Which of the following property is not true for a random walk process?a. volatility clusteringb. nonstationaryc. strong memoryd. has a unit root
Question
Which of the following property is not true for a random walk process?a. volatility clusteringb. nonstationaryc. strong memoryd. has a unit root
Solution 1
A random walk process has the following properties:
a. Volatility clustering: This is not a property of a random walk. Volatility clustering refers to the phenomenon when large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes. This is a characteristic of financial time series, not a random walk.
b. Nonstationary: This is true for a random walk. A nonstationary process has a statistical property, such as mean or variance, that changes over time.
c. Strong memory: This is not a property of a random walk. In a random walk, each step is independent of the previous ones.
d. Has a unit root: This is true for a random walk. A unit root is a feature of some stochastic processes that can cause problems in statistical inference involving time series models.
So, the properties that are not true for a random walk process are volatility clustering and strong memory.
Solution 2
A random walk process has the following properties:
a. Nonstationary: This is true. A random walk is nonstationary because its mean and variance change over time.
b. Has a unit root: This is also true. A unit root is a feature of some stochastic processes that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. A random walk has a unit root.
c. Volatility clustering: This is not true. Volatility clustering refers to the phenomenon when large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes. A random walk does not exhibit this property.
d. Strong memory: This is not true. A random walk does not have a strong memory because the value at time t is independent of the value at time t-1.
So, the properties that are not true for a random walk process are volatility clustering and strong memory.
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