Affiliation:
1. The Research Institute of Energy Management and Planning (RIEMP), University of Tehran, Tehran 19395-4697, Iran
2. Department of Statistics, Payame Noor University, Tehran 19395-4697, Iran
3. The International Institute for Applied Systems Analysis (IIASA), 2361 Laxenburg, Austria
Abstract
The objective of this paper is to assess the distribution of the Partial Autocorrelation Function (PACF), both theoretically and empirically, emphasizing its crucial role in modeling and forecasting time series data. Additionally, it evaluates the deviation of the sum of sample PACF from normality: identifying the lag at which departure occurs. Our investigation reveals that the sum of the sample PACF, and consequently its components, diverges from the expected normal distribution beyond a certain lag. This observation challenges conventional assumptions in time series modeling and forecasting, indicating a necessity for reassessment of existing methodologies. Through our analysis, we illustrate the practical implications of our findings using real-world scenarios, highlighting their significance in unraveling complex data patterns. This study delves into 185 years of monthly Bank of England Rate data, utilizing this extensive dataset to conduct an empirical analysis. Furthermore, our research paves the way for future exploration, offering insights into the complexities and potential revisions in time series analysis, modeling, and forecasting.
Reference28 articles.
1. Tsay, R.S. (2010). Analysis of Financial Time Series, John Wiley & Sons. [3rd ed.].
2. Kirman, A., and Teyssière, G. (2002). Microeconomic Models for Long Memory in the Volatility of Financial Time Series. Stud. Nonlinear Dyn. Econom., 5.
3. Structural Time Series Models and Trend Detection in Global and Regional Temperature Series;Zheng;J. Clim.,1999
4. Sanei, S., and Hassani, H. (2015). Singular Spectrum Analysis of Biomedical Signals, CRC Press.
5. Wei, W.W. (2006). Time Series Analysis: Univariate and Multivariate Methods, Pearson Addison Wesley. [2nd ed.].