Introduction
The article presents a depth analysis of a time series estimation alongside prediction methods that are specifically aided with classic and advanced tools. The forecasting methods will be based on a hardly utilized practice approach, that is, spectral analysis, to accurately identify the patterns and predict. Spectral analysis is beneficial in the sense that it entails the estimation of prediction model type of parameters (Grzesica & Więcek, 2016). The assumption as far as the research is concerned is that the model in use has a trigonometric function that is combined with a set of unique frequencies. The model has frequencies expected to have the greatest contribution to the process variation, and the effectiveness of the method under investigation will be examined via a numerical example.
Research and Analysis Conducted
Time series analysis offers an opportunity to detect the nature that has been exposed by a line of observation as well as the ability to evaluate the future. In case there are changes that have been noted to the time series figures, this can be specifically attributed to exposure to unlimited yet unique factors. In order to deal with uncertainties related to the dealing with quantity, type and effect, it is imperative to utilize strong dependencies that have been recorded (Grzesica & Więcek, 2016). Cyclical variations often describe such variables alongside random fluctuations (Grzesica & Więcek, 2016).
Furthermore, it is important to note that for the time series, there is a need to postulate the observed values for the variables in a manner that it is easy to determine the nature of dependencies that takes place between various values. Another important thing to note is that the spectral analysis, as part of demand foresting methods, will be used to transform time series, especially in the frequency domain (Grzesica & Więcek, 2016). As part of the analysis, the mass spectra of the time series can be termed as an infinite sum of time series for varying frequencies, which relate to the oscillations periods.
Findings
The transformation for the analysis will entail the use of trigonometric functions that is sine and cosine. Additional transformation for the said analysis involves using discrete Fourier transformation specifically for the product demand data for at least two months. Under the unique circumstances when cyclic fluctuation will take place, the Bartlett time window will be utilized. It offers an example of a filter that can be employed to smooth the spectrum collected in the time series transformation process (Grzesica & Więcek, 2016). One should note that this kind of analysis aids the researcher in categorizing frequency components that lead to significant changes in the researched time series.
Spectral analysis has been involved in the cyclical process. This entails consideration of the wave structure of specific variables for the stochastic process making it possible to utilize trigonometric functions that are referred to as harmonics. On the other hand, the analysis of the charts, as evident in the article, reveals that the pattern of the demand for the product under analysis takes the form of a number of cycles in terms of lengths and random changes (Grzesica & Więcek, 2016). In order to predict the demand cycles that have a massive influence on the variable, the spectrum of data should be computed.
Conclusions
It is evident that the requirements for the prognostic models that are ideally based on the time series occur due to the utilization of the time series. In the modern world, it is increasingly evident that computer technology can be used to predict various future events via use of sophisticated techniques. Evaluating the research and data presented in the article, it is easy to note that basing an argument on absolute and relative errors of the forecast, the Brown model of demand forecasting is a less accurate method of prediction. However, advanced methods such as ARMA present accurate results as compared to the use of the exponential smoothing method.
Specifically, and evidently, from the article, the spectral analysis, which is used to evaluate time series in events of the frequency domain, is the most accurate and reliable. Based on the results and findings after the experiments, it was noted that spectral analysis presented three-time accurate results than the ARMA model and up to 4 times when compared to the Brown Model. Ideally, this means that demand forecasting can be achieved accurately if the spectral analysis approach can be prioritized.
Summary of Learnings
Spectral analysis proved to be a reliable mode of forecasting as compared to ARMA and Brown models. When used appropriately, spectral analysis could be useful in providing accurate demand forecast results, which can be used in decision-making for various sectors in the economy. Therefore, it is essential for different businesses across the board to consider adopting spectral analysis and seek qualified professionals who can run the systems to come up with accurate results.
References
Grzesica, D., & Więcek, P. (2016). Advanced forecasting methods based on spectral analysis. Procedia Engineering, 161, 253-258.