Development of a first order integrated moving average model corrupted with a Markov modulated convex combination of autoregressive moving average errors

ABSTRACT

With a view to providing a tool to accurately model time series processes which may be corrupted with errors such as measurement, round-off and data aggregation, this study developed an integrated moving average (IMA) model with a transition matrix for the errors resulting in a convex combination of two ARMA errors. Datasets on interest rates in the United States and Nigeria were used to demonstrate the application of the formulated model. Basic tools such as the autocovariance function, maximum likelihood method, Newton–Raphson iterative method and Kolmogorov–Smirnov test statistic were employed to examine and fit the formulated specification to data. Test results showed that the proposed model provided a generalisation and a more flexible specification than the existing models of AR error and ARMA error in fitting time series processes in the presence of errors.

KEYWORDS:

• Structural relationship
• measurement error
• correlated errors
• autocovariance function

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Readers interested in simulations and estimations of IMA process under the two error patterns of AR and ARMA may kindly refer to Eni and Mahmud (2008) and Eni (2013).

2 One may argue that the p- and z-values of the proposed are just marginally better than the existing models; however, it is known that when sample size is small, as we have in both illustrations, (i.e. for Nigeria, sample size used in Kolmogorov test is 12 while that of US is 16), Kolmogorov test usually masks the extent of deviation between the two distributions under consideration. Tables 2 and 3 of Absolute deviations displayed clear deviations of the existing two models from the Observed compared to the Proposed.

Additional information

Notes on contributors

S. A. Komolafe

S. A. Komolafe is a student at the Department of Mathematics, Obafemi Awolowo University, Ile-Ife. He obtained M.Sc. in Statistics in Obafemi Awolowo University, Ile-Ife. His area of research includes time series analysis and econometrics.

T. O. Obilade

T. O. Obilade is a Professor of Statistics at the Department of Mathematics, Obafemi Awolowo University in Ile-Ife, Nigeria. He has taught most of the Mathematics and Statistics courses in the department for several decades. Professor Obilade has written many articles. He has also supervised several M.Sc. and Ph.D. theses.

I. O. Ayodeji

I. O. Ayodeji is a Lecturer at the Department of Mathematics, Obafemi Awolowo University, Ile-Ife. She received her Ph.D. in Statistics from Obafemi Awolowo University, Ile- Ife, in 2015. She has to her credit quality articles published in top journals in economics and statistics, including Communications in Statistics – Theory and Methods, African Development Review and the Journal of Applied Mathematics.

A. R. Babalola

A. R. Babalola is an Assistant Lecturer and a Ph.D. student at the Department of Mathematics, Obafemi Awolowo University in Ile-Ife, Nigeria. His research interests include queueing theory and time series analysis.