Do an ACF and PACF analysis (inclusive of the portmanteau or Q test) on the foll

Question

Do an ACF and PACF analysis (inclusive of the portmanteau or Q test) on the following data set : tornado data for the USA. The data indicates the number of tornadoes for each month all the way back to 1950 as well as the total tornadoes for each year..
* Examine the ACF and PACF on the total number of tornadoes per year, May only, October only. Do the exact t tests on the total tornadoes as well as the rule of thumb tests on autocorrelations and partial autocorrelations. The other 2 series use only the rule of thumb test. What do you notice on the individual months? Comment on your findings.

Time Series total 925.59701 332.0178 67 Zero Mean ADF 0.755923 Single Mean ADF -3.595678 5.611783 2000 Mean Std 1500 1000 Trend ADF 500 1950 1963 1976 1989 2002 2015 year Time Series Basic Diagnostics Lag AutoCorr-8-.6-.4-.20 .2 .4.6.8 Ljung-Box Q p-Value Lag Partial 8-.6-.4-.2 0 .2.4.6 .8 0 1.0000 1 0.7036 2 0.2191 0 1.0000 1 0.7036 2 0.6057 3 0.5721 4 0.5241 5 0.4847 6 0.4847 7 0.4863 8 0.4146 90.3587 10 0.3393 1 0.3100 12 0.3136 13 0.2640 14 0.1805 15 0.1581 16 0.1804 7 0.1423 18 0.1428 19 0.1037 20 0.0278 21 -0.0137 22 -0.0338 23 -0.0916 24 -0.0440 25 0.0029 34.6766 .0001 60.7680 .0001 84.4081 .0001 104.564 .0001 122.084 .0001 139.893 .0001 158.117

Explanation / Answer

Examine the ACF and PACF on the total number of tornadoes per year, May only, October only.

The ACF is showing a decaying pattern and the PACF cuts off after lag 2. Hence, it suggests that an MA model of order 2 might be the most appropriate ARIMA model here.

The ACF and PACF plots for the May month don't suggest any suitable ARIMA order here.

Similarly, the ACF and PACF plot for October is also not suggesting any appropriate ARIMA model.

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