Question

List several potential problems with standard unit root tests, and some possible solutions

Answer 1

In Economics we assume that all the processes are working efficiently and resources are fully utilized, there is no room for improvement in the output production ability.

But while changing time there comes one issue that the realized value of output (y) in each time period should originate from same distribution[1] it means they should be working with same efficiency all the time, in other words year in year out same labor and same capital in terms of quality should be used to produce output with consistent[2] motivation, efficiency and productivity.

Stationarity Assumption

Because of this practical limitation, we imply a second-best assumption called weak stationarity which specifies variables should have a constant mean, variance and zero co-variance. Fulfilling these assumptions will weakly ensure us that we have same variable throughout the time period and it is not being influenced by any means.

In conclusion, when we talk about citrus peribus assumption our motive is to see pure effect of one variable on other, hence this stationarity concept talk about same phenomenon that the variable should be stay original throughout time. See the graph below a stationary (weak) should look like this where mean and spread of observations (variance) seem constant.

Origin of Non-Stationarity

Before we can see how non stationarity can come in a variable, we have to look first what kind of possible sources from where a variable can be changed.

This above illustration shows that there four possible sources that can cause a variable to change.

As the concept of regression is to see the effect of independent variables on the dependent variable hence DL component is not considered an enemy. While most of our regression analysis is based on calculating the effects of DL component, the minimization of other components is the main problem that a researcher faces when he turns up to estimate a model

Trend Component:

The trend component is a qualitative component that shows the effect of improvement or depreciation in the series because of repetition, experience, or growth. Certainly, if we start constructing houses even though we do not have any experience, we will take ages to make one house, but with time our speed and finishing will improve, this evolution is called a trend. Consider a simple trend model below where Y is affected by trend and intercept

MA Component

MA component describes the effect of any event that has changed the nature of the behavior of series. Just like the fall of the Breton woods system of the exchange rate, it started to deviate faster and independently. Unknown events are random shocks before they have occurred. When random shocks have long-lasting effects they are considered as structural breaks. There will be a visible change in the behavior of the variable.

AR component

Consider a simple model below where Y is affected by its past. In other words, it is also called inertia in the series. it is because of natural phenomena, like in output the economy is not always fully employed, the population is always growing so there will be opportunities to employ them and increase the output. The following mode is AR(1) means there is only one lag (past) value of the variable directly involved.