What is non-stationarity?

Non-stationarity refers to a property of a time series where the statistical properties of the data change over time. In other words, the mean, variance, or other statistical characteristics of the data series are not constant across different time periods. Non-stationarity can manifest in various ways, including trends, seasonality, and other irregular patterns.

Here are the key components of non-stationarity:

• Trend: A trend exists when there is a long-term increase or decrease in the data over time. This could be linear, exponential, or some other form. Trends indicate systematic changes in the series over time.
• Seasonality: Seasonality refers to periodic fluctuations or patterns that occur at regular intervals within the data. For example, retail sales might exhibit higher values during holiday season each year.
• Variance: Variance refers to the measure of dispersion or spread of the data points around the mean. Non-constant variance, also known as heteroscedasticity, can indicate non-stationarity.
• Autocorrelation: Autocorrelation occurs when the correlation between observations at different time points is not constant. This can also indicate non-stationarity, particularly if the autocorrelation structure changes over time.

Removing non-stationarity in time series data is crucial for accurate forecasting because many time series forecasting models assume stationarity, where the statistical properties of the time series do not change over time. Non-stationarity can manifest as trends, seasonality, or other forms of irregular patterns in the data.

The article comprehensively covers techniques and tests for removing non-stationarity in time series data, crucial for accurate forecasting, including detrending, seasonal adjustment, logarithmic transformation, differencing, and ADF/KPSS tests for stationarity validation.