0

I have obtained these plots for my residuals, I used type = "pearson" as I am working with poisson distributed response data recorded yearly.

enter image description here

Looking at the ACF plot I thought a MA(2) process would be appropriate to fit or would it be an ARMA(1,1)?

Alexis
  • 26,219
  • 5
  • 78
  • 131
elaine
  • 11
  • 2

1 Answers1

0

I would first take the differences $x_{t}-x_{t-4}$ as there seems to be a correlation every 4 lags (drawback: you will lose 4 observations). Afterwards, you can look the ACF and pACF graphs of the resulting time series and maybe try an MA(1) (for model parsimony) and if not then an MA(2) indeed.

Vasilis Vasileiou
  • 1,158
  • 1
  • 9
  • 16
  • I am working with poisson data will this not pose a problem as the response can only be discrete, specifically non-negative? – elaine Mar 07 '21 at 10:03
  • No this won't be an issue. The new resulted time series will take negative values sometimes but that's OK as you will now be looking to model the difference between t and t-4 instead of the raw values. After you take the differences and you model this resulted time series, you can take the predictions and adjust them to your original time series. Now, If the result of the original time series is negative, you can apply some transformations for instance: see this post: https://stackoverflow.com/a/41715282 or if it's for very few cases then simply return 0 for those cases. – Vasilis Vasileiou Mar 07 '21 at 10:38
  • I dont have a univariate time series. I have a dataset in the form Year, Ethnicity( categorical), Gender (categorical), Country( categorical), No. candidates( count), no.accepted (count) with my response no.accepted. I am having bother using the 'diff()' function in R as its not allowing me to fit my full data set to it. When i try use 'diff(data$No.accepted)' it gives me negative values... I cannot model it as my response is following a poisson distribution. – elaine Mar 08 '21 at 11:19
  • It may also be useful to note that my goal of analysis is to make inferences on the data, not to forecast and make predictions on future values. – elaine Mar 08 '21 at 11:25
  • In that case, I would suggest you use a different model rather than time series to model that. Based on what we saw in the ACF and pACF plots, I would create a new column in the dataset No.accepted_t_minus_4 which is No.accepted lag 4. Then I would use a count regression model such as a Poisson, Negative binomial, hurdle or zero inflated to model that. https://stats.stackexchange.com/questions/81457/what-is-the-difference-between-zero-inflated-and-hurdle-models – Vasilis Vasileiou Mar 14 '21 at 10:06