Is time series data normally distributed?

Is time series data normally distributed?

In other words, about 96% of the throughput time series data follows a normal distribution. The other 4% are scattered outliers at both ends.

Why are residuals not normally distributed?

When the residuals are not normally distributed, then the hypothesis that they are a random dataset, takes the value NO. This means that in that case your (regression) model does not explain all trends in the dataset. Thus, your predictors technically mean different things at different levels of the dependent variable.

Do you plot the time series of residuals?

Always plot the time series of residuals and check the ACF/PACF of residuals. We’ll get back to this later. Some people mistakenly believe that you can choose the best time series model based on the ACF and PACF alone. This is true only for pure AR or pure MA processes, but those are rare. These are mainly diagnostics plots.

Is the normal probability plot of the residuals linear?

The normal probability plot of the residuals is approximately linear supporting the condition that the error terms are normally distributed. The following histogram of residuals suggests that the residuals (and hence the error terms) are normally distributed. But, there is one extreme outlier (with a value larger than 4):

Why are the error terms not normally distributed?

Clearly, the condition that the error terms are normally distributed is not met. The following histogram of residuals suggests that the residuals (and hence the error terms) are not normally distributed. There are too many extreme positive and negative residuals.

How are the residuals in a histogram normally distributed?

The following histogram of residuals suggests that the residuals (and hence the error terms) are normally distributed: The normal probability plot of the residuals is approximately linear supporting the condition that the error terms are normally distributed.