A zero-inflated geometric INAR(1) process with random coefficient

Hassan S. Bakouch; Mehrnaz Mohammadpour; Masumeh Shirozhan

Applications of Mathematics (2018)

  • Volume: 63, Issue: 1, page 79-105
  • ISSN: 0862-7940

Abstract

top
Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINAR RC ( 1 ) process, which contains some sub-models as special cases. Several properties of the process are established. Estimators of the model parameters are obtained and their performance is checked by a small Monte Carlo simulation. Also, the behavior of the inflation parameter of the model is justified. We investigate an application of the process using a real count climate data set with excessive zeros for the number of tornados deaths and illustrate the best performance of the proposed process as compared with a set of competitive INAR(1) models via some goodness-of-fit statistics. Consequently, forecasting for the data is discussed with estimation of the transition probability and expected run length at state zero. Moreover, for the considered data, a test of the random coefficient for the proposed process is investigated.

How to cite

top

Bakouch, Hassan S., Mohammadpour, Mehrnaz, and Shirozhan, Masumeh. "A zero-inflated geometric INAR(1) process with random coefficient." Applications of Mathematics 63.1 (2018): 79-105. <http://eudml.org/doc/294358>.

@article{Bakouch2018,
abstract = {Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINAR$_\{\rm RC\}(1)$ process, which contains some sub-models as special cases. Several properties of the process are established. Estimators of the model parameters are obtained and their performance is checked by a small Monte Carlo simulation. Also, the behavior of the inflation parameter of the model is justified. We investigate an application of the process using a real count climate data set with excessive zeros for the number of tornados deaths and illustrate the best performance of the proposed process as compared with a set of competitive INAR(1) models via some goodness-of-fit statistics. Consequently, forecasting for the data is discussed with estimation of the transition probability and expected run length at state zero. Moreover, for the considered data, a test of the random coefficient for the proposed process is investigated.},
author = {Bakouch, Hassan S., Mohammadpour, Mehrnaz, Shirozhan, Masumeh},
journal = {Applications of Mathematics},
keywords = {randomized binomial thinning; geometric minima; estimation; likelihood ratio test; mixture distribution; realization with random size},
language = {eng},
number = {1},
pages = {79-105},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A zero-inflated geometric INAR(1) process with random coefficient},
url = {http://eudml.org/doc/294358},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Bakouch, Hassan S.
AU - Mohammadpour, Mehrnaz
AU - Shirozhan, Masumeh
TI - A zero-inflated geometric INAR(1) process with random coefficient
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 79
EP - 105
AB - Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINAR$_{\rm RC}(1)$ process, which contains some sub-models as special cases. Several properties of the process are established. Estimators of the model parameters are obtained and their performance is checked by a small Monte Carlo simulation. Also, the behavior of the inflation parameter of the model is justified. We investigate an application of the process using a real count climate data set with excessive zeros for the number of tornados deaths and illustrate the best performance of the proposed process as compared with a set of competitive INAR(1) models via some goodness-of-fit statistics. Consequently, forecasting for the data is discussed with estimation of the transition probability and expected run length at state zero. Moreover, for the considered data, a test of the random coefficient for the proposed process is investigated.
LA - eng
KW - randomized binomial thinning; geometric minima; estimation; likelihood ratio test; mixture distribution; realization with random size
UR - http://eudml.org/doc/294358
ER -

References

top
  1. Al-Osh, M. A., Aly, E.-E. A. A., 10.1080/03610929208830925, Commun. Stat. Theory. Methods. 21 (1992), 2483-2492. (1992) Zbl0775.62225MR1186065DOI10.1080/03610929208830925
  2. Al-Osh, M. A., Alzaid, A. A., 10.1111/j.1467-9892.1987.tb00438.x, J. Time. Ser. Anal. 8 (1987), 261-275. (1987) Zbl0617.62096MR0903755DOI10.1111/j.1467-9892.1987.tb00438.x
  3. Aly, E.-E. A. A., Bouzar, N., 10.1006/jmva.1994.1038, J. Multivariate Anal. 50 (1994), 132-151. (1994) Zbl0811.62084MR1292612DOI10.1006/jmva.1994.1038
  4. Alzaid, A. A., Al-Osh, M. A., 10.1111/j.1467-9574.1988.tb01521.x, Stat. Neerl. 42 (1988), 53-61. (1988) Zbl0647.62086MR0959714DOI10.1111/j.1467-9574.1988.tb01521.x
  5. Alzaid, A. A., Al-Osh, M. A., 10.1007/BF00775809, Ann. Inst. Stat. Math. 45 (1993), 223-232. (1993) Zbl0777.62085MR1232490DOI10.1007/BF00775809
  6. Bakouch, H. S., Ristić, M. M., 10.1007/s00184-009-0252-5, Metrika 72 (2010), 265-280. (2010) Zbl1200.62099MR2725101DOI10.1007/s00184-009-0252-5
  7. Barreto-Souza, W., 10.1111/jtsa.12131, J. Time. Ser. Anal. 36 (2015), 839-852. (2015) Zbl1330.62333MR3419670DOI10.1111/jtsa.12131
  8. Bourguignon, M., Vasconcellos, K. L. P., 10.1214/13-BJPS229, Braz. J. Probab. Stat. 29 (2015), 71-93. (2015) Zbl1329.62370MR3299108DOI10.1214/13-BJPS229
  9. Gomes, D., Castro, L. C. e, 10.1016/j.jspi.2009.05.037, J. Stat. Plann. Inference 139 (2009), 4088-4097. (2009) Zbl1183.62149MR2558352DOI10.1016/j.jspi.2009.05.037
  10. Jacobs, P. A., Lewis, P. A. W., Discrete time series generated by mixtures. I: Correlational and runs properties, J. R. Stat. Soc., Ser. B. 40 (1978), 94-105. (1978) Zbl0374.62087MR0512147
  11. Jazi, M. A., Jones, G., Lai, C.-D., 10.1111/j.1467-9892.2012.00809.x, J. Time. Ser. Anal. 33 (2012), 954-963. (2012) Zbl1281.62197MR2991911DOI10.1111/j.1467-9892.2012.00809.x
  12. Jazi, M. A., Jones, G., Lai, C.-D., Integer valued AR(1) with geometric innovations, J. Iran. Stat. Soc. JIRSS 11 (2012), 173-190. (2012) Zbl1278.62136MR3010343
  13. Khoo, W. C., Ong, S. H., Biswas, A., 10.1007/s00362-015-0704-0, Stat. Pap. 58 (2017), 393-416. (2017) Zbl1367.60033MR3649495DOI10.1007/s00362-015-0704-0
  14. Li, C., Wang, D., Zhang, H., 10.1016/j.jkss.2014.08.004, J. Korean Stat. Soc. 44 (2015), 232-246. (2015) Zbl1328.62527MR3342635DOI10.1016/j.jkss.2014.08.004
  15. McKenzie, E., 10.1111/j.1752-1688.1985.tb05379.x, J. Water Res. Bull. 21 (1985), 645-650. (1985) DOI10.1111/j.1752-1688.1985.tb05379.x
  16. Nicholls, D. F., Quinn, B. G., 10.1007/978-1-4684-6273-9, Lecture Notes in Statistics 11, Springer, New York (1982). (1982) Zbl0497.62081MR0671255DOI10.1007/978-1-4684-6273-9
  17. Pavlopoulos, H., Karlis, D., 10.1002/env.883, Environmetrics 19 (2008), 369-393. (2008) MR2440038DOI10.1002/env.883
  18. Ridout, M., Demétrio, C. G. B., Hinde, J., Models for count data with many zeros, Proceedings of the 19th International Biometrics Conference, Cape Town, South Africa (1998), 179-190. (1998) 
  19. Ristić, M. M., Bakouch, H. S., Nastić, A. S., 10.1016/j.jspi.2008.10.007, J. Stat. Plan. Inference. 139 (2009), 2218-2226. (2009) Zbl1160.62083MR2507983DOI10.1016/j.jspi.2008.10.007
  20. Ristić, M. M., Nastić, A. S., Bakouch, H. S., 10.1080/03610926.2010.529528, Commun. Stat., Theory Methods 41 (2012), 606-618. (2012) Zbl1237.62125MR2874378DOI10.1080/03610926.2010.529528
  21. Schweer, S., Weiß, C. H., 10.1016/j.csda.2014.03.005, J. Comput. Stat. Data Anal. 77 (2014), 267-284. (2014) MR3210062DOI10.1016/j.csda.2014.03.005
  22. Steutel, F. W., Harn, K. van, 10.1214/aop/1176994950, Ann. Probab. 7 (1979), 893-899. (1979) Zbl0418.60020MR0542141DOI10.1214/aop/1176994950
  23. stheim, D. Tjø, 10.1016/0304-4149(86)90099-2, Stochastic Processes Appl. 21 (1986), 251-273. (1986) Zbl0598.62109MR0833954DOI10.1016/0304-4149(86)90099-2
  24. Weiß, C. H., 10.1007/s10182-008-0072-3, AStA, Adv. Stat. Anal. 92 (2008), 319-341. (2008) MR2426093DOI10.1007/s10182-008-0072-3
  25. Zhang, H., Wang, D., 10.1080/03610918.2013.804556, Commun. Stat., Simulation Comput. 44 (2015), 1078-1100. (2015) Zbl1315.62074MR3264922DOI10.1080/03610918.2013.804556
  26. Zhao, Z., Hu, Y., 10.1186/s13660-015-0886-y, J. Inequal. Appl. 2015 (2015), Paper No. 359, 12 pages. (2015) Zbl1333.62219MR3424785DOI10.1186/s13660-015-0886-y
  27. Zheng, H., Basawa, I. V., Datta, S., 10.1016/j.jspi.2005.12.003, J. Stat. Plan. Inference 137 (2007), 212-229. (2007) Zbl1098.62117MR2292852DOI10.1016/j.jspi.2005.12.003
  28. Zuur, A. F., Ieno, E. N., Walker, N. J., Saveliev, A. A., Smith, G. M., 10.1007/978-0-387-87458-6, Statistics for Biology and Health, Springer, New York (2009). (2009) Zbl1284.62024MR2722501DOI10.1007/978-0-387-87458-6

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.