# Timeseries: sig. Ljung-box Q, but residuals normally distributed

#### Eyecatcher

##### New Member
Hi all,

Hope someone can help me with the following problem/question I encounter.

I'm working with a monthly time-serie consisting of 36 data points (i know 50 is the rule of thumb). Spss expert modeler chose Winter's multiplicative model, which is fine with me because I know how such a model works. Stationary R-Square is .72, also fine.

Now the problem;
- My Ljung-Box Q statistic is significant (p= .001) indicating a problem with my model; it can't explain a part in my model or there is autocorrelation left if i'm right (?).

- I thought, well let's first look if the residuals are non-normal, but Shapiro-Wilk statistic is non-significant (p=.65), which i didn't expect.

Question 1: What is the relation between Ljung-Box Q statistic and the normality of my residuals?

After asking myself that question, I plotted the residual acf and pacf which resulted in the following graph, showing values out of the boundaries.

Question 2: I suppose this causes my Ljung-Box Q statistic to be significant, but how can I solve this?

Hope someone can help me, I got lost..

#### vinux

##### Dark Knight
Question 1: What is the relation between Ljung-Box Q statistic and the normality of my residuals?

Question 2: I suppose this causes my Ljung-Box Q statistic to be significant, but how can I solve this?
Q1. There is not really a strong relation between Ljung-Box Q statistic and normality of residuals. IID residuals(not necessary normal) is assumed in the null hypothesis of Ljung Box test

Q2. I guess you are doing a univariate analysis. You need to fit an AR or ARMA or SARMA model.

#### Eyecatcher

##### New Member
Q2. I guess you are doing a univariate analysis. You need to fit an AR or ARMA or SARMA model.
Thanks Vinux for the quick response; I understand Q1.

Regarding Q2; yes, it's a univariate analysis. I tried to fit the ones you mentioned, but the in sample fit is remarkable lower. The expert modeler in spss chooses (if i'm right) the best model and came up with the exponential smoothing model, which in my opinion did the trick quite good (and also takes seasonality into account). However, now I'm stuck with the Ljung-Box Q statistic, which is significant.

So perhaps my question should be; is it bad if you have a Ljung-Box Q statistic which is significant, but the model-fit is high? Or would you recommend I an ARIMA class model with no significant Ljung-box Q statistic, but with less in sample fit?

#### vinux

##### Dark Knight
By looking at ACF/PACF my suggestion would be try ARIMA(1,0,0) + SARIMA(1,0,0) [ which is same as AR(1) and Seasonal AR(1), you could also try MA instead of AR]. Again check the residual ACF/PACF plot.

Also check is there any outlier in the series. Since you have only 36 data points even one outlier can change influence ACF/PACF.

#### Eyecatcher

##### New Member
I will try to do it again and check the plots. Perhaps you are right with the outlier..
Thanks!