Question

Explain the difference between a non-stationary variable and a stationary variable. Give examples for both of them. then

Explain the difference between a stationary variable and white noise variable. Give an example of a white noise variable. Why is a white noise variable also a stationary variable? Explain

Answer 1

1) Difference between a non-stationary variable and a stationary variable?

- Non-stationary variables the data points are often non-stationary or have means, variance and covariance that change over time. Non-stationary behaviors can be trend cycles, random walks or combination of three non-stationary data.

-Stationary variable is one whose statistical properties such as the mean, variance, and autocorrelation are all constant over time. Hence,

examples- Non-stationary variables are random walk with or without a drift (a slow steady change) and deterministic trends (trends that are constant, positive or negative, independent of time for the whole life of the series)

2) Explain the difference between the stationary variable and white noise variable.

-Stationary variable is one whose statistical properties such as the mean, variance, and autocorrelation are all constant over time.

- A time series may be white noise. A time series is white noise if the variables are independent and identically distributed with a mean of zero. This means that all variables have the same variance and each value has a zero correlation with all other values in the series.

For an example of white noise, a sequence of zero's and one's would be white if the sequence is statistically uncorrelated.

3) Why is a white noise variable also a stationary variable?

- This is because a multivariate Gaussian distribution is fully characterized by its first two moments. For example, a white noise is stationary but may not be strict stationary, but a Gaussian white noise is a strict stationary.