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I’m using auto.arima and forecast package to forecast the COVID-19 dataset. I got my results and graphed them in R. As I’m no statistician, I read many papers available online related to COVID-19 and tried to interpret the graphs and their meaning for my results. For example, p-value, I have greater than 0.05? Some said it’s acceptable, and others reject it. I found some tutorials that say if the p-value is close to 1, it means I have a good forecast model. Some recommend using a Q-Q plot to get an impression of my forecasting distribution. Others recommend I use the histogram of my residuals, and others recommend just to use residuals graphs. Some recommend only using ACF, and (Optionally) include PACF. Some suggest using accuracy in R, which return the measures such as ME, RMSE, MAE, MPE, MAPE, MASE, ACF1. Some recommend only to run summary command and study AIC, AICc, BIC, sigma^2.
I know for an expert; one or two graphs could be enough to conclude the data. I agree the answer depends on my data and results; that’s why I include my results. The question is, what is suitable to judge the forecast performance?
Ljung-Box test data: Residuals from ARIMA(0,2,5) Q* = 6.8118, df = 5, p-value = 0.235 Model df: 5. Total lags used: 10 ME RMSE MAE MPE MAPE MASE ACF1 Training set -2.591304 100.283 60.15786 -0.4603156 3.484356 0.2205352 -0.1870562

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I don't think you can actually forecast covid19 at this point. There is too little data and too little is known about the process which, since it is a new disease, is likely to change anyhow (a structural break I guess you could see this as). A second issue are your questions on arima - which there really are too many to answer at one time. You ask for example about p values when they mean different things depending on whether (for example) you are asking about the null hypothesis for a coefficient or the Box-Ljung test of serial correlation (which has an entirely different null hypothesis and so p values are interpreted differently). I think you should start with a monograph on ARIMA. This https://people.duke.edu/~rnau/411arim.htm might help although I would use auto.arima rather than spend a lot of time trying to identify the model - I think automated searches has replaced the formal methodology these days (because even experts have trouble with formal searches).

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