Identifying distributions in time series

[fastier]

Given a time series Yt, how can you decide what distribution the values obey, if any? In particular, is there a way to make sure the time series obeys a Gaussian distribution?

Thanks,

Frank

 

[mathman]

Essentially you have a statistics question, not a probability question. In other words, without any other information, all you can do is set up some sort of interval structure and count how many events fall into each interval.

 

[tacman]

Hi Frank,

Identifying distributions in time series can be a challenging task, as time series data can often exhibit complex patterns and trends. However, there are a few ways to determine the distribution of a time series.

One method is to plot a histogram of the time series data and visually inspect it for any patterns or shapes that may indicate a specific distribution. For example, a bell-shaped curve may indicate a Gaussian or normal distribution.

Another approach is to use statistical tests, such as the Kolmogorov-Smirnov test or the Shapiro-Wilk test, to determine if the data follows a specific distribution. These tests compare the observed data to the expected distribution and provide a p-value, which can indicate the likelihood of the data following a particular distribution.

Additionally, you can also use quantile-quantile (Q-Q) plots to compare the distribution of the data to a theoretical distribution. If the points on the Q-Q plot fall along a straight line, it can indicate that the data follows the expected distribution.

However, it is important to note that even if a time series appears to follow a specific distribution, it may not necessarily be the best fit for the data. It is always important to consider the context and characteristics of the data before deciding on a distribution.

In terms of ensuring a time series follows a Gaussian distribution, there are techniques such as data transformation or fitting a Gaussian distribution to the data. However, it is also important to consider the underlying factors and processes that may be influencing the data and if a Gaussian distribution is truly the most appropriate.

I hope this helps answer your question. Let me know if you have any further questions or need clarification.