Using some spectral methods to analyze short memory time series with an application

A thesis

Submitted to the council of the college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the Master degree in Statistics Sciences

 By
Mustafa Sattar Obaid Rumaid Al-Ghurairy

Supervision
Asst. Prof.  Dr. Enas Abdul Hafedh Mohammed

In this thesis, we deal with spectral analysis in time series and work on estimating some spectral methods based on a hypothetical model for the process . The Power Spectrum Density function is determined by It represents the function of the parameters of the model, and then the spectral power function PSD of the model is estimated by replacing the estimated parameters with an algebraic function of the spectral power function.

tan method to estimate the spectral density function for common time series models, which is the autoregressive model ( AR) ) – moving media (MA) The mixed model (ARMA) which is the traditional greatest possibility method for the spectrum density function according to the special functions of these models and the greatest pain was method according to the normal distribution and its function by using Monte Carlo simulation using the program  (ARMA ).  Matlab R 2015 a  Four models were used for different sample sizes  (small – medium – large)  and four frequency values. Different values were chosen for the distribution parameters. The aim was to study the behavior of the scales by using the standard  ( MAPE (  Mean Absuolte percentage error square error  Mean square error ( MSE ) preference in estimating the parameters. The method of greatest possibility of normal distribution was better than the method of approximate greatest possibility for all sample sizes and for all  ( initial   values, as well as for all Default   (Wi )  values.

the Iraqi Ministry of Agriculture were used Meteorological Center Iraqi meteorological network for the years  2016 – 2022 , which represents the monthly averages of wind speed in Baghdad governorate with a volume of )84( observations measured in kilometers per hour . The appropriate model for the data was selected, which is the  ARMA (1, 1) model. By applying the two methods , it was shown that the method of greatest possibility for the normal distribution of real data is better than the method of greatest possibility .

And that there is an increase in the wind speed in 2023 from what it is in 2022, as the average wind speed in 2023 reached )4.9133( kilometers per hour, while in 2022 it reached )4.8341( kilometers per hour, i.e. )0.0791( kilometers per hour . By finding predictive values, we find that the values were close with a difference in confidence intervals due to the nature of the model used in future prediction.

Using some spectral methods to analyze short memory time series with an application

A thesis

Submitted to the council of the college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the Master degree in Statistics Sciences

 By
Mustafa Sattar Obaid Rumaid Al-Ghurairy

Supervision
Asst. Prof.  Dr. Enas Abdul Hafedh Mohammed

In this thesis, we deal with spectral analysis in time series and work on estimating some spectral methods based on a hypothetical model for the process . The Power Spectrum Density function is determined by It represents the function of the parameters of the model, and then the spectral power function PSD of the model is estimated by replacing the estimated parameters with an algebraic function of the spectral power function.

tan method to estimate the spectral density function for common time series models, which is the autoregressive model ( AR) ) – moving media (MA) The mixed model (ARMA) which is the traditional greatest possibility method for the spectrum density function according to the special functions of these models and the greatest pain was method according to the normal distribution and its function by using Monte Carlo simulation using the program  (ARMA ).  Matlab R 2015 a  Four models were used for different sample sizes  (small – medium – large)  and four frequency values. Different values were chosen for the distribution parameters. The aim was to study the behavior of the scales by using the standard  ( MAPE (  Mean Absuolte percentage error square error  Mean square error ( MSE ) preference in estimating the parameters. The method of greatest possibility of normal distribution was better than the method of approximate greatest possibility for all sample sizes and for all  ( initial   values, as well as for all Default   (Wi )  values.

the Iraqi Ministry of Agriculture were used Meteorological Center Iraqi meteorological network for the years  2016 – 2022 , which represents the monthly averages of wind speed in Baghdad governorate with a volume of )84( observations measured in kilometers per hour . The appropriate model for the data was selected, which is the  ARMA (1, 1) model. By applying the two methods , it was shown that the method of greatest possibility for the normal distribution of real data is better than the method of greatest possibility .

And that there is an increase in the wind speed in 2023 from what it is in 2022, as the average wind speed in 2023 reached )4.9133( kilometers per hour, while in 2022 it reached )4.8341( kilometers per hour, i.e. )0.0791( kilometers per hour . By finding predictive values, we find that the values were close with a difference in confidence intervals due to the nature of the model used in future prediction.