Contents
Does independence imply stationarity?
Conceptually, independence is a much broader concept, whereas stationarity of a time-series is a particular condition on the series that can be framed as a particular kind of independence.
What is the issue with forecasting data that is non-stationary?
Using non-stationary time series data in financial models produces unreliable and spurious results and leads to poor understanding and forecasting. The solution to the problem is to transform the time series data so that it becomes stationary.
What kinds of variables are likely to be non-stationary How can such variables be made stationary?
Examples would be most kinds of asset or goods prices, GDP, unemployment, money supply, etc. Such variables can usually be made stationary by transforming them into their differences or by constructing percentage changes of them. (b) Non-stationarity can be an important determinant of the properties of a series.
Is stationary an iid?
An iid process is a strongly stationary process. This follows almost immediate from the definition. So the knowledge of the past has no value for predicting the future. An iid process is unpredictable.
Is time series data independent?
A sequence of random variables X(1), …, X(n) that satisfies the two conditions of independence and identical distribution is called independent and identically distributed or i.i.d. A time series is a collection of random variables indexed by time, for example X(1), …, X(n). …
How is a stationary time series not dependent on time?
The observations in a stationary time series are not dependent on time. Time series are stationary if they do not have trend or seasonal effects. Summary statistics calculated on the time series are consistent over time, like the mean or the variance of the observations.
Is there a better way to test the independence of a time series?
So what am I getting wrong or is there a different/better way to test the independence of my time series where I don’t know its distribution? If you want to conduct a hypothesis test to evaluate whether a time series has an autocorrelation that differs from 0 then the Ljung-Box test is a perfectly reasonable approach.
How to determine stationarity in time series analysis?
Indeed, for many cases involving time series, you will find that you have to be able to determine if the data was generated by a stationary process, and possibly to transform it so it has the properties of a sample generated by such a process.
When to reject null hypothesis in non stationary time series?
Test for stationarity: If the test statistic is less than the critical value, we can reject the null hypothesis (aka the series is stationary). When the test statistic is greater than the critical value, we fail to reject the null hypothesis (which means the series is not stationary).