modeling time series. Modeling was done by using Multiscale Autoregressive (MAR). In a certain area, inflation to it is important that he had made the standard-bearer of the economic well-being of society, the factors Directors investors in selecting a kind of investment, and the determining factor for the government to formulate policy fiscal, monetary, as well as non-monetary that will be applied. Inflation can be analyzed using methods Shift Invariant Discrete Wavelet Transform (SIDWT) which had been modeled for them to use Multiscale Autoregressive (MAR) with the R^{2} value 93.62%.

**Keywords**: Shift Invariant Discrete Wavelet Transform (SIDWT), Time Series, Multiscale Autoregressive (MAR), Inflation.

**INTRODUCTION**

Accord In a certain area, inflation to it is an important that had made the standard-bearer of the economic well-being of society, the factors Directors investors in selecting a kind of investment, and the determining factor for the government to formulate policy fiscal, monetary, as well as non-monetary that will be applied. In general, inflation can lead to less investment in a country, encouraging an increase in interest rate, to encourage investment that is speculative, failure execution of development, the instability, economic balance of payments and a decline, life, and welfare of the people. Understanding investors will impact of inflation in a high rate of return or profits investment is needed at the time investors will choose the kind of investment that will be done. This is because inflation has an impact on the value of the money that was invested by investors. High inflation will increase the risk investment projects in the long term [8]

According to the Bank Indonesia, the inflation is defined as well as the price in general and on an ongoing basis. In this sense there are two things, namely definition price increase, there will a persistent upward shift at request movement and price rises in all the groups goods and services or the general price level movement. The price of one or two work is not to be called inflation unless that increase widespread or lead to price increases in many other things. The count inflation will be done through approach consumer price index, known as Capital Price Index (CPI) as indicators to measure to consume fees from the market and services. Inflation as measured by the Indonesian CPI grouped into 7 groups spending (based on the Classification of individual measured by purpose-COICOP), which is: A group food, the group food, drinks, and tobacco, the group housing, the group clothing, the group health, education and sports group, as well as groups transport and communications. Monetary Policy is not just to react to inflationary pressure is going on now, but should respond to inflationary pressures that will come (forward-looking monetary policy. Inflation that is relatively high and to draw up a policy that was able to respond to inflationary pressure in the future, so it needs to be the prediction of inflation. The prediction that accurate will give important role in determining the policy of the government had an impact on people’s welfare, and investment world. Because of its importance, of the forecasting of the inflation rate to be important in order to assist the government in taking a policy to maintain monetary stability and the economy. Predictions can give an idea about the future of the closest to reality. To predict future data can be done by studying the past historical data or time. The data has been sorted by, time will be studied pattern forming time series model to determine the fluctuations in the data.

Modeling of time series with classic parametric method Box-Jenkins ARIMA is the method most commonly used. This method requires assumptions to be met in that the data must be stationary and residual followed the white noise process. Meanwhile, inflation data is the data which tend to fluctuate so it is difficult to satisfy both of these assumptions. One type of transformation used in time series is a Fourier transformation. Fourier transformation can detect disturbances, but Fourier transformation has some limitations, which require stationary data in the average so that the trend must be removed before using the Fourier transform. In addition, the results of the analysis of the data can only provide information on the frequency. This causes the Fourier transformation cannot be used to analyze the data nonstationary. A different approach was developed to overcome the weaknesses of Fourier transform in signal processing, the wavelet transform. The wavelet transform is able to represent time and frequency information simultaneously. Representation of time and frequency resulting wavelet transform can be used to analyze the data nonstationary. Wavelet is a mathematical function that cuts the data into different components and studies each component with a resolution that corresponds to the scale. The wavelet transform is divided into two major parts, namely Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT). In DWT is assumed that the sample size N can be divided into to a positive integer J. The new concept was developed to overcome the limitations of DWT in the sample size, which is known as The Shift Invariant Discrete Wavelet Transform. SIDWT than DWT has an advantage among others, can be used for each sample size N.

This research aims to transform using The Shift Invariant Discrete Wavelet Transform (SIDWT). It is hoped that this method can be one of the alternative to the government in predicting inflation

**Acknowledgement. **

This research is fully supported by Directorate of Research and Devotion to Society (DITLITABMAS DIKTI), and their support is gratefully acknowledged

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