Exploring
the depths of Autocorrelation Function: its departure from normality
H. Hassani, M. Royer
Carenzi, L.M. Mashad, M. Yarmohammadi and M.R. Yeganegi
Information, 2024, 15, 449, pp. 1-26
In the main paper, we study the simulations of
-
White Noises of length
n=500.
-
ARIMA(0,2,2) processes
of length n=500. We
estimate every simulated series as an ARIMA(0,2,0) process, and compute its
residuals.
In the Supplementary, we consider
-
White Noises of length
n=100
-
Residuals of
well-specified models :
MA(2) processes of length n=500. We estimate every simulated series
as a MA(2) process, and compute its residuals.
AR(2) processes of length n=500. We estimate every simulated series as an AR(2) process, and compute
its residuals.
ARIMA(0,2,2) processes of length n=500. We estimate every simulated series as an
ARIMA(0,2,2) process, and compute its residuals.
ARIMA(1,1,1) processes of length n=500. We estimate every simulated series
as an ARIMA(1,1,1) process, and compute its residuals.
-
Residuals of misspecified models
MA(2) processes of length n=500. We estimate every simulated series
as a WN process.
AR(2) processes of length n=500. We estimate every simulated series
as as a WN process.
ARIMA(0,2,2) processes of length n=500. We estimate every simulated series
as an AR(1) process, and compute its residuals.
ARIMA(1,1,1) processes of length n=500. We estimate every simulated series
as an ARIMA(2,1,2) process, and compute its residuals.
R Code associated to previous projects
Several functions, aimed to facilitate time series
modeling, were developed in previous projects from M. Royer-Carenzi.
You can
refer either to an English paper or to a French book, and to their associated web pages for R-codes and explanations
:
Identifying trend nature in time series using autocorrelation functions
and
International Journal of Economics and Econometrics, vol.
14, n°1 (2024) pp.1-22
M.
Boutahar and M. Royer Carenzi
Méthodes
en séries temporelles et applications avec R
Ellipses, Références Sciences
(2019)
M. Boutahar and M. Royer Carenzi
R Code associated to the current paper
R-functions useful to study the departure of ACF from
normality:
Plot of the standardized cumulative sum of the ACF (SACF / 
)
Test of the normality of the successive ACF
Function_normality.test.succACF.R
Example of
normality.test.succACF use
Diagnosis for an estimated ARMA(p,q) model
Data and associated scripts:
Money Stock in USA