What does a non-stationary data suggest in econometrics?

Answer 1

To answer this, let's first consider what it means for a time series to be stationarys A time series is stationary when all statistical characteristics of that series are unchanged by shifts in time. In technical terms, strict stationarity implies that the joint distribution of (y_t, …, y_t-h) depends only on the lag, h, and not on the time period, t. Strict stationarity is not widely necessary in time series analysis.

This is not to imply that stationarity is not an important concept in time series analysis. Many time series models are valid only under the assumption of weak stationarity (also known as covariance stationarity).

Weak stationarity, henceforth stationarity, requires only that:

1. A series has the same finite unconditional mean and finite unconditional variance at all time periods.
2. That the series autocovariances are independent of time.

Nonstationary time series are any data series that do not meet the conditions of a weakly stationary time series. Hence, in purely technical terms, nonstationarity implies that the unconditional mean and/or autocovariances are NOT independent of time.

One form of nonstationarity is the presence of a time trend. When a time trend in present in data, the data does NOT have a time-invariant unconditional mean. This type of series is often referred to as trend stationary and can be transformed into stationary data by detrending.

Another form of stationary can arise when there is a structural break in the data. This data may exhibit mean-reverting behavior in two separate time-periods, before and after the break. However, it may revert to different means in each of those time-periods.

In addition, nonstationarity may occur if data is truly non-mean reverting at exhibits explosive behavior. This data can often be transformed into stationary data by taking differences.