Wavelet transform

In general, energy prices, such as those of crude oil, are affected by deterministic events such as seasonal changes as well as non-deterministic events such as geopolitical events. It is the non-deterministic events which cause the prices to vary randomly and makes price prediction a difficult task. One could argue that these random changes act like noise which effects the deterministic variations in prices. In this paper, we employ the wavelet transform as a tool for smoothing and minimizing the noise presented in crude oil prices, and then investigate the effect of wavelet smoothing on oil price forecasting while using the GMDH neural network as the forecasting model. Furthermore, the Generalized Auto-Regressive Conditional Hetroscedasticity model is used for capturing time varying variance of crude oil price. In order to evaluate the proposed hybrid model, we employ crude oil spot price of New York and Los Angles markets. Results reveal that the prediction performance improves by more than 40% when the effect of noise is minimized and variance is captured by Auto-Regressive Conditional Hetroscedasticity model.

Controlling the business cycle and minimizing the inflation gap are considered as two major goals for monetary policy. Hence, the policymaker will be able to make more decisive decisions with an awareness of the dynamic relationship and causal relationship between these two variables. Accordingly, the present study uses a discrete and continuous wavelet transform to provide a new understanding of the relationship between these two variables in Iran's economy during the years 1990:2 – 2017:1. According to the results of the research, in the short-run (less than one year), the causal relationship has been bidirectional and procyclical. In the medium run (1 to 4 years), the causal relationship is countercyclical and from the inflation gap to the business cycle. In the long run (4 to 8 years), the business cycle is leading, and the two variables are in phase. Besides, the relationship between variables is highly unstable over time and depends on different scales. Therefore, inflation in Iran's economy is not merely a monetary phenomenon, and in the medium-term is affected by changes in the real sector. According to the results of the research, for the output and the inflation to be stable, it is recommended that the policymaker take both goals simultaneously.

Electrocardiogram (ECG) is a tool used for the electrical analysis of the status of human heart activity. When the ECG signal is recorded, it gets contaminated with different types of noises. So, for accurate analysis, noises must be eliminated from the ECG signal. There are different types of noises that contaminate the characteristics of ECG signal i.e Power line interference, baseline wander, Electromyogram (EMG). In this paper, different techniques have implemented for the removal of noises. A median filter is used for removal of DC component and Savitzky-Golay filter (SG) is used for smoothing noised waveform and then wavelet transform (db4) is used to decompose the ECG signal for removal of various artifacts. Wavelet transform provides the information in frequency and time domain and then thresholding has been applied for the implementation of algorithms in MATLAB. The measured results i.e. SNR(Signal to Noise ratio) and MSE(Mean square error) have been calculated using different databases like MIT-BIH, Long-term ST database, European ST-T database. The results are examined with proposed methods that are better than those reported in the literature.